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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
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<span class="md-ellipsis">
|
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第 0 章 前言
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第 0 章 前言
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0.1 关于本书
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|
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|
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0.2 如何使用本书
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0.3 小结
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第 1 章 初识算法
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第 1 章 初识算法
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1.1 算法无处不在
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</a>
|
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1.2 算法是什么
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1.3 小结
|
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</span>
|
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|
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|
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<span class="md-ellipsis">
|
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第 2 章 复杂度分析
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
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第 2 章 复杂度分析
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<a href="../performance_evaluation/" class="md-nav__link">
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2.1 算法效率评估
|
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</span>
|
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|
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|
||
</a>
|
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</li>
|
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2.2 迭代与递归
|
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</span>
|
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|
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|
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|
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|
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<span class="md-status md-status--new" title="最近添加">
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2.3 时间复杂度
|
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<span class="md-ellipsis">
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2.3 时间复杂度
|
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|
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|
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|
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</a>
|
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|
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|
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|
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<nav class="md-nav md-nav--secondary" aria-label="目录">
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目录
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|
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2.3.1 统计时间增长趋势
|
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|
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|
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|
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<a href="#232" class="md-nav__link">
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2.3.2 函数渐近上界
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|
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|
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|
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|
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2.3.3 推算方法
|
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<a href="#1" class="md-nav__link">
|
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1. 第一步：统计操作数量
|
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</a>
|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="#2" class="md-nav__link">
|
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2. 第二步：判断渐近上界
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|
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|
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|
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|
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</ul>
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</nav>
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|
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|
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<li class="md-nav__item">
|
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<a href="#234" class="md-nav__link">
|
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2.3.4 常见类型
|
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|
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|
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<nav class="md-nav" aria-label="2.3.4 常见类型">
|
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<ul class="md-nav__list">
|
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|
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<li class="md-nav__item">
|
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<a href="#1-o1" class="md-nav__link">
|
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1. 常数阶 \(O(1)\)
|
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</a>
|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="#2-on" class="md-nav__link">
|
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2. 线性阶 \(O(n)\)
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="#3-on2" class="md-nav__link">
|
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3. 平方阶 \(O(n^2)\)
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="#4-o2n" class="md-nav__link">
|
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4. 指数阶 \(O(2^n)\)
|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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|
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5. 对数阶 \(O(\log n)\)
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="#6-on-log-n" class="md-nav__link">
|
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6. 线性对数阶 \(O(n \log n)\)
|
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|
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|
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|
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|
||
<li class="md-nav__item">
|
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<a href="#7-on" class="md-nav__link">
|
||
7. 阶乘阶 \(O(n!)\)
|
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|
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|
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|
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|
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</ul>
|
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</nav>
|
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|
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|
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<li class="md-nav__item">
|
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<a href="#235" class="md-nav__link">
|
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2.3.5 最差、最佳、平均时间复杂度
|
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|
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|
||
</li>
|
||
|
||
</ul>
|
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|
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</nav>
|
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|
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|
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|
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<a href="../space_complexity/" class="md-nav__link">
|
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|
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|
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|
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2.4 空间复杂度
|
||
</span>
|
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|
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|
||
</a>
|
||
</li>
|
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|
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|
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|
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<a href="../summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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2.5 小结
|
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</span>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<span class="md-ellipsis">
|
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第 3 章 数据结构
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|
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|
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|
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</a>
|
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|
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<label class="md-nav__link " for="__nav_4">
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第 3 章 数据结构
|
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<li class="md-nav__item">
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|
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|
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<span class="md-ellipsis">
|
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3.1 数据结构分类
|
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</span>
|
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|
||
|
||
</a>
|
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</li>
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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3.2 基本数据类型
|
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</span>
|
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|
||
|
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</a>
|
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</li>
|
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|
||
|
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|
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|
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|
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|
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
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3.3 数字编码 *
|
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</span>
|
||
|
||
|
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</a>
|
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</li>
|
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|
||
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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3.4 字符编码 *
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
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|
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3.5 小结
|
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|
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|
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|
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5.2 队列
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5.3 双向队列
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5.4 小结
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第 6 章 哈希表
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6.1 哈希表
|
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|
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|
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|
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</a>
|
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</li>
|
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6.2 哈希冲突
|
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|
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|
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|
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</a>
|
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</li>
|
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|
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6.3 哈希算法
|
||
</span>
|
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|
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|
||
</a>
|
||
</li>
|
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|
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|
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6.4 小结
|
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</span>
|
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|
||
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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7.1 二叉树
|
||
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|
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|
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|
||
</a>
|
||
</li>
|
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|
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|
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7.2 二叉树遍历
|
||
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|
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|
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|
||
</a>
|
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</li>
|
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|
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7.3 二叉树数组表示
|
||
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|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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7.4 二叉搜索树
|
||
</span>
|
||
|
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|
||
</a>
|
||
</li>
|
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7.5 AVL 树 *
|
||
</span>
|
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|
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|
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</a>
|
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</li>
|
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7.6 小结
|
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|
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|
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|
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<a href="../../chapter_heap/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 8 章 堆
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_9">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 8 章 堆
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.1 堆
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.2 建堆操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/top_k/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.3 Top-K 问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
8.4 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_graph/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 9 章 图
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_10">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 9 章 图
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.1 图
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.2 图基础操作
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.3 图的遍历
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_graph/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
9.4 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_searching/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 10 章 搜索
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_11">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 10 章 搜索
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.1 二分查找
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.2 二分查找插入点
|
||
</span>
|
||
|
||
|
||
|
||
|
||
<span class="md-status md-status--new" title="最近添加">
|
||
</span>
|
||
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.3 二分查找边界
|
||
</span>
|
||
|
||
|
||
|
||
|
||
<span class="md-status md-status--new" title="最近添加">
|
||
</span>
|
||
|
||
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.4 哈希优化策略
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.5 重识搜索算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
10.6 小结
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
</ul>
|
||
</nav>
|
||
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item md-nav__item--nested">
|
||
|
||
|
||
|
||
|
||
|
||
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
|
||
|
||
|
||
|
||
<div class="md-nav__link md-nav__container">
|
||
<a href="../../chapter_sorting/" class="md-nav__link ">
|
||
|
||
|
||
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
|
||
|
||
<span class="md-ellipsis">
|
||
第 11 章 排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
|
||
<label class="md-nav__link " for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
</label>
|
||
|
||
</div>
|
||
|
||
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
||
<label class="md-nav__title" for="__nav_12">
|
||
<span class="md-nav__icon md-icon"></span>
|
||
第 11 章 排序
|
||
</label>
|
||
<ul class="md-nav__list" data-md-scrollfix>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.1 排序算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.2 选择排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.3 冒泡排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.4 插入排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.5 快速排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.6 归并排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.7 堆排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.8 桶排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
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|
||
<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.9 计数排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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<li class="md-nav__item">
|
||
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
||
|
||
|
||
<span class="md-ellipsis">
|
||
11.10 基数排序
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
||
|
||
|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_sorting/summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
11.11 小结
|
||
</span>
|
||
|
||
|
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</a>
|
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</li>
|
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|
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|
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|
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|
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</ul>
|
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</nav>
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|
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|
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||
|
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|
||
|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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<span class="md-ellipsis">
|
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第 12 章 分治
|
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|
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<span class="md-status md-status--new" title="最近添加">
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<span class="md-nav__icon md-icon"></span>
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第 12 章 分治
|
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|
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12.1 分治算法
|
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</span>
|
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|
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|
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|
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|
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<span class="md-status md-status--new" title="最近添加">
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
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|
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12.2 分治搜索策略
|
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</span>
|
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|
||
|
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|
||
|
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<span class="md-status md-status--new" title="最近添加">
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|
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
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|
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12.3 构建树问题
|
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|
||
|
||
|
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|
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|
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<span class="md-status md-status--new" title="最近添加">
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</span>
|
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|
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|
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</a>
|
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</li>
|
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<a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
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<span class="md-ellipsis">
|
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12.4 汉诺塔问题
|
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</span>
|
||
|
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|
||
|
||
|
||
<span class="md-status md-status--new" title="最近添加">
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</span>
|
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|
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</a>
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</li>
|
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|
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<li class="md-nav__item">
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<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
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12.5 小结
|
||
</span>
|
||
|
||
|
||
|
||
|
||
<span class="md-status md-status--new" title="最近添加">
|
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</span>
|
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|
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|
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|
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|
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</a>
|
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</li>
|
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|
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|
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|
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|
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</ul>
|
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</nav>
|
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|
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</li>
|
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|
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|
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|
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|
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|
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||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
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|
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|
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|
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|
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<li class="md-nav__item md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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|
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|
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<span class="md-ellipsis">
|
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第 13 章 回溯
|
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|
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<label class="md-nav__link " for="__nav_14">
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_14">
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<span class="md-nav__icon md-icon"></span>
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第 13 章 回溯
|
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
|
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|
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|
||
<span class="md-ellipsis">
|
||
13.1 回溯算法
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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13.2 全排列问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
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13.3 子集和问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
13.4 N 皇后问题
|
||
</span>
|
||
|
||
|
||
</a>
|
||
</li>
|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_backtracking/summary/" class="md-nav__link">
|
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|
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|
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<span class="md-ellipsis">
|
||
13.5 小结
|
||
</span>
|
||
|
||
|
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</a>
|
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</li>
|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||
|
||
|
||
|
||
|
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|
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|
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|
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<span class="md-ellipsis">
|
||
第 14 章 动态规划
|
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|
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|
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|
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|
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第 14 章 动态规划
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|
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<span class="md-ellipsis">
|
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14.1 初探动态规划
|
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</span>
|
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|
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|
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|
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|
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<span class="md-status md-status--new" title="最近添加">
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</a>
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<a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
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|
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<span class="md-ellipsis">
|
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14.2 DP 问题特性
|
||
</span>
|
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|
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|
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|
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|
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<span class="md-status md-status--new" title="最近添加">
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</a>
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<a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
|
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|
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<span class="md-ellipsis">
|
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14.3 DP 解题思路
|
||
</span>
|
||
|
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|
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|
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|
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<span class="md-status md-status--new" title="最近添加">
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
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|
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14.4 0-1 背包问题
|
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</span>
|
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|
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|
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|
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|
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<span class="md-status md-status--new" title="最近添加">
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|
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
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<span class="md-ellipsis">
|
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14.5 完全背包问题
|
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</span>
|
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|
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|
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|
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|
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<span class="md-status md-status--new" title="最近添加">
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</span>
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|
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</a>
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</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
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<span class="md-ellipsis">
|
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14.6 编辑距离问题
|
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</span>
|
||
|
||
|
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|
||
|
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<span class="md-status md-status--new" title="最近添加">
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</span>
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|
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|
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|
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|
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</a>
|
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</li>
|
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|
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|
||
|
||
|
||
|
||
|
||
|
||
|
||
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2.3.1 统计时间增长趋势
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1. 第一步：统计操作数量
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1. 常数阶 \(O(1)\)
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2. 线性阶 \(O(n)\)
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4. 指数阶 \(O(2^n)\)
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2.3.5 最差、最佳、平均时间复杂度
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_computational_complexity/time_complexity.md" title="编辑此页" class="md-content__button md-icon">
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|
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<h1 id="23">2.3 时间复杂度<a class="headerlink" href="#23" title="Permanent link">¶</a></h1>
|
||
<p>运行时间可以直观且准确地反映算法的效率。如果我们想要准确预估一段代码的运行时间，应该如何操作呢？</p>
|
||
<ol>
|
||
<li><strong>确定运行平台</strong>，包括硬件配置、编程语言、系统环境等，这些因素都会影响代码的运行效率。</li>
|
||
<li><strong>评估各种计算操作所需的运行时间</strong>，例如加法操作 <code>+</code> 需要 1 ns ，乘法操作 <code>*</code> 需要 10 ns ，打印操作 <code>print()</code> 需要 5 ns 等。</li>
|
||
<li><strong>统计代码中所有的计算操作</strong>，并将所有操作的执行时间求和，从而得到运行时间。</li>
|
||
</ol>
|
||
<p>例如在以下代码中，输入数据大小为 <span class="arithmatex">\(n\)</span> ：</p>
|
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<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Zig</label></div>
|
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<div class="tabbed-content">
|
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<div class="tabbed-block">
|
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<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 在某运行平台下</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="k">def</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a> <span class="n">a</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1"># 1 ns</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span> <span class="c1"># 1 ns</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span> <span class="c1"># 10 ns</span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a> <span class="c1"># 循环 n 次</span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span> <span class="c1"># 1 ns</span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="c1"># 5 ns</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns ，每轮都要执行 i++</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span><span class="w"> </span><span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns ，每轮都要执行 i++</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns ，每轮都要执行 i++</span>
|
||
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a> <span class="kd">var</span> <span class="nv">a</span> <span class="p">=</span> <span class="mi">2</span> <span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a> <span class="n">a</span> <span class="p">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span> <span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a> <span class="n">a</span> <span class="p">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span> <span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a> <span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span> <span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a> <span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a> <span class="p">}</span>
|
||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns ，每轮都要执行 i++</span>
|
||
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns ，每轮都要执行 i++</span>
|
||
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns ，每轮都要执行 i++</span>
|
||
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns ，每轮都要执行 i++</span>
|
||
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">"{}"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// 在某运行平台下</span>
|
||
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
|
||
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
|
||
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns ，每轮都要执行 i++</span>
|
||
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"%d"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
|
||
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>根据以上方法，可以得到算法运行时间为 <span class="arithmatex">\(6n + 12\)</span> ns ：</p>
|
||
<div class="arithmatex">\[
|
||
1 + 1 + 10 + (1 + 5) \times n = 6n + 12
|
||
\]</div>
|
||
<p>但实际上，<strong>统计算法的运行时间既不合理也不现实</strong>。首先，我们不希望将预估时间和运行平台绑定，因为算法需要在各种不同的平台上运行。其次，我们很难获知每种操作的运行时间，这给预估过程带来了极大的难度。</p>
|
||
<h2 id="231">2.3.1 统计时间增长趋势<a class="headerlink" href="#231" title="Permanent link">¶</a></h2>
|
||
<p>时间复杂度分析统计的不是算法运行时间，<strong>而是算法运行时间随着数据量变大时的增长趋势</strong>。</p>
|
||
<p>“时间增长趋势”这个概念比较抽象，我们通过一个例子来加以理解。假设输入数据大小为 <span class="arithmatex">\(n\)</span> ，给定三个算法函数 <code>A</code>、<code>B</code> 和 <code>C</code> ：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1"># 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span> <span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="c1"># 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="k">def</span> <span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="c1"># 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="k">def</span> <span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000000</span><span class="p">):</span>
|
||
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="k">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="k">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span> <span class="nf">algorithmA</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a> <span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a>
|
||
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="kd">func</span> <span class="nf">algorithmB</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span>
|
||
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a> <span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a> <span class="p">}</span>
|
||
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="p">}</span>
|
||
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a>
|
||
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="kd">func</span> <span class="nf">algorithmC</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="mi">1000000</span> <span class="p">{</span>
|
||
<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a> <span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a> <span class="p">}</span>
|
||
<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmA</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmB</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmC</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="k">fn</span> <span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">"{}"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="k">fn</span> <span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">"{}"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="k">fn</span> <span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="mi">1000000</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">"{}"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// 算法 A 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"%d"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="p">}</span>
|
||
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="c1">// 算法 B 的时间复杂度：线性阶</span>
|
||
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"%d"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="p">}</span>
|
||
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="c1">// 算法 C 的时间复杂度：常数阶</span>
|
||
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"%d"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>图 2-7 展示了以上三个算法函数的时间复杂度。</p>
|
||
<ul>
|
||
<li>算法 <code>A</code> 只有 <span class="arithmatex">\(1\)</span> 个打印操作，算法运行时间不随着 <span class="arithmatex">\(n\)</span> 增大而增长。我们称此算法的时间复杂度为“常数阶”。</li>
|
||
<li>算法 <code>B</code> 中的打印操作需要循环 <span class="arithmatex">\(n\)</span> 次，算法运行时间随着 <span class="arithmatex">\(n\)</span> 增大呈线性增长。此算法的时间复杂度被称为“线性阶”。</li>
|
||
<li>算法 <code>C</code> 中的打印操作需要循环 <span class="arithmatex">\(1000000\)</span> 次，虽然运行时间很长，但它与输入数据大小 <span class="arithmatex">\(n\)</span> 无关。因此 <code>C</code> 的时间复杂度和 <code>A</code> 相同，仍为“常数阶”。</li>
|
||
</ul>
|
||
<p><img alt="算法 A、B 和 C 的时间增长趋势" src="../time_complexity.assets/time_complexity_simple_example.png" /></p>
|
||
<p align="center"> 图 2-7 算法 A、B 和 C 的时间增长趋势 </p>
|
||
|
||
<p>相较于直接统计算法运行时间，时间复杂度分析有哪些特点呢？</p>
|
||
<ul>
|
||
<li><strong>时间复杂度能够有效评估算法效率</strong>。例如，算法 <code>B</code> 的运行时间呈线性增长，在 <span class="arithmatex">\(n > 1\)</span> 时比算法 <code>A</code> 更慢，在 <span class="arithmatex">\(n > 1000000\)</span> 时比算法 <code>C</code> 更慢。事实上，只要输入数据大小 <span class="arithmatex">\(n\)</span> 足够大，复杂度为“常数阶”的算法一定优于“线性阶”的算法，这正是时间增长趋势所表达的含义。</li>
|
||
<li><strong>时间复杂度的推算方法更简便</strong>。显然，运行平台和计算操作类型都与算法运行时间的增长趋势无关。因此在时间复杂度分析中，我们可以简单地将所有计算操作的执行时间视为相同的“单位时间”，从而将“计算操作的运行时间的统计”简化为“计算操作的数量的统计”，这样以来估算难度就大大降低了。</li>
|
||
<li><strong>时间复杂度也存在一定的局限性</strong>。例如，尽管算法 <code>A</code> 和 <code>C</code> 的时间复杂度相同，但实际运行时间差别很大。同样，尽管算法 <code>B</code> 的时间复杂度比 <code>C</code> 高，但在输入数据大小 <span class="arithmatex">\(n\)</span> 较小时，算法 <code>B</code> 明显优于算法 <code>C</code> 。在这些情况下，我们很难仅凭时间复杂度判断算法效率的高低。当然，尽管存在上述问题，复杂度分析仍然是评判算法效率最有效且常用的方法。</li>
|
||
</ul>
|
||
<h2 id="232">2.3.2 函数渐近上界<a class="headerlink" href="#232" title="Permanent link">¶</a></h2>
|
||
<p>给定一个输入大小为 <span class="arithmatex">\(n\)</span> 的函数：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="3:12"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="k">def</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a> <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span> <span class="c1"># +1</span>
|
||
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span> <span class="c1"># +1</span>
|
||
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span> <span class="c1"># +1</span>
|
||
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a> <span class="c1"># 循环 n 次</span>
|
||
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span> <span class="c1"># +1</span>
|
||
<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="c1"># +1</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（每轮都执行 i ++）</span>
|
||
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（每轮都执行 i ++）</span>
|
||
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（每轮都执行 i ++）</span>
|
||
<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="kd">func</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a> <span class="kd">var</span> <span class="nv">a</span> <span class="p">=</span> <span class="mi">1</span> <span class="c1">// +1</span>
|
||
<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a> <span class="n">a</span> <span class="p">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span> <span class="c1">// +1</span>
|
||
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a> <span class="n">a</span> <span class="p">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span> <span class="c1">// +1</span>
|
||
<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a> <span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span> <span class="c1">// +1</span>
|
||
<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a> <span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="c1">// +1</span>
|
||
<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a> <span class="p">}</span>
|
||
<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w"> </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1（每轮都执行 i ++）</span>
|
||
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="p">{</span>
|
||
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1（每轮都执行 i ++）</span>
|
||
<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（每轮都执行 i ++）</span>
|
||
<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="k">fn</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a>
|
||
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（每轮都执行 i ++）</span>
|
||
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">"{}"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w"> </span><span class="c1">// 循环 n 次</span>
|
||
<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1（每轮都执行 i ++）</span>
|
||
<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"%d"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
|
||
<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="p">}</span><span class="w"> </span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>设算法的操作数量是一个关于输入数据大小 <span class="arithmatex">\(n\)</span> 的函数，记为 <span class="arithmatex">\(T(n)\)</span> ，则以上函数的的操作数量为：</p>
|
||
<div class="arithmatex">\[
|
||
T(n) = 3 + 2n
|
||
\]</div>
|
||
<p><span class="arithmatex">\(T(n)\)</span> 是一次函数，说明其运行时间的增长趋势是线性的，因此它的时间复杂度是线性阶。</p>
|
||
<p>我们将线性阶的时间复杂度记为 <span class="arithmatex">\(O(n)\)</span> ，这个数学符号称为「大 <span class="arithmatex">\(O\)</span> 记号 big-<span class="arithmatex">\(O\)</span> notation」，表示函数 <span class="arithmatex">\(T(n)\)</span> 的「渐近上界 asymptotic upper bound」。</p>
|
||
<p>时间复杂度分析本质上是计算“操作数量函数 <span class="arithmatex">\(T(n)\)</span>”的渐近上界，其具有明确的数学定义。</p>
|
||
<div class="admonition abstract">
|
||
<p class="admonition-title">函数渐近上界</p>
|
||
<p>若存在正实数 <span class="arithmatex">\(c\)</span> 和实数 <span class="arithmatex">\(n_0\)</span> ，使得对于所有的 <span class="arithmatex">\(n > n_0\)</span> ，均有 <span class="arithmatex">\(T(n) \leq c \cdot f(n)\)</span> ，则可认为 <span class="arithmatex">\(f(n)\)</span> 给出了 <span class="arithmatex">\(T(n)\)</span> 的一个渐近上界，记为 <span class="arithmatex">\(T(n) = O(f(n))\)</span> 。</p>
|
||
</div>
|
||
<p>如图 2-8 所示，计算渐近上界就是寻找一个函数 <span class="arithmatex">\(f(n)\)</span> ，使得当 <span class="arithmatex">\(n\)</span> 趋向于无穷大时，<span class="arithmatex">\(T(n)\)</span> 和 <span class="arithmatex">\(f(n)\)</span> 处于相同的增长级别，仅相差一个常数项 <span class="arithmatex">\(c\)</span> 的倍数。</p>
|
||
<p><img alt="函数的渐近上界" src="../time_complexity.assets/asymptotic_upper_bound.png" /></p>
|
||
<p align="center"> 图 2-8 函数的渐近上界 </p>
|
||
|
||
<h2 id="233">2.3.3 推算方法<a class="headerlink" href="#233" title="Permanent link">¶</a></h2>
|
||
<p>渐近上界的数学味儿有点重，如果你感觉没有完全理解，也无须担心。因为在实际使用中，我们只需要掌握推算方法，数学意义就可以逐渐领悟。</p>
|
||
<p>根据定义，确定 <span class="arithmatex">\(f(n)\)</span> 之后，我们便可得到时间复杂度 <span class="arithmatex">\(O(f(n))\)</span> 。那么如何确定渐近上界 <span class="arithmatex">\(f(n)\)</span> 呢？总体分为两步：首先统计操作数量，然后判断渐近上界。</p>
|
||
<h3 id="1">1. 第一步：统计操作数量<a class="headerlink" href="#1" title="Permanent link">¶</a></h3>
|
||
<p>针对代码，逐行从上到下计算即可。然而，由于上述 <span class="arithmatex">\(c \cdot f(n)\)</span> 中的常数项 <span class="arithmatex">\(c\)</span> 可以取任意大小，<strong>因此操作数量 <span class="arithmatex">\(T(n)\)</span> 中的各种系数、常数项都可以被忽略</strong>。根据此原则，可以总结出以下计数简化技巧。</p>
|
||
<ol>
|
||
<li><strong>忽略 <span class="arithmatex">\(T(n)\)</span> 中的常数项</strong>。因为它们都与 <span class="arithmatex">\(n\)</span> 无关，所以对时间复杂度不产生影响。</li>
|
||
<li><strong>省略所有系数</strong>。例如，循环 <span class="arithmatex">\(2n\)</span> 次、<span class="arithmatex">\(5n + 1\)</span> 次等，都可以简化记为 <span class="arithmatex">\(n\)</span> 次，因为 <span class="arithmatex">\(n\)</span> 前面的系数对时间复杂度没有影响。</li>
|
||
<li><strong>循环嵌套时使用乘法</strong>。总操作数量等于外层循环和内层循环操作数量之积，每一层循环依然可以分别套用第 <code>1.</code> 点和第 <code>2.</code> 点的技巧。</li>
|
||
</ol>
|
||
<p>给定一个函数，我们可以用上述技巧来统计操作数量。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="4:12"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="k">def</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
|
||
<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a> <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span> <span class="c1"># +0（技巧 1）</span>
|
||
<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a> <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">n</span> <span class="c1"># +0（技巧 1）</span>
|
||
<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a> <span class="c1"># +n（技巧 2）</span>
|
||
<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span> <span class="o">*</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a> <span class="c1"># +n*n（技巧 3）</span>
|
||
<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a> <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="w"> </span><span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-37-7" name="__codelineno-37-7" href="#__codelineno-37-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-37-8" name="__codelineno-37-8" href="#__codelineno-37-8"></a><span class="w"> </span><span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-37-9" name="__codelineno-37-9" href="#__codelineno-37-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-10" name="__codelineno-37-10" href="#__codelineno-37-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-37-11" name="__codelineno-37-11" href="#__codelineno-37-11"></a><span class="w"> </span><span class="n">cout</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o"><<</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
|
||
<a id="__codelineno-37-12" name="__codelineno-37-12" href="#__codelineno-37-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-37-13" name="__codelineno-37-13" href="#__codelineno-37-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-37-14" name="__codelineno-37-14" href="#__codelineno-37-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w"> </span><span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w"> </span><span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="w"> </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="w"> </span><span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a><span class="w"> </span><span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a><span class="w"> </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="kd">func</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a> <span class="kd">var</span> <span class="nv">a</span> <span class="p">=</span> <span class="mi">1</span> <span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a> <span class="n">a</span> <span class="p">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">n</span> <span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a> <span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="p">(</span><span class="mi">5</span> <span class="o">*</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a> <span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a> <span class="p">}</span>
|
||
<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a> <span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a> <span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a> <span class="p">}</span>
|
||
<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a> <span class="p">}</span>
|
||
<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w"> </span><span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w"> </span><span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w"> </span><span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w"> </span><span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w"> </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
|
||
<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w"> </span><span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w"> </span><span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w"> </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="k">fn</span> <span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a>
|
||
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">"{}"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a>
|
||
<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w"> </span><span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w"> </span><span class="fm">println!</span><span class="p">(</span><span class="s">"{}"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0（技巧 1）</span>
|
||
<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w"> </span><span class="c1">// +n（技巧 2）</span>
|
||
<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"%d"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w"> </span><span class="c1">// +n*n（技巧 3）</span>
|
||
<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"%d"</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
|
||
<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>以下公式展示了使用上述技巧前后的统计结果，两者推出的时间复杂度都为 <span class="arithmatex">\(O(n^2)\)</span> 。</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
T(n) & = 2n(n + 1) + (5n + 1) + 2 & \text{完整统计 (-.-|||)} \newline
|
||
& = 2n^2 + 7n + 3 \newline
|
||
T(n) & = n^2 + n & \text{偷懒统计 (o.O)}
|
||
\end{aligned}
|
||
\]</div>
|
||
<h3 id="2">2. 第二步：判断渐近上界<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
|
||
<p><strong>时间复杂度由多项式 <span class="arithmatex">\(T(n)\)</span> 中最高阶的项来决定</strong>。这是因为在 <span class="arithmatex">\(n\)</span> 趋于无穷大时，最高阶的项将发挥主导作用，其他项的影响都可以被忽略。</p>
|
||
<p>表 2-2 展示了一些例子，其中一些夸张的值是为了强调“系数无法撼动阶数”这一结论。当 <span class="arithmatex">\(n\)</span> 趋于无穷大时，这些常数变得无足轻重。</p>
|
||
<p align="center"> 表 2-2 不同操作数量对应的时间复杂度 </p>
|
||
|
||
<div class="center-table">
|
||
<table>
|
||
<thead>
|
||
<tr>
|
||
<th>操作数量 <span class="arithmatex">\(T(n)\)</span></th>
|
||
<th>时间复杂度 <span class="arithmatex">\(O(f(n))\)</span></th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr>
|
||
<td><span class="arithmatex">\(100000\)</span></td>
|
||
<td><span class="arithmatex">\(O(1)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(3n + 2\)</span></td>
|
||
<td><span class="arithmatex">\(O(n)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(2n^2 + 3n + 2\)</span></td>
|
||
<td><span class="arithmatex">\(O(n^2)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(n^3 + 10000n^2\)</span></td>
|
||
<td><span class="arithmatex">\(O(n^3)\)</span></td>
|
||
</tr>
|
||
<tr>
|
||
<td><span class="arithmatex">\(2^n + 10000n^{10000}\)</span></td>
|
||
<td><span class="arithmatex">\(O(2^n)\)</span></td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<h2 id="234">2.3.4 常见类型<a class="headerlink" href="#234" title="Permanent link">¶</a></h2>
|
||
<p>设输入数据大小为 <span class="arithmatex">\(n\)</span> ，常见的时间复杂度类型如图 2-9 所示（按照从低到高的顺序排列）。</p>
|
||
<div class="arithmatex">\[
|
||
\begin{aligned}
|
||
O(1) < O(\log n) < O(n) < O(n \log n) < O(n^2) < O(2^n) < O(n!) \newline
|
||
\text{常数阶} < \text{对数阶} < \text{线性阶} < \text{线性对数阶} < \text{平方阶} < \text{指数阶} < \text{阶乘阶}
|
||
\end{aligned}
|
||
\]</div>
|
||
<p><img alt="常见的时间复杂度类型" src="../time_complexity.assets/time_complexity_common_types.png" /></p>
|
||
<p align="center"> 图 2-9 常见的时间复杂度类型 </p>
|
||
|
||
<h3 id="1-o1">1. 常数阶 <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">¶</a></h3>
|
||
<p>常数阶的操作数量与输入数据大小 <span class="arithmatex">\(n\)</span> 无关，即不随着 <span class="arithmatex">\(n\)</span> 的变化而变化。</p>
|
||
<p>在以下函数中，尽管操作数量 <code>size</code> 可能很大，但由于其与输入数据大小 <span class="arithmatex">\(n\)</span> 无关，因此时间复杂度仍为 <span class="arithmatex">\(O(1)\)</span> ：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="5:12"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="k">def</span> <span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="w"> </span><span class="sd">"""常数阶"""</span>
|
||
<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a> <span class="n">size</span> <span class="o">=</span> <span class="mi">100000</span>
|
||
<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">size</span><span class="p">):</span>
|
||
<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a> <span class="k">return</span> <span class="n">count</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
|
||
<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
|
||
<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
|
||
<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
|
||
<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">100000</span><span class="p">;</span>
|
||
<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
|
||
<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">100000</span>
|
||
<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
|
||
<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||
<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">func</span> <span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a> <span class="kd">let</span> <span class="nv">size</span> <span class="p">=</span> <span class="mi">100_000</span>
|
||
<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">size</span> <span class="p">{</span>
|
||
<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a> <span class="p">}</span>
|
||
<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a> <span class="k">return</span> <span class="bp">count</span>
|
||
<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">100000</span><span class="p">;</span>
|
||
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constant</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">100000</span><span class="p">;</span>
|
||
<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">size</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">100000</span><span class="p">;</span>
|
||
<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="k">fn</span> <span class="nf">constant</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
|
||
<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100_000</span><span class="p">;</span>
|
||
<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">size</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w"> </span><span class="n">count</span>
|
||
<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 常数阶 */</span>
|
||
<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
|
||
<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="c1">// 常数阶</span>
|
||
<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">constant</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
|
||
<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w"> </span><span class="kr">const</span><span class="w"> </span><span class="n">size</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100</span><span class="n">_000</span><span class="p">;</span>
|
||
<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w"> </span><span class="k">while</span><span class="p">(</span><span class="n">i</span><span class="o"><</span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="2-on">2. 线性阶 <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">¶</a></h3>
|
||
<p>线性阶的操作数量相对于输入数据大小 <span class="arithmatex">\(n\)</span> 以线性级别增长。线性阶通常出现在单层循环中：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="6:12"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="k">def</span> <span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="w"> </span><span class="sd">"""线性阶"""</span>
|
||
<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a> <span class="k">return</span> <span class="n">count</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
|
||
<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
|
||
<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
|
||
<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
|
||
<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||
<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="kd">func</span> <span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span>
|
||
<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a> <span class="p">}</span>
|
||
<a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a> <span class="k">return</span> <span class="bp">count</span>
|
||
<a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linear</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="k">fn</span> <span class="nf">linear</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w"> </span><span class="n">count</span>
|
||
<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 线性阶 */</span>
|
||
<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="c1">// 线性阶</span>
|
||
<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">linear</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-71-9" name="__codelineno-71-9" href="#__codelineno-71-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>遍历数组和遍历链表等操作的时间复杂度均为 <span class="arithmatex">\(O(n)\)</span> ，其中 <span class="arithmatex">\(n\)</span> 为数组或链表的长度：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="7:12"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="k">def</span> <span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="w"> </span><span class="sd">"""线性阶（遍历数组）"""</span>
|
||
<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a> <span class="c1"># 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a> <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
|
||
<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a> <span class="k">return</span> <span class="n">count</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-3" name="__codelineno-73-3" href="#__codelineno-73-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-73-4" name="__codelineno-73-4" href="#__codelineno-73-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-73-5" name="__codelineno-73-5" href="#__codelineno-73-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-73-6" name="__codelineno-73-6" href="#__codelineno-73-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-73-7" name="__codelineno-73-7" href="#__codelineno-73-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-73-8" name="__codelineno-73-8" href="#__codelineno-73-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-73-9" name="__codelineno-73-9" href="#__codelineno-73-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-74-3" name="__codelineno-74-3" href="#__codelineno-74-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-74-4" name="__codelineno-74-4" href="#__codelineno-74-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-74-5" name="__codelineno-74-5" href="#__codelineno-74-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-74-6" name="__codelineno-74-6" href="#__codelineno-74-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-74-7" name="__codelineno-74-7" href="#__codelineno-74-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-74-8" name="__codelineno-74-8" href="#__codelineno-74-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-74-9" name="__codelineno-74-9" href="#__codelineno-74-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-75-2" name="__codelineno-75-2" href="#__codelineno-75-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-75-3" name="__codelineno-75-3" href="#__codelineno-75-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-75-4" name="__codelineno-75-4" href="#__codelineno-75-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-75-5" name="__codelineno-75-5" href="#__codelineno-75-5"></a><span class="w"> </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-75-6" name="__codelineno-75-6" href="#__codelineno-75-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-75-7" name="__codelineno-75-7" href="#__codelineno-75-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-75-8" name="__codelineno-75-8" href="#__codelineno-75-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-75-9" name="__codelineno-75-9" href="#__codelineno-75-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-76-2" name="__codelineno-76-2" href="#__codelineno-76-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">arrayTraversal</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-76-3" name="__codelineno-76-3" href="#__codelineno-76-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-76-4" name="__codelineno-76-4" href="#__codelineno-76-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-76-5" name="__codelineno-76-5" href="#__codelineno-76-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-76-6" name="__codelineno-76-6" href="#__codelineno-76-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
|
||
<a id="__codelineno-76-7" name="__codelineno-76-7" href="#__codelineno-76-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-76-8" name="__codelineno-76-8" href="#__codelineno-76-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||
<a id="__codelineno-76-9" name="__codelineno-76-9" href="#__codelineno-76-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="kd">func</span> <span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-77-3" name="__codelineno-77-3" href="#__codelineno-77-3"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-77-4" name="__codelineno-77-4" href="#__codelineno-77-4"></a> <span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-77-5" name="__codelineno-77-5" href="#__codelineno-77-5"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="n">nums</span> <span class="p">{</span>
|
||
<a id="__codelineno-77-6" name="__codelineno-77-6" href="#__codelineno-77-6"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-77-7" name="__codelineno-77-7" href="#__codelineno-77-7"></a> <span class="p">}</span>
|
||
<a id="__codelineno-77-8" name="__codelineno-77-8" href="#__codelineno-77-8"></a> <span class="k">return</span> <span class="bp">count</span>
|
||
<a id="__codelineno-77-9" name="__codelineno-77-9" href="#__codelineno-77-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">arrayTraversal</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">arrayTraversal</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">arrayTraversal</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="k">fn</span> <span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w"> </span><span class="n">count</span>
|
||
<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* 线性阶（遍历数组） */</span>
|
||
<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="c1">// 线性阶（遍历数组）</span>
|
||
<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">arrayTraversal</span><span class="p">(</span><span class="n">nums</span><span class="o">:</span><span class="w"> </span><span class="p">[]</span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成正比</span>
|
||
<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="n">_</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>值得注意的是，<strong>输入数据大小 <span class="arithmatex">\(n\)</span> 需根据输入数据的类型来具体确定</strong>。比如在第一个示例中，变量 <span class="arithmatex">\(n\)</span> 为输入数据大小；在第二个示例中，数组长度 <span class="arithmatex">\(n\)</span> 为数据大小。</p>
|
||
<h3 id="3-on2">3. 平方阶 <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">¶</a></h3>
|
||
<p>平方阶的操作数量相对于输入数据大小 <span class="arithmatex">\(n\)</span> 以平方级别增长。平方阶通常出现在嵌套循环中，外层循环和内层循环都为 <span class="arithmatex">\(O(n)\)</span> ，因此总体为 <span class="arithmatex">\(O(n^2)\)</span> ：</p>
|
||
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|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="k">def</span> <span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="w"> </span><span class="sd">"""平方阶"""</span>
|
||
<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a> <span class="c1"># 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a> <span class="k">return</span> <span class="n">count</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-87-11" name="__codelineno-87-11" href="#__codelineno-87-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
|
||
<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-9" name="__codelineno-88-9" href="#__codelineno-88-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-88-10" name="__codelineno-88-10" href="#__codelineno-88-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||
<a id="__codelineno-88-11" name="__codelineno-88-11" href="#__codelineno-88-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">func</span> <span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a> <span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span>
|
||
<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a> <span class="p">}</span>
|
||
<a id="__codelineno-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a> <span class="k">return</span> <span class="bp">count</span>
|
||
<a id="__codelineno-89-11" name="__codelineno-89-11" href="#__codelineno-89-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-90-8" name="__codelineno-90-8" href="#__codelineno-90-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-90-9" name="__codelineno-90-9" href="#__codelineno-90-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-90-10" name="__codelineno-90-10" href="#__codelineno-90-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-90-11" name="__codelineno-90-11" href="#__codelineno-90-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">quadratic</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-91-9" name="__codelineno-91-9" href="#__codelineno-91-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-91-10" name="__codelineno-91-10" href="#__codelineno-91-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-91-11" name="__codelineno-91-11" href="#__codelineno-91-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-92-9" name="__codelineno-92-9" href="#__codelineno-92-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-92-11" name="__codelineno-92-11" href="#__codelineno-92-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-93-2" name="__codelineno-93-2" href="#__codelineno-93-2"></a><span class="k">fn</span> <span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-93-4" name="__codelineno-93-4" href="#__codelineno-93-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-93-5" name="__codelineno-93-5" href="#__codelineno-93-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-6" name="__codelineno-93-6" href="#__codelineno-93-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-93-7" name="__codelineno-93-7" href="#__codelineno-93-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-93-8" name="__codelineno-93-8" href="#__codelineno-93-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-9" name="__codelineno-93-9" href="#__codelineno-93-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-93-10" name="__codelineno-93-10" href="#__codelineno-93-10"></a><span class="w"> </span><span class="n">count</span>
|
||
<a id="__codelineno-93-11" name="__codelineno-93-11" href="#__codelineno-93-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="cm">/* 平方阶 */</span>
|
||
<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-94-8" name="__codelineno-94-8" href="#__codelineno-94-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-9" name="__codelineno-94-9" href="#__codelineno-94-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-94-10" name="__codelineno-94-10" href="#__codelineno-94-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-94-11" name="__codelineno-94-11" href="#__codelineno-94-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="c1">// 平方阶</span>
|
||
<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">quadratic</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a><span class="w"> </span><span class="c1">// 循环次数与数组长度成平方关系</span>
|
||
<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">j</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-95-9" name="__codelineno-95-9" href="#__codelineno-95-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-95-10" name="__codelineno-95-10" href="#__codelineno-95-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-95-11" name="__codelineno-95-11" href="#__codelineno-95-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-95-12" name="__codelineno-95-12" href="#__codelineno-95-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-95-13" name="__codelineno-95-13" href="#__codelineno-95-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>图 2-10 对比了常数阶、线性阶和平方阶三种时间复杂度。</p>
|
||
<p><img alt="常数阶、线性阶和平方阶的时间复杂度" src="../time_complexity.assets/time_complexity_constant_linear_quadratic.png" /></p>
|
||
<p align="center"> 图 2-10 常数阶、线性阶和平方阶的时间复杂度 </p>
|
||
|
||
<p>以冒泡排序为例，外层循环执行 <span class="arithmatex">\(n - 1\)</span> 次，内层循环执行 <span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(n-2\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> 次，平均为 <span class="arithmatex">\(n / 2\)</span> 次，因此时间复杂度为 <span class="arithmatex">\(O((n - 1) n / 2) = O(n^2)\)</span> 。</p>
|
||
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|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="k">def</span> <span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="w"> </span><span class="sd">"""平方阶（冒泡排序）"""</span>
|
||
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1"># 计数器</span>
|
||
<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a> <span class="c1"># 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a> <span class="c1"># 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端</span>
|
||
<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a> <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
|
||
<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a> <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">></span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
|
||
<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a> <span class="c1"># 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a> <span class="n">tmp</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
|
||
<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
|
||
<a id="__codelineno-96-12" name="__codelineno-96-12" href="#__codelineno-96-12"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span>
|
||
<a id="__codelineno-96-13" name="__codelineno-96-13" href="#__codelineno-96-13"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">3</span> <span class="c1"># 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-96-14" name="__codelineno-96-14" href="#__codelineno-96-14"></a> <span class="k">return</span> <span class="n">count</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计数器</span>
|
||
<a id="__codelineno-97-4" name="__codelineno-97-4" href="#__codelineno-97-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-97-5" name="__codelineno-97-5" href="#__codelineno-97-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-97-6" name="__codelineno-97-6" href="#__codelineno-97-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端</span>
|
||
<a id="__codelineno-97-7" name="__codelineno-97-7" href="#__codelineno-97-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-97-8" name="__codelineno-97-8" href="#__codelineno-97-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-97-9" name="__codelineno-97-9" href="#__codelineno-97-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-97-10" name="__codelineno-97-10" href="#__codelineno-97-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
|
||
<a id="__codelineno-97-11" name="__codelineno-97-11" href="#__codelineno-97-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||
<a id="__codelineno-97-12" name="__codelineno-97-12" href="#__codelineno-97-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-97-13" name="__codelineno-97-13" href="#__codelineno-97-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-97-14" name="__codelineno-97-14" href="#__codelineno-97-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-97-15" name="__codelineno-97-15" href="#__codelineno-97-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-97-16" name="__codelineno-97-16" href="#__codelineno-97-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-97-17" name="__codelineno-97-17" href="#__codelineno-97-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-97-18" name="__codelineno-97-18" href="#__codelineno-97-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计数器</span>
|
||
<a id="__codelineno-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端</span>
|
||
<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-98-8" name="__codelineno-98-8" href="#__codelineno-98-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-98-9" name="__codelineno-98-9" href="#__codelineno-98-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-98-10" name="__codelineno-98-10" href="#__codelineno-98-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-98-11" name="__codelineno-98-11" href="#__codelineno-98-11"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-98-12" name="__codelineno-98-12" href="#__codelineno-98-12"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-98-13" name="__codelineno-98-13" href="#__codelineno-98-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-98-14" name="__codelineno-98-14" href="#__codelineno-98-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-98-15" name="__codelineno-98-15" href="#__codelineno-98-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-98-16" name="__codelineno-98-16" href="#__codelineno-98-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-98-17" name="__codelineno-98-17" href="#__codelineno-98-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-98-18" name="__codelineno-98-18" href="#__codelineno-98-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计数器</span>
|
||
<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端 </span>
|
||
<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-99-8" name="__codelineno-99-8" href="#__codelineno-99-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-99-9" name="__codelineno-99-9" href="#__codelineno-99-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-99-10" name="__codelineno-99-10" href="#__codelineno-99-10"></a><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]);</span>
|
||
<a id="__codelineno-99-11" name="__codelineno-99-11" href="#__codelineno-99-11"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-99-12" name="__codelineno-99-12" href="#__codelineno-99-12"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-99-13" name="__codelineno-99-13" href="#__codelineno-99-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-99-14" name="__codelineno-99-14" href="#__codelineno-99-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-99-15" name="__codelineno-99-15" href="#__codelineno-99-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-99-16" name="__codelineno-99-16" href="#__codelineno-99-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// 计数器</span>
|
||
<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端</span>
|
||
<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span>
|
||
<a id="__codelineno-100-11" name="__codelineno-100-11" href="#__codelineno-100-11"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span>
|
||
<a id="__codelineno-100-12" name="__codelineno-100-12" href="#__codelineno-100-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span>
|
||
<a id="__codelineno-100-13" name="__codelineno-100-13" href="#__codelineno-100-13"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-100-14" name="__codelineno-100-14" href="#__codelineno-100-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-100-15" name="__codelineno-100-15" href="#__codelineno-100-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-100-16" name="__codelineno-100-16" href="#__codelineno-100-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-100-17" name="__codelineno-100-17" href="#__codelineno-100-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||
<a id="__codelineno-100-18" name="__codelineno-100-18" href="#__codelineno-100-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a><span class="kd">func</span> <span class="nf">bubbleSort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="kr">inout</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span> <span class="c1">// 计数器</span>
|
||
<a id="__codelineno-101-4" name="__codelineno-101-4" href="#__codelineno-101-4"></a> <span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-101-5" name="__codelineno-101-5" href="#__codelineno-101-5"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="n">nums</span><span class="p">.</span><span class="bp">count</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-101-6" name="__codelineno-101-6" href="#__codelineno-101-6"></a> <span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端 </span>
|
||
<a id="__codelineno-101-7" name="__codelineno-101-7" href="#__codelineno-101-7"></a> <span class="k">for</span> <span class="n">j</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">i</span> <span class="p">{</span>
|
||
<a id="__codelineno-101-8" name="__codelineno-101-8" href="#__codelineno-101-8"></a> <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">></span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="p">{</span>
|
||
<a id="__codelineno-101-9" name="__codelineno-101-9" href="#__codelineno-101-9"></a> <span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-101-10" name="__codelineno-101-10" href="#__codelineno-101-10"></a> <span class="kd">let</span> <span class="nv">tmp</span> <span class="p">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
|
||
<a id="__codelineno-101-11" name="__codelineno-101-11" href="#__codelineno-101-11"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="p">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
|
||
<a id="__codelineno-101-12" name="__codelineno-101-12" href="#__codelineno-101-12"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="p">=</span> <span class="n">tmp</span>
|
||
<a id="__codelineno-101-13" name="__codelineno-101-13" href="#__codelineno-101-13"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">3</span> <span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-101-14" name="__codelineno-101-14" href="#__codelineno-101-14"></a> <span class="p">}</span>
|
||
<a id="__codelineno-101-15" name="__codelineno-101-15" href="#__codelineno-101-15"></a> <span class="p">}</span>
|
||
<a id="__codelineno-101-16" name="__codelineno-101-16" href="#__codelineno-101-16"></a> <span class="p">}</span>
|
||
<a id="__codelineno-101-17" name="__codelineno-101-17" href="#__codelineno-101-17"></a> <span class="k">return</span> <span class="bp">count</span>
|
||
<a id="__codelineno-101-18" name="__codelineno-101-18" href="#__codelineno-101-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计数器</span>
|
||
<a id="__codelineno-102-4" name="__codelineno-102-4" href="#__codelineno-102-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-102-5" name="__codelineno-102-5" href="#__codelineno-102-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-102-6" name="__codelineno-102-6" href="#__codelineno-102-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端</span>
|
||
<a id="__codelineno-102-7" name="__codelineno-102-7" href="#__codelineno-102-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-102-8" name="__codelineno-102-8" href="#__codelineno-102-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-102-9" name="__codelineno-102-9" href="#__codelineno-102-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-102-10" name="__codelineno-102-10" href="#__codelineno-102-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
|
||
<a id="__codelineno-102-11" name="__codelineno-102-11" href="#__codelineno-102-11"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
|
||
<a id="__codelineno-102-12" name="__codelineno-102-12" href="#__codelineno-102-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-102-13" name="__codelineno-102-13" href="#__codelineno-102-13"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-102-14" name="__codelineno-102-14" href="#__codelineno-102-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-15" name="__codelineno-102-15" href="#__codelineno-102-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-16" name="__codelineno-102-16" href="#__codelineno-102-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-102-17" name="__codelineno-102-17" href="#__codelineno-102-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-102-18" name="__codelineno-102-18" href="#__codelineno-102-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">bubbleSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计数器</span>
|
||
<a id="__codelineno-103-4" name="__codelineno-103-4" href="#__codelineno-103-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-103-5" name="__codelineno-103-5" href="#__codelineno-103-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-103-6" name="__codelineno-103-6" href="#__codelineno-103-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端</span>
|
||
<a id="__codelineno-103-7" name="__codelineno-103-7" href="#__codelineno-103-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-103-8" name="__codelineno-103-8" href="#__codelineno-103-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-103-9" name="__codelineno-103-9" href="#__codelineno-103-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-103-10" name="__codelineno-103-10" href="#__codelineno-103-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span>
|
||
<a id="__codelineno-103-11" name="__codelineno-103-11" href="#__codelineno-103-11"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
|
||
<a id="__codelineno-103-12" name="__codelineno-103-12" href="#__codelineno-103-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-103-13" name="__codelineno-103-13" href="#__codelineno-103-13"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-103-14" name="__codelineno-103-14" href="#__codelineno-103-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-103-15" name="__codelineno-103-15" href="#__codelineno-103-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-103-16" name="__codelineno-103-16" href="#__codelineno-103-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-103-17" name="__codelineno-103-17" href="#__codelineno-103-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-103-18" name="__codelineno-103-18" href="#__codelineno-103-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-104-2" name="__codelineno-104-2" href="#__codelineno-104-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">bubbleSort</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-104-3" name="__codelineno-104-3" href="#__codelineno-104-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计数器</span>
|
||
<a id="__codelineno-104-4" name="__codelineno-104-4" href="#__codelineno-104-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-104-5" name="__codelineno-104-5" href="#__codelineno-104-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-104-6" name="__codelineno-104-6" href="#__codelineno-104-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端</span>
|
||
<a id="__codelineno-104-7" name="__codelineno-104-7" href="#__codelineno-104-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-104-8" name="__codelineno-104-8" href="#__codelineno-104-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-104-9" name="__codelineno-104-9" href="#__codelineno-104-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-104-10" name="__codelineno-104-10" href="#__codelineno-104-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
|
||
<a id="__codelineno-104-11" name="__codelineno-104-11" href="#__codelineno-104-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">];</span>
|
||
<a id="__codelineno-104-12" name="__codelineno-104-12" href="#__codelineno-104-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-104-13" name="__codelineno-104-13" href="#__codelineno-104-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-104-14" name="__codelineno-104-14" href="#__codelineno-104-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-104-15" name="__codelineno-104-15" href="#__codelineno-104-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-104-16" name="__codelineno-104-16" href="#__codelineno-104-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-104-17" name="__codelineno-104-17" href="#__codelineno-104-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-104-18" name="__codelineno-104-18" href="#__codelineno-104-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-105-2" name="__codelineno-105-2" href="#__codelineno-105-2"></a><span class="k">fn</span> <span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-105-3" name="__codelineno-105-3" href="#__codelineno-105-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计数器</span>
|
||
<a id="__codelineno-105-4" name="__codelineno-105-4" href="#__codelineno-105-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-105-5" name="__codelineno-105-5" href="#__codelineno-105-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()).</span><span class="n">rev</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-105-6" name="__codelineno-105-6" href="#__codelineno-105-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端 </span>
|
||
<a id="__codelineno-105-7" name="__codelineno-105-7" href="#__codelineno-105-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-105-8" name="__codelineno-105-8" href="#__codelineno-105-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-105-9" name="__codelineno-105-9" href="#__codelineno-105-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-105-10" name="__codelineno-105-10" href="#__codelineno-105-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
|
||
<a id="__codelineno-105-11" name="__codelineno-105-11" href="#__codelineno-105-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||
<a id="__codelineno-105-12" name="__codelineno-105-12" href="#__codelineno-105-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-105-13" name="__codelineno-105-13" href="#__codelineno-105-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-105-14" name="__codelineno-105-14" href="#__codelineno-105-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-105-15" name="__codelineno-105-15" href="#__codelineno-105-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-105-16" name="__codelineno-105-16" href="#__codelineno-105-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-105-17" name="__codelineno-105-17" href="#__codelineno-105-17"></a><span class="w"> </span><span class="n">count</span>
|
||
<a id="__codelineno-105-18" name="__codelineno-105-18" href="#__codelineno-105-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="cm">/* 平方阶（冒泡排序） */</span>
|
||
<a id="__codelineno-106-2" name="__codelineno-106-2" href="#__codelineno-106-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-3" name="__codelineno-106-3" href="#__codelineno-106-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计数器</span>
|
||
<a id="__codelineno-106-4" name="__codelineno-106-4" href="#__codelineno-106-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-106-5" name="__codelineno-106-5" href="#__codelineno-106-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-6" name="__codelineno-106-6" href="#__codelineno-106-6"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端</span>
|
||
<a id="__codelineno-106-7" name="__codelineno-106-7" href="#__codelineno-106-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-8" name="__codelineno-106-8" href="#__codelineno-106-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-106-9" name="__codelineno-106-9" href="#__codelineno-106-9"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-106-10" name="__codelineno-106-10" href="#__codelineno-106-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
|
||
<a id="__codelineno-106-11" name="__codelineno-106-11" href="#__codelineno-106-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||
<a id="__codelineno-106-12" name="__codelineno-106-12" href="#__codelineno-106-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-106-13" name="__codelineno-106-13" href="#__codelineno-106-13"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-106-14" name="__codelineno-106-14" href="#__codelineno-106-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-106-15" name="__codelineno-106-15" href="#__codelineno-106-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-106-16" name="__codelineno-106-16" href="#__codelineno-106-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-106-17" name="__codelineno-106-17" href="#__codelineno-106-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-106-18" name="__codelineno-106-18" href="#__codelineno-106-18"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="c1">// 平方阶（冒泡排序）</span>
|
||
<a id="__codelineno-107-2" name="__codelineno-107-2" href="#__codelineno-107-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">bubbleSort</span><span class="p">(</span><span class="n">nums</span><span class="o">:</span><span class="w"> </span><span class="p">[]</span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-3" name="__codelineno-107-3" href="#__codelineno-107-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计数器 </span>
|
||
<a id="__codelineno-107-4" name="__codelineno-107-4" href="#__codelineno-107-4"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
|
||
<a id="__codelineno-107-5" name="__codelineno-107-5" href="#__codelineno-107-5"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">@as</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="nb">@intCast</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">))</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-107-6" name="__codelineno-107-6" href="#__codelineno-107-6"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-7" name="__codelineno-107-7" href="#__codelineno-107-7"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">j</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-107-8" name="__codelineno-107-8" href="#__codelineno-107-8"></a><span class="w"> </span><span class="c1">// 内循环：将未排序区间 [0, i] 中的最大元素交换至该区间的最右端 </span>
|
||
<a id="__codelineno-107-9" name="__codelineno-107-9" href="#__codelineno-107-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-10" name="__codelineno-107-10" href="#__codelineno-107-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-107-11" name="__codelineno-107-11" href="#__codelineno-107-11"></a><span class="w"> </span><span class="c1">// 交换 nums[j] 与 nums[j + 1]</span>
|
||
<a id="__codelineno-107-12" name="__codelineno-107-12" href="#__codelineno-107-12"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
|
||
<a id="__codelineno-107-13" name="__codelineno-107-13" href="#__codelineno-107-13"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
|
||
<a id="__codelineno-107-14" name="__codelineno-107-14" href="#__codelineno-107-14"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-107-15" name="__codelineno-107-15" href="#__codelineno-107-15"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 元素交换包含 3 个单元操作</span>
|
||
<a id="__codelineno-107-16" name="__codelineno-107-16" href="#__codelineno-107-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-17" name="__codelineno-107-17" href="#__codelineno-107-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-18" name="__codelineno-107-18" href="#__codelineno-107-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-107-19" name="__codelineno-107-19" href="#__codelineno-107-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-107-20" name="__codelineno-107-20" href="#__codelineno-107-20"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<h3 id="4-o2n">4. 指数阶 <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">¶</a></h3>
|
||
<p>生物学的“细胞分裂”是指数阶增长的典型例子：初始状态为 <span class="arithmatex">\(1\)</span> 个细胞，分裂一轮后变为 <span class="arithmatex">\(2\)</span> 个，分裂两轮后变为 <span class="arithmatex">\(4\)</span> 个，以此类推，分裂 <span class="arithmatex">\(n\)</span> 轮后有 <span class="arithmatex">\(2^n\)</span> 个细胞。</p>
|
||
<p>图 2-11 和以下代码模拟了细胞分裂的过程，时间复杂度为 <span class="arithmatex">\(O(2^n)\)</span> 。</p>
|
||
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|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="k">def</span> <span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-108-2" name="__codelineno-108-2" href="#__codelineno-108-2"></a><span class="w"> </span><span class="sd">"""指数阶（循环实现）"""</span>
|
||
<a id="__codelineno-108-3" name="__codelineno-108-3" href="#__codelineno-108-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-108-4" name="__codelineno-108-4" href="#__codelineno-108-4"></a> <span class="n">base</span> <span class="o">=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-108-5" name="__codelineno-108-5" href="#__codelineno-108-5"></a> <span class="c1"># 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-108-6" name="__codelineno-108-6" href="#__codelineno-108-6"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-108-7" name="__codelineno-108-7" href="#__codelineno-108-7"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">base</span><span class="p">):</span>
|
||
<a id="__codelineno-108-8" name="__codelineno-108-8" href="#__codelineno-108-8"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-108-9" name="__codelineno-108-9" href="#__codelineno-108-9"></a> <span class="n">base</span> <span class="o">*=</span> <span class="mi">2</span>
|
||
<a id="__codelineno-108-10" name="__codelineno-108-10" href="#__codelineno-108-10"></a> <span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-108-11" name="__codelineno-108-11" href="#__codelineno-108-11"></a> <span class="k">return</span> <span class="n">count</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
|
||
<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-109-4" name="__codelineno-109-4" href="#__codelineno-109-4"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-109-5" name="__codelineno-109-5" href="#__codelineno-109-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-109-6" name="__codelineno-109-6" href="#__codelineno-109-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-109-7" name="__codelineno-109-7" href="#__codelineno-109-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-109-8" name="__codelineno-109-8" href="#__codelineno-109-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-109-9" name="__codelineno-109-9" href="#__codelineno-109-9"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-109-10" name="__codelineno-109-10" href="#__codelineno-109-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-109-11" name="__codelineno-109-11" href="#__codelineno-109-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-109-12" name="__codelineno-109-12" href="#__codelineno-109-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-109-13" name="__codelineno-109-13" href="#__codelineno-109-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
|
||
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-110-8" name="__codelineno-110-8" href="#__codelineno-110-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-110-9" name="__codelineno-110-9" href="#__codelineno-110-9"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-110-10" name="__codelineno-110-10" href="#__codelineno-110-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-110-11" name="__codelineno-110-11" href="#__codelineno-110-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-110-12" name="__codelineno-110-12" href="#__codelineno-110-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-110-13" name="__codelineno-110-13" href="#__codelineno-110-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
|
||
<a id="__codelineno-111-2" name="__codelineno-111-2" href="#__codelineno-111-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-111-3" name="__codelineno-111-3" href="#__codelineno-111-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-111-4" name="__codelineno-111-4" href="#__codelineno-111-4"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-111-5" name="__codelineno-111-5" href="#__codelineno-111-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-111-6" name="__codelineno-111-6" href="#__codelineno-111-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">bas</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-111-7" name="__codelineno-111-7" href="#__codelineno-111-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-111-8" name="__codelineno-111-8" href="#__codelineno-111-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-111-9" name="__codelineno-111-9" href="#__codelineno-111-9"></a><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
|
||
<a id="__codelineno-111-10" name="__codelineno-111-10" href="#__codelineno-111-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-111-11" name="__codelineno-111-11" href="#__codelineno-111-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-111-12" name="__codelineno-111-12" href="#__codelineno-111-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-111-13" name="__codelineno-111-13" href="#__codelineno-111-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="cm">/* 指数阶（循环实现）*/</span>
|
||
<a id="__codelineno-112-2" name="__codelineno-112-2" href="#__codelineno-112-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">exponential</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-112-3" name="__codelineno-112-3" href="#__codelineno-112-3"></a><span class="w"> </span><span class="nx">count</span><span class="p">,</span><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-112-4" name="__codelineno-112-4" href="#__codelineno-112-4"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-112-5" name="__codelineno-112-5" href="#__codelineno-112-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-112-6" name="__codelineno-112-6" href="#__codelineno-112-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-112-7" name="__codelineno-112-7" href="#__codelineno-112-7"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
|
||
<a id="__codelineno-112-8" name="__codelineno-112-8" href="#__codelineno-112-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-112-9" name="__codelineno-112-9" href="#__codelineno-112-9"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span>
|
||
<a id="__codelineno-112-10" name="__codelineno-112-10" href="#__codelineno-112-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-112-11" name="__codelineno-112-11" href="#__codelineno-112-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-112-12" name="__codelineno-112-12" href="#__codelineno-112-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||
<a id="__codelineno-112-13" name="__codelineno-112-13" href="#__codelineno-112-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-113-1" name="__codelineno-113-1" href="#__codelineno-113-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
|
||
<a id="__codelineno-113-2" name="__codelineno-113-2" href="#__codelineno-113-2"></a><span class="kd">func</span> <span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-113-3" name="__codelineno-113-3" href="#__codelineno-113-3"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-113-4" name="__codelineno-113-4" href="#__codelineno-113-4"></a> <span class="kd">var</span> <span class="nv">base</span> <span class="p">=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-113-5" name="__codelineno-113-5" href="#__codelineno-113-5"></a> <span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-113-6" name="__codelineno-113-6" href="#__codelineno-113-6"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span>
|
||
<a id="__codelineno-113-7" name="__codelineno-113-7" href="#__codelineno-113-7"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">base</span> <span class="p">{</span>
|
||
<a id="__codelineno-113-8" name="__codelineno-113-8" href="#__codelineno-113-8"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-113-9" name="__codelineno-113-9" href="#__codelineno-113-9"></a> <span class="p">}</span>
|
||
<a id="__codelineno-113-10" name="__codelineno-113-10" href="#__codelineno-113-10"></a> <span class="n">base</span> <span class="o">*=</span> <span class="mi">2</span>
|
||
<a id="__codelineno-113-11" name="__codelineno-113-11" href="#__codelineno-113-11"></a> <span class="p">}</span>
|
||
<a id="__codelineno-113-12" name="__codelineno-113-12" href="#__codelineno-113-12"></a> <span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-113-13" name="__codelineno-113-13" href="#__codelineno-113-13"></a> <span class="k">return</span> <span class="bp">count</span>
|
||
<a id="__codelineno-113-14" name="__codelineno-113-14" href="#__codelineno-113-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-114-1" name="__codelineno-114-1" href="#__codelineno-114-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
|
||
<a id="__codelineno-114-2" name="__codelineno-114-2" href="#__codelineno-114-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">exponential</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-114-3" name="__codelineno-114-3" href="#__codelineno-114-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
|
||
<a id="__codelineno-114-4" name="__codelineno-114-4" href="#__codelineno-114-4"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-114-5" name="__codelineno-114-5" href="#__codelineno-114-5"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-114-6" name="__codelineno-114-6" href="#__codelineno-114-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-114-7" name="__codelineno-114-7" href="#__codelineno-114-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-114-8" name="__codelineno-114-8" href="#__codelineno-114-8"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-114-9" name="__codelineno-114-9" href="#__codelineno-114-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-114-10" name="__codelineno-114-10" href="#__codelineno-114-10"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
|
||
<a id="__codelineno-114-11" name="__codelineno-114-11" href="#__codelineno-114-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-114-12" name="__codelineno-114-12" href="#__codelineno-114-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-114-13" name="__codelineno-114-13" href="#__codelineno-114-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-114-14" name="__codelineno-114-14" href="#__codelineno-114-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-115-1" name="__codelineno-115-1" href="#__codelineno-115-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
|
||
<a id="__codelineno-115-2" name="__codelineno-115-2" href="#__codelineno-115-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">exponential</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-115-3" name="__codelineno-115-3" href="#__codelineno-115-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span>
|
||
<a id="__codelineno-115-4" name="__codelineno-115-4" href="#__codelineno-115-4"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-115-5" name="__codelineno-115-5" href="#__codelineno-115-5"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-115-6" name="__codelineno-115-6" href="#__codelineno-115-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-115-7" name="__codelineno-115-7" href="#__codelineno-115-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-115-8" name="__codelineno-115-8" href="#__codelineno-115-8"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-115-9" name="__codelineno-115-9" href="#__codelineno-115-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-115-10" name="__codelineno-115-10" href="#__codelineno-115-10"></a><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
|
||
<a id="__codelineno-115-11" name="__codelineno-115-11" href="#__codelineno-115-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-115-12" name="__codelineno-115-12" href="#__codelineno-115-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-115-13" name="__codelineno-115-13" href="#__codelineno-115-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-115-14" name="__codelineno-115-14" href="#__codelineno-115-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-116-1" name="__codelineno-116-1" href="#__codelineno-116-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
|
||
<a id="__codelineno-116-2" name="__codelineno-116-2" href="#__codelineno-116-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-116-3" name="__codelineno-116-3" href="#__codelineno-116-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-116-4" name="__codelineno-116-4" href="#__codelineno-116-4"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-116-5" name="__codelineno-116-5" href="#__codelineno-116-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-116-6" name="__codelineno-116-6" href="#__codelineno-116-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-116-7" name="__codelineno-116-7" href="#__codelineno-116-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-116-8" name="__codelineno-116-8" href="#__codelineno-116-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-116-9" name="__codelineno-116-9" href="#__codelineno-116-9"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
|
||
<a id="__codelineno-116-10" name="__codelineno-116-10" href="#__codelineno-116-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-116-11" name="__codelineno-116-11" href="#__codelineno-116-11"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-116-12" name="__codelineno-116-12" href="#__codelineno-116-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-116-13" name="__codelineno-116-13" href="#__codelineno-116-13"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-117-1" name="__codelineno-117-1" href="#__codelineno-117-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
|
||
<a id="__codelineno-117-2" name="__codelineno-117-2" href="#__codelineno-117-2"></a><span class="k">fn</span> <span class="nf">exponential</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-117-3" name="__codelineno-117-3" href="#__codelineno-117-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-117-4" name="__codelineno-117-4" href="#__codelineno-117-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-117-5" name="__codelineno-117-5" href="#__codelineno-117-5"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-117-6" name="__codelineno-117-6" href="#__codelineno-117-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-117-7" name="__codelineno-117-7" href="#__codelineno-117-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">base</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-117-8" name="__codelineno-117-8" href="#__codelineno-117-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-117-9" name="__codelineno-117-9" href="#__codelineno-117-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-117-10" name="__codelineno-117-10" href="#__codelineno-117-10"></a><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-117-11" name="__codelineno-117-11" href="#__codelineno-117-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-117-12" name="__codelineno-117-12" href="#__codelineno-117-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-117-13" name="__codelineno-117-13" href="#__codelineno-117-13"></a><span class="w"> </span><span class="n">count</span>
|
||
<a id="__codelineno-117-14" name="__codelineno-117-14" href="#__codelineno-117-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-118-1" name="__codelineno-118-1" href="#__codelineno-118-1"></a><span class="cm">/* 指数阶（循环实现） */</span>
|
||
<a id="__codelineno-118-2" name="__codelineno-118-2" href="#__codelineno-118-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-118-3" name="__codelineno-118-3" href="#__codelineno-118-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-118-4" name="__codelineno-118-4" href="#__codelineno-118-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-118-5" name="__codelineno-118-5" href="#__codelineno-118-5"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-118-6" name="__codelineno-118-6" href="#__codelineno-118-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-118-7" name="__codelineno-118-7" href="#__codelineno-118-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">bas</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-118-8" name="__codelineno-118-8" href="#__codelineno-118-8"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-118-9" name="__codelineno-118-9" href="#__codelineno-118-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-118-10" name="__codelineno-118-10" href="#__codelineno-118-10"></a><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-118-11" name="__codelineno-118-11" href="#__codelineno-118-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-118-12" name="__codelineno-118-12" href="#__codelineno-118-12"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-118-13" name="__codelineno-118-13" href="#__codelineno-118-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-118-14" name="__codelineno-118-14" href="#__codelineno-118-14"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-119-1" name="__codelineno-119-1" href="#__codelineno-119-1"></a><span class="c1">// 指数阶（循环实现）</span>
|
||
<a id="__codelineno-119-2" name="__codelineno-119-2" href="#__codelineno-119-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">exponential</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-119-3" name="__codelineno-119-3" href="#__codelineno-119-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-119-4" name="__codelineno-119-4" href="#__codelineno-119-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">bas</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-119-5" name="__codelineno-119-5" href="#__codelineno-119-5"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-119-6" name="__codelineno-119-6" href="#__codelineno-119-6"></a><span class="w"> </span><span class="c1">// 细胞每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)</span>
|
||
<a id="__codelineno-119-7" name="__codelineno-119-7" href="#__codelineno-119-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-119-8" name="__codelineno-119-8" href="#__codelineno-119-8"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">j</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-119-9" name="__codelineno-119-9" href="#__codelineno-119-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">bas</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-119-10" name="__codelineno-119-10" href="#__codelineno-119-10"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-119-11" name="__codelineno-119-11" href="#__codelineno-119-11"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-119-12" name="__codelineno-119-12" href="#__codelineno-119-12"></a><span class="w"> </span><span class="n">bas</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-119-13" name="__codelineno-119-13" href="#__codelineno-119-13"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-119-14" name="__codelineno-119-14" href="#__codelineno-119-14"></a><span class="w"> </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
|
||
<a id="__codelineno-119-15" name="__codelineno-119-15" href="#__codelineno-119-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-119-16" name="__codelineno-119-16" href="#__codelineno-119-16"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p><img alt="指数阶的时间复杂度" src="../time_complexity.assets/time_complexity_exponential.png" /></p>
|
||
<p align="center"> 图 2-11 指数阶的时间复杂度 </p>
|
||
|
||
<p>在实际算法中，指数阶常出现于递归函数中。例如在以下代码中，其递归地一分为二，经过 <span class="arithmatex">\(n\)</span> 次分裂后停止：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="11:12"><input checked="checked" id="__tabbed_11_1" name="__tabbed_11" type="radio" /><input id="__tabbed_11_2" name="__tabbed_11" type="radio" /><input id="__tabbed_11_3" name="__tabbed_11" type="radio" /><input id="__tabbed_11_4" name="__tabbed_11" type="radio" /><input id="__tabbed_11_5" name="__tabbed_11" type="radio" /><input id="__tabbed_11_6" name="__tabbed_11" type="radio" /><input id="__tabbed_11_7" name="__tabbed_11" type="radio" /><input id="__tabbed_11_8" name="__tabbed_11" type="radio" /><input id="__tabbed_11_9" name="__tabbed_11" type="radio" /><input id="__tabbed_11_10" name="__tabbed_11" type="radio" /><input id="__tabbed_11_11" name="__tabbed_11" type="radio" /><input id="__tabbed_11_12" name="__tabbed_11" type="radio" /><div class="tabbed-labels"><label for="__tabbed_11_1">Python</label><label for="__tabbed_11_2">C++</label><label for="__tabbed_11_3">Java</label><label for="__tabbed_11_4">C#</label><label for="__tabbed_11_5">Go</label><label for="__tabbed_11_6">Swift</label><label for="__tabbed_11_7">JS</label><label for="__tabbed_11_8">TS</label><label for="__tabbed_11_9">Dart</label><label for="__tabbed_11_10">Rust</label><label for="__tabbed_11_11">C</label><label for="__tabbed_11_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-120-1" name="__codelineno-120-1" href="#__codelineno-120-1"></a><span class="k">def</span> <span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-120-2" name="__codelineno-120-2" href="#__codelineno-120-2"></a><span class="w"> </span><span class="sd">"""指数阶（递归实现）"""</span>
|
||
<a id="__codelineno-120-3" name="__codelineno-120-3" href="#__codelineno-120-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-120-4" name="__codelineno-120-4" href="#__codelineno-120-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||
<a id="__codelineno-120-5" name="__codelineno-120-5" href="#__codelineno-120-5"></a> <span class="k">return</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-121-1" name="__codelineno-121-1" href="#__codelineno-121-1"></a><span class="cm">/* 指数阶（递归实现） */</span>
|
||
<a id="__codelineno-121-2" name="__codelineno-121-2" href="#__codelineno-121-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-121-3" name="__codelineno-121-3" href="#__codelineno-121-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-121-4" name="__codelineno-121-4" href="#__codelineno-121-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-121-5" name="__codelineno-121-5" href="#__codelineno-121-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-121-6" name="__codelineno-121-6" href="#__codelineno-121-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-122-1" name="__codelineno-122-1" href="#__codelineno-122-1"></a><span class="cm">/* 指数阶（递归实现） */</span>
|
||
<a id="__codelineno-122-2" name="__codelineno-122-2" href="#__codelineno-122-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-122-3" name="__codelineno-122-3" href="#__codelineno-122-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-122-4" name="__codelineno-122-4" href="#__codelineno-122-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-122-5" name="__codelineno-122-5" href="#__codelineno-122-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-122-6" name="__codelineno-122-6" href="#__codelineno-122-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-123-1" name="__codelineno-123-1" href="#__codelineno-123-1"></a><span class="cm">/* 指数阶（递归实现） */</span>
|
||
<a id="__codelineno-123-2" name="__codelineno-123-2" href="#__codelineno-123-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-123-3" name="__codelineno-123-3" href="#__codelineno-123-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-123-4" name="__codelineno-123-4" href="#__codelineno-123-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-123-5" name="__codelineno-123-5" href="#__codelineno-123-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-124-1" name="__codelineno-124-1" href="#__codelineno-124-1"></a><span class="cm">/* 指数阶（递归实现）*/</span>
|
||
<a id="__codelineno-124-2" name="__codelineno-124-2" href="#__codelineno-124-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-124-3" name="__codelineno-124-3" href="#__codelineno-124-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-124-4" name="__codelineno-124-4" href="#__codelineno-124-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-124-5" name="__codelineno-124-5" href="#__codelineno-124-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-124-6" name="__codelineno-124-6" href="#__codelineno-124-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-124-7" name="__codelineno-124-7" href="#__codelineno-124-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-125-1" name="__codelineno-125-1" href="#__codelineno-125-1"></a><span class="cm">/* 指数阶（递归实现） */</span>
|
||
<a id="__codelineno-125-2" name="__codelineno-125-2" href="#__codelineno-125-2"></a><span class="kd">func</span> <span class="nf">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-125-3" name="__codelineno-125-3" href="#__codelineno-125-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">1</span> <span class="p">{</span>
|
||
<a id="__codelineno-125-4" name="__codelineno-125-4" href="#__codelineno-125-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||
<a id="__codelineno-125-5" name="__codelineno-125-5" href="#__codelineno-125-5"></a> <span class="p">}</span>
|
||
<a id="__codelineno-125-6" name="__codelineno-125-6" href="#__codelineno-125-6"></a> <span class="k">return</span> <span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
|
||
<a id="__codelineno-125-7" name="__codelineno-125-7" href="#__codelineno-125-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-126-1" name="__codelineno-126-1" href="#__codelineno-126-1"></a><span class="cm">/* 指数阶（递归实现） */</span>
|
||
<a id="__codelineno-126-2" name="__codelineno-126-2" href="#__codelineno-126-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-126-3" name="__codelineno-126-3" href="#__codelineno-126-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-126-4" name="__codelineno-126-4" href="#__codelineno-126-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-126-5" name="__codelineno-126-5" href="#__codelineno-126-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-127-1" name="__codelineno-127-1" href="#__codelineno-127-1"></a><span class="cm">/* 指数阶（递归实现） */</span>
|
||
<a id="__codelineno-127-2" name="__codelineno-127-2" href="#__codelineno-127-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-127-3" name="__codelineno-127-3" href="#__codelineno-127-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-127-4" name="__codelineno-127-4" href="#__codelineno-127-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">expRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-127-5" name="__codelineno-127-5" href="#__codelineno-127-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-128-1" name="__codelineno-128-1" href="#__codelineno-128-1"></a><span class="cm">/* 指数阶（递归实现） */</span>
|
||
<a id="__codelineno-128-2" name="__codelineno-128-2" href="#__codelineno-128-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-128-3" name="__codelineno-128-3" href="#__codelineno-128-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-128-4" name="__codelineno-128-4" href="#__codelineno-128-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-128-5" name="__codelineno-128-5" href="#__codelineno-128-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-129-1" name="__codelineno-129-1" href="#__codelineno-129-1"></a><span class="cm">/* 指数阶（递归实现） */</span>
|
||
<a id="__codelineno-129-2" name="__codelineno-129-2" href="#__codelineno-129-2"></a><span class="k">fn</span> <span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-129-3" name="__codelineno-129-3" href="#__codelineno-129-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-129-4" name="__codelineno-129-4" href="#__codelineno-129-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-129-5" name="__codelineno-129-5" href="#__codelineno-129-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-129-6" name="__codelineno-129-6" href="#__codelineno-129-6"></a><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-129-7" name="__codelineno-129-7" href="#__codelineno-129-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-130-1" name="__codelineno-130-1" href="#__codelineno-130-1"></a><span class="cm">/* 指数阶（递归实现） */</span>
|
||
<a id="__codelineno-130-2" name="__codelineno-130-2" href="#__codelineno-130-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-130-3" name="__codelineno-130-3" href="#__codelineno-130-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-130-4" name="__codelineno-130-4" href="#__codelineno-130-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-130-5" name="__codelineno-130-5" href="#__codelineno-130-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-130-6" name="__codelineno-130-6" href="#__codelineno-130-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-131-1" name="__codelineno-131-1" href="#__codelineno-131-1"></a><span class="c1">// 指数阶（递归实现）</span>
|
||
<a id="__codelineno-131-2" name="__codelineno-131-2" href="#__codelineno-131-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-131-3" name="__codelineno-131-3" href="#__codelineno-131-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-131-4" name="__codelineno-131-4" href="#__codelineno-131-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-131-5" name="__codelineno-131-5" href="#__codelineno-131-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>指数阶增长非常迅速，在穷举法（暴力搜索、回溯等）中比较常见。对于数据规模较大的问题，指数阶是不可接受的，通常需要使用动态规划或贪心等算法来解决。</p>
|
||
<h3 id="5-olog-n">5. 对数阶 <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">¶</a></h3>
|
||
<p>与指数阶相反，对数阶反映了“每轮缩减到一半”的情况。设输入数据大小为 <span class="arithmatex">\(n\)</span> ，由于每轮缩减到一半，因此循环次数是 <span class="arithmatex">\(\log_2 n\)</span> ，即 <span class="arithmatex">\(2^n\)</span> 的反函数。</p>
|
||
<p>图 2-12 和以下代码模拟了“每轮缩减到一半”的过程，时间复杂度为 <span class="arithmatex">\(O(\log_2 n)\)</span> ，简记为 <span class="arithmatex">\(O(\log n)\)</span> 。</p>
|
||
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|
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<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
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<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-132-1" name="__codelineno-132-1" href="#__codelineno-132-1"></a><span class="k">def</span> <span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">float</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-132-2" name="__codelineno-132-2" href="#__codelineno-132-2"></a><span class="w"> </span><span class="sd">"""对数阶（循环实现）"""</span>
|
||
<a id="__codelineno-132-3" name="__codelineno-132-3" href="#__codelineno-132-3"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-132-4" name="__codelineno-132-4" href="#__codelineno-132-4"></a> <span class="k">while</span> <span class="n">n</span> <span class="o">></span> <span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-132-5" name="__codelineno-132-5" href="#__codelineno-132-5"></a> <span class="n">n</span> <span class="o">=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span>
|
||
<a id="__codelineno-132-6" name="__codelineno-132-6" href="#__codelineno-132-6"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-132-7" name="__codelineno-132-7" href="#__codelineno-132-7"></a> <span class="k">return</span> <span class="n">count</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-133-1" name="__codelineno-133-1" href="#__codelineno-133-1"></a><span class="cm">/* 对数阶（循环实现） */</span>
|
||
<a id="__codelineno-133-2" name="__codelineno-133-2" href="#__codelineno-133-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-133-3" name="__codelineno-133-3" href="#__codelineno-133-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-133-4" name="__codelineno-133-4" href="#__codelineno-133-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-133-5" name="__codelineno-133-5" href="#__codelineno-133-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-133-6" name="__codelineno-133-6" href="#__codelineno-133-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-133-7" name="__codelineno-133-7" href="#__codelineno-133-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-133-8" name="__codelineno-133-8" href="#__codelineno-133-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-133-9" name="__codelineno-133-9" href="#__codelineno-133-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-134-1" name="__codelineno-134-1" href="#__codelineno-134-1"></a><span class="cm">/* 对数阶（循环实现） */</span>
|
||
<a id="__codelineno-134-2" name="__codelineno-134-2" href="#__codelineno-134-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-134-3" name="__codelineno-134-3" href="#__codelineno-134-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-134-4" name="__codelineno-134-4" href="#__codelineno-134-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-134-5" name="__codelineno-134-5" href="#__codelineno-134-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-134-6" name="__codelineno-134-6" href="#__codelineno-134-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-134-7" name="__codelineno-134-7" href="#__codelineno-134-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-134-8" name="__codelineno-134-8" href="#__codelineno-134-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-134-9" name="__codelineno-134-9" href="#__codelineno-134-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-135-1" name="__codelineno-135-1" href="#__codelineno-135-1"></a><span class="cm">/* 对数阶（循环实现） */</span>
|
||
<a id="__codelineno-135-2" name="__codelineno-135-2" href="#__codelineno-135-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-135-3" name="__codelineno-135-3" href="#__codelineno-135-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-135-4" name="__codelineno-135-4" href="#__codelineno-135-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-135-5" name="__codelineno-135-5" href="#__codelineno-135-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
|
||
<a id="__codelineno-135-6" name="__codelineno-135-6" href="#__codelineno-135-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-135-7" name="__codelineno-135-7" href="#__codelineno-135-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-135-8" name="__codelineno-135-8" href="#__codelineno-135-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-135-9" name="__codelineno-135-9" href="#__codelineno-135-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-136-1" name="__codelineno-136-1" href="#__codelineno-136-1"></a><span class="cm">/* 对数阶（循环实现）*/</span>
|
||
<a id="__codelineno-136-2" name="__codelineno-136-2" href="#__codelineno-136-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">float64</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-136-3" name="__codelineno-136-3" href="#__codelineno-136-3"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-136-4" name="__codelineno-136-4" href="#__codelineno-136-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-136-5" name="__codelineno-136-5" href="#__codelineno-136-5"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
|
||
<a id="__codelineno-136-6" name="__codelineno-136-6" href="#__codelineno-136-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
|
||
<a id="__codelineno-136-7" name="__codelineno-136-7" href="#__codelineno-136-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-136-8" name="__codelineno-136-8" href="#__codelineno-136-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||
<a id="__codelineno-136-9" name="__codelineno-136-9" href="#__codelineno-136-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-137-1" name="__codelineno-137-1" href="#__codelineno-137-1"></a><span class="cm">/* 对数阶（循环实现） */</span>
|
||
<a id="__codelineno-137-2" name="__codelineno-137-2" href="#__codelineno-137-2"></a><span class="kd">func</span> <span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Double</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-137-3" name="__codelineno-137-3" href="#__codelineno-137-3"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-137-4" name="__codelineno-137-4" href="#__codelineno-137-4"></a> <span class="kd">var</span> <span class="nv">n</span> <span class="p">=</span> <span class="n">n</span>
|
||
<a id="__codelineno-137-5" name="__codelineno-137-5" href="#__codelineno-137-5"></a> <span class="k">while</span> <span class="n">n</span> <span class="o">></span> <span class="mi">1</span> <span class="p">{</span>
|
||
<a id="__codelineno-137-6" name="__codelineno-137-6" href="#__codelineno-137-6"></a> <span class="n">n</span> <span class="p">=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span>
|
||
<a id="__codelineno-137-7" name="__codelineno-137-7" href="#__codelineno-137-7"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-137-8" name="__codelineno-137-8" href="#__codelineno-137-8"></a> <span class="p">}</span>
|
||
<a id="__codelineno-137-9" name="__codelineno-137-9" href="#__codelineno-137-9"></a> <span class="k">return</span> <span class="bp">count</span>
|
||
<a id="__codelineno-137-10" name="__codelineno-137-10" href="#__codelineno-137-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-138-1" name="__codelineno-138-1" href="#__codelineno-138-1"></a><span class="cm">/* 对数阶（循环实现） */</span>
|
||
<a id="__codelineno-138-2" name="__codelineno-138-2" href="#__codelineno-138-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-138-3" name="__codelineno-138-3" href="#__codelineno-138-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-138-4" name="__codelineno-138-4" href="#__codelineno-138-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-138-5" name="__codelineno-138-5" href="#__codelineno-138-5"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
|
||
<a id="__codelineno-138-6" name="__codelineno-138-6" href="#__codelineno-138-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-138-7" name="__codelineno-138-7" href="#__codelineno-138-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-138-8" name="__codelineno-138-8" href="#__codelineno-138-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-138-9" name="__codelineno-138-9" href="#__codelineno-138-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-139-1" name="__codelineno-139-1" href="#__codelineno-139-1"></a><span class="cm">/* 对数阶（循环实现） */</span>
|
||
<a id="__codelineno-139-2" name="__codelineno-139-2" href="#__codelineno-139-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logarithmic</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-139-3" name="__codelineno-139-3" href="#__codelineno-139-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-139-4" name="__codelineno-139-4" href="#__codelineno-139-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-139-5" name="__codelineno-139-5" href="#__codelineno-139-5"></a><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
|
||
<a id="__codelineno-139-6" name="__codelineno-139-6" href="#__codelineno-139-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-139-7" name="__codelineno-139-7" href="#__codelineno-139-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-139-8" name="__codelineno-139-8" href="#__codelineno-139-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-139-9" name="__codelineno-139-9" href="#__codelineno-139-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-140-1" name="__codelineno-140-1" href="#__codelineno-140-1"></a><span class="cm">/* 对数阶（循环实现） */</span>
|
||
<a id="__codelineno-140-2" name="__codelineno-140-2" href="#__codelineno-140-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logarithmic</span><span class="p">(</span><span class="kt">num</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-140-3" name="__codelineno-140-3" href="#__codelineno-140-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-140-4" name="__codelineno-140-4" href="#__codelineno-140-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-140-5" name="__codelineno-140-5" href="#__codelineno-140-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
|
||
<a id="__codelineno-140-6" name="__codelineno-140-6" href="#__codelineno-140-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-140-7" name="__codelineno-140-7" href="#__codelineno-140-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-140-8" name="__codelineno-140-8" href="#__codelineno-140-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-140-9" name="__codelineno-140-9" href="#__codelineno-140-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-141-1" name="__codelineno-141-1" href="#__codelineno-141-1"></a><span class="cm">/* 对数阶（循环实现） */</span>
|
||
<a id="__codelineno-141-2" name="__codelineno-141-2" href="#__codelineno-141-2"></a><span class="k">fn</span> <span class="nf">logarithmic</span><span class="p">(</span><span class="k">mut</span><span class="w"> </span><span class="n">n</span>: <span class="kt">f32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-141-3" name="__codelineno-141-3" href="#__codelineno-141-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-141-4" name="__codelineno-141-4" href="#__codelineno-141-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mf">1.0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-141-5" name="__codelineno-141-5" href="#__codelineno-141-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2.0</span><span class="p">;</span>
|
||
<a id="__codelineno-141-6" name="__codelineno-141-6" href="#__codelineno-141-6"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-141-7" name="__codelineno-141-7" href="#__codelineno-141-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-141-8" name="__codelineno-141-8" href="#__codelineno-141-8"></a><span class="w"> </span><span class="n">count</span>
|
||
<a id="__codelineno-141-9" name="__codelineno-141-9" href="#__codelineno-141-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-142-1" name="__codelineno-142-1" href="#__codelineno-142-1"></a><span class="cm">/* 对数阶（循环实现） */</span>
|
||
<a id="__codelineno-142-2" name="__codelineno-142-2" href="#__codelineno-142-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-142-3" name="__codelineno-142-3" href="#__codelineno-142-3"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-142-4" name="__codelineno-142-4" href="#__codelineno-142-4"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-142-5" name="__codelineno-142-5" href="#__codelineno-142-5"></a><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-142-6" name="__codelineno-142-6" href="#__codelineno-142-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-142-7" name="__codelineno-142-7" href="#__codelineno-142-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-142-8" name="__codelineno-142-8" href="#__codelineno-142-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-142-9" name="__codelineno-142-9" href="#__codelineno-142-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-143-1" name="__codelineno-143-1" href="#__codelineno-143-1"></a><span class="c1">// 对数阶（循环实现）</span>
|
||
<a id="__codelineno-143-2" name="__codelineno-143-2" href="#__codelineno-143-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-143-3" name="__codelineno-143-3" href="#__codelineno-143-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-143-4" name="__codelineno-143-4" href="#__codelineno-143-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">n_var</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
|
||
<a id="__codelineno-143-5" name="__codelineno-143-5" href="#__codelineno-143-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n_var</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-143-6" name="__codelineno-143-6" href="#__codelineno-143-6"></a><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-143-7" name="__codelineno-143-7" href="#__codelineno-143-7"></a><span class="w"> </span><span class="n">n_var</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n_var</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
||
<a id="__codelineno-143-8" name="__codelineno-143-8" href="#__codelineno-143-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-143-9" name="__codelineno-143-9" href="#__codelineno-143-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-143-10" name="__codelineno-143-10" href="#__codelineno-143-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-143-11" name="__codelineno-143-11" href="#__codelineno-143-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p><img alt="对数阶的时间复杂度" src="../time_complexity.assets/time_complexity_logarithmic.png" /></p>
|
||
<p align="center"> 图 2-12 对数阶的时间复杂度 </p>
|
||
|
||
<p>与指数阶类似，对数阶也常出现于递归函数中。以下代码形成了一个高度为 <span class="arithmatex">\(\log_2 n\)</span> 的递归树：</p>
|
||
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|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-144-1" name="__codelineno-144-1" href="#__codelineno-144-1"></a><span class="k">def</span> <span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">float</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-144-2" name="__codelineno-144-2" href="#__codelineno-144-2"></a><span class="w"> </span><span class="sd">"""对数阶（递归实现）"""</span>
|
||
<a id="__codelineno-144-3" name="__codelineno-144-3" href="#__codelineno-144-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-144-4" name="__codelineno-144-4" href="#__codelineno-144-4"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-144-5" name="__codelineno-144-5" href="#__codelineno-144-5"></a> <span class="k">return</span> <span class="n">log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-145-1" name="__codelineno-145-1" href="#__codelineno-145-1"></a><span class="cm">/* 对数阶（递归实现） */</span>
|
||
<a id="__codelineno-145-2" name="__codelineno-145-2" href="#__codelineno-145-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-145-3" name="__codelineno-145-3" href="#__codelineno-145-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-145-4" name="__codelineno-145-4" href="#__codelineno-145-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-145-5" name="__codelineno-145-5" href="#__codelineno-145-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-145-6" name="__codelineno-145-6" href="#__codelineno-145-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-146-1" name="__codelineno-146-1" href="#__codelineno-146-1"></a><span class="cm">/* 对数阶（递归实现） */</span>
|
||
<a id="__codelineno-146-2" name="__codelineno-146-2" href="#__codelineno-146-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-146-3" name="__codelineno-146-3" href="#__codelineno-146-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-146-4" name="__codelineno-146-4" href="#__codelineno-146-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-146-5" name="__codelineno-146-5" href="#__codelineno-146-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-146-6" name="__codelineno-146-6" href="#__codelineno-146-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-147-1" name="__codelineno-147-1" href="#__codelineno-147-1"></a><span class="cm">/* 对数阶（递归实现） */</span>
|
||
<a id="__codelineno-147-2" name="__codelineno-147-2" href="#__codelineno-147-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-147-3" name="__codelineno-147-3" href="#__codelineno-147-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-147-4" name="__codelineno-147-4" href="#__codelineno-147-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-147-5" name="__codelineno-147-5" href="#__codelineno-147-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-148-1" name="__codelineno-148-1" href="#__codelineno-148-1"></a><span class="cm">/* 对数阶（递归实现）*/</span>
|
||
<a id="__codelineno-148-2" name="__codelineno-148-2" href="#__codelineno-148-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">float64</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-148-3" name="__codelineno-148-3" href="#__codelineno-148-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-148-4" name="__codelineno-148-4" href="#__codelineno-148-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-148-5" name="__codelineno-148-5" href="#__codelineno-148-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-148-6" name="__codelineno-148-6" href="#__codelineno-148-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-148-7" name="__codelineno-148-7" href="#__codelineno-148-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-149-1" name="__codelineno-149-1" href="#__codelineno-149-1"></a><span class="cm">/* 对数阶（递归实现） */</span>
|
||
<a id="__codelineno-149-2" name="__codelineno-149-2" href="#__codelineno-149-2"></a><span class="kd">func</span> <span class="nf">logRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Double</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-149-3" name="__codelineno-149-3" href="#__codelineno-149-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span> <span class="p">{</span>
|
||
<a id="__codelineno-149-4" name="__codelineno-149-4" href="#__codelineno-149-4"></a> <span class="k">return</span> <span class="mi">0</span>
|
||
<a id="__codelineno-149-5" name="__codelineno-149-5" href="#__codelineno-149-5"></a> <span class="p">}</span>
|
||
<a id="__codelineno-149-6" name="__codelineno-149-6" href="#__codelineno-149-6"></a> <span class="k">return</span> <span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
|
||
<a id="__codelineno-149-7" name="__codelineno-149-7" href="#__codelineno-149-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-150-1" name="__codelineno-150-1" href="#__codelineno-150-1"></a><span class="cm">/* 对数阶（递归实现） */</span>
|
||
<a id="__codelineno-150-2" name="__codelineno-150-2" href="#__codelineno-150-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-150-3" name="__codelineno-150-3" href="#__codelineno-150-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-150-4" name="__codelineno-150-4" href="#__codelineno-150-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-150-5" name="__codelineno-150-5" href="#__codelineno-150-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-151-1" name="__codelineno-151-1" href="#__codelineno-151-1"></a><span class="cm">/* 对数阶（递归实现） */</span>
|
||
<a id="__codelineno-151-2" name="__codelineno-151-2" href="#__codelineno-151-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-151-3" name="__codelineno-151-3" href="#__codelineno-151-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-151-4" name="__codelineno-151-4" href="#__codelineno-151-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">logRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-151-5" name="__codelineno-151-5" href="#__codelineno-151-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-152-1" name="__codelineno-152-1" href="#__codelineno-152-1"></a><span class="cm">/* 对数阶（递归实现） */</span>
|
||
<a id="__codelineno-152-2" name="__codelineno-152-2" href="#__codelineno-152-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="kt">num</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-152-3" name="__codelineno-152-3" href="#__codelineno-152-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-152-4" name="__codelineno-152-4" href="#__codelineno-152-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-152-5" name="__codelineno-152-5" href="#__codelineno-152-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-153-1" name="__codelineno-153-1" href="#__codelineno-153-1"></a><span class="cm">/* 对数阶（递归实现） */</span>
|
||
<a id="__codelineno-153-2" name="__codelineno-153-2" href="#__codelineno-153-2"></a><span class="k">fn</span> <span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span>: <span class="kt">f32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-153-3" name="__codelineno-153-3" href="#__codelineno-153-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mf">1.0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-153-4" name="__codelineno-153-4" href="#__codelineno-153-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-153-5" name="__codelineno-153-5" href="#__codelineno-153-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-153-6" name="__codelineno-153-6" href="#__codelineno-153-6"></a><span class="w"> </span><span class="n">log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2.0</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-153-7" name="__codelineno-153-7" href="#__codelineno-153-7"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-154-1" name="__codelineno-154-1" href="#__codelineno-154-1"></a><span class="cm">/* 对数阶（递归实现） */</span>
|
||
<a id="__codelineno-154-2" name="__codelineno-154-2" href="#__codelineno-154-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-154-3" name="__codelineno-154-3" href="#__codelineno-154-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-154-4" name="__codelineno-154-4" href="#__codelineno-154-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-154-5" name="__codelineno-154-5" href="#__codelineno-154-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-154-6" name="__codelineno-154-6" href="#__codelineno-154-6"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-155-1" name="__codelineno-155-1" href="#__codelineno-155-1"></a><span class="c1">// 对数阶（递归实现）</span>
|
||
<a id="__codelineno-155-2" name="__codelineno-155-2" href="#__codelineno-155-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-155-3" name="__codelineno-155-3" href="#__codelineno-155-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-155-4" name="__codelineno-155-4" href="#__codelineno-155-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-155-5" name="__codelineno-155-5" href="#__codelineno-155-5"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>对数阶常出现于基于分治策略的算法中，体现了“一分为多”和“化繁为简”的算法思想。它增长缓慢，是仅次于常数阶的理想的时间复杂度。</p>
|
||
<div class="admonition tip">
|
||
<p class="admonition-title"><span class="arithmatex">\(O(\log n)\)</span> 的底数是多少？</p>
|
||
<p>准确来说，“一分为 <span class="arithmatex">\(m\)</span>”对应的时间复杂度是 <span class="arithmatex">\(O(\log_m n)\)</span> 。而通过对数换底公式，我们可以得到具有不同底数的、相等的时间复杂度：</p>
|
||
<div class="arithmatex">\[
|
||
O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
|
||
\]</div>
|
||
<p>也就是说，底数 <span class="arithmatex">\(m\)</span> 可以在不影响复杂度的前提下转换。因此我们通常会省略底数 <span class="arithmatex">\(m\)</span> ，将对数阶直接记为 <span class="arithmatex">\(O(\log n)\)</span> 。</p>
|
||
</div>
|
||
<h3 id="6-on-log-n">6. 线性对数阶 <span class="arithmatex">\(O(n \log n)\)</span><a class="headerlink" href="#6-on-log-n" title="Permanent link">¶</a></h3>
|
||
<p>线性对数阶常出现于嵌套循环中，两层循环的时间复杂度分别为 <span class="arithmatex">\(O(\log n)\)</span> 和 <span class="arithmatex">\(O(n)\)</span> 。相关代码如下：</p>
|
||
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|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-156-1" name="__codelineno-156-1" href="#__codelineno-156-1"></a><span class="k">def</span> <span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">float</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-156-2" name="__codelineno-156-2" href="#__codelineno-156-2"></a><span class="w"> </span><span class="sd">"""线性对数阶"""</span>
|
||
<a id="__codelineno-156-3" name="__codelineno-156-3" href="#__codelineno-156-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-156-4" name="__codelineno-156-4" href="#__codelineno-156-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||
<a id="__codelineno-156-5" name="__codelineno-156-5" href="#__codelineno-156-5"></a> <span class="n">count</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
|
||
<a id="__codelineno-156-6" name="__codelineno-156-6" href="#__codelineno-156-6"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-156-7" name="__codelineno-156-7" href="#__codelineno-156-7"></a> <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-156-8" name="__codelineno-156-8" href="#__codelineno-156-8"></a> <span class="k">return</span> <span class="n">count</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-157-1" name="__codelineno-157-1" href="#__codelineno-157-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-157-2" name="__codelineno-157-2" href="#__codelineno-157-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-157-3" name="__codelineno-157-3" href="#__codelineno-157-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-157-4" name="__codelineno-157-4" href="#__codelineno-157-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-157-5" name="__codelineno-157-5" href="#__codelineno-157-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
|
||
<a id="__codelineno-157-6" name="__codelineno-157-6" href="#__codelineno-157-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-157-7" name="__codelineno-157-7" href="#__codelineno-157-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-157-8" name="__codelineno-157-8" href="#__codelineno-157-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-157-9" name="__codelineno-157-9" href="#__codelineno-157-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-157-10" name="__codelineno-157-10" href="#__codelineno-157-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-158-1" name="__codelineno-158-1" href="#__codelineno-158-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-158-2" name="__codelineno-158-2" href="#__codelineno-158-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-158-3" name="__codelineno-158-3" href="#__codelineno-158-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-158-4" name="__codelineno-158-4" href="#__codelineno-158-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-158-5" name="__codelineno-158-5" href="#__codelineno-158-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span>
|
||
<a id="__codelineno-158-6" name="__codelineno-158-6" href="#__codelineno-158-6"></a><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
|
||
<a id="__codelineno-158-7" name="__codelineno-158-7" href="#__codelineno-158-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-158-8" name="__codelineno-158-8" href="#__codelineno-158-8"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-158-9" name="__codelineno-158-9" href="#__codelineno-158-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-158-10" name="__codelineno-158-10" href="#__codelineno-158-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-158-11" name="__codelineno-158-11" href="#__codelineno-158-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-159-1" name="__codelineno-159-1" href="#__codelineno-159-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-159-2" name="__codelineno-159-2" href="#__codelineno-159-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-159-3" name="__codelineno-159-3" href="#__codelineno-159-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-159-4" name="__codelineno-159-4" href="#__codelineno-159-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span>
|
||
<a id="__codelineno-159-5" name="__codelineno-159-5" href="#__codelineno-159-5"></a><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
|
||
<a id="__codelineno-159-6" name="__codelineno-159-6" href="#__codelineno-159-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-159-7" name="__codelineno-159-7" href="#__codelineno-159-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-159-8" name="__codelineno-159-8" href="#__codelineno-159-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-159-9" name="__codelineno-159-9" href="#__codelineno-159-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-159-10" name="__codelineno-159-10" href="#__codelineno-159-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-160-1" name="__codelineno-160-1" href="#__codelineno-160-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-160-2" name="__codelineno-160-2" href="#__codelineno-160-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">float64</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-160-3" name="__codelineno-160-3" href="#__codelineno-160-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-160-4" name="__codelineno-160-4" href="#__codelineno-160-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-160-5" name="__codelineno-160-5" href="#__codelineno-160-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-160-6" name="__codelineno-160-6" href="#__codelineno-160-6"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span>
|
||
<a id="__codelineno-160-7" name="__codelineno-160-7" href="#__codelineno-160-7"></a><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
|
||
<a id="__codelineno-160-8" name="__codelineno-160-8" href="#__codelineno-160-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mf">0.0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-160-9" name="__codelineno-160-9" href="#__codelineno-160-9"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span>
|
||
<a id="__codelineno-160-10" name="__codelineno-160-10" href="#__codelineno-160-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-160-11" name="__codelineno-160-11" href="#__codelineno-160-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||
<a id="__codelineno-160-12" name="__codelineno-160-12" href="#__codelineno-160-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-161-1" name="__codelineno-161-1" href="#__codelineno-161-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-161-2" name="__codelineno-161-2" href="#__codelineno-161-2"></a><span class="kd">func</span> <span class="nf">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Double</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-161-3" name="__codelineno-161-3" href="#__codelineno-161-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o"><=</span> <span class="mi">1</span> <span class="p">{</span>
|
||
<a id="__codelineno-161-4" name="__codelineno-161-4" href="#__codelineno-161-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||
<a id="__codelineno-161-5" name="__codelineno-161-5" href="#__codelineno-161-5"></a> <span class="p">}</span>
|
||
<a id="__codelineno-161-6" name="__codelineno-161-6" href="#__codelineno-161-6"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span>
|
||
<a id="__codelineno-161-7" name="__codelineno-161-7" href="#__codelineno-161-7"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">n</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
|
||
<a id="__codelineno-161-8" name="__codelineno-161-8" href="#__codelineno-161-8"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-161-9" name="__codelineno-161-9" href="#__codelineno-161-9"></a> <span class="p">}</span>
|
||
<a id="__codelineno-161-10" name="__codelineno-161-10" href="#__codelineno-161-10"></a> <span class="k">return</span> <span class="bp">count</span>
|
||
<a id="__codelineno-161-11" name="__codelineno-161-11" href="#__codelineno-161-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-162-1" name="__codelineno-162-1" href="#__codelineno-162-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-162-2" name="__codelineno-162-2" href="#__codelineno-162-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-162-3" name="__codelineno-162-3" href="#__codelineno-162-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-162-4" name="__codelineno-162-4" href="#__codelineno-162-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
|
||
<a id="__codelineno-162-5" name="__codelineno-162-5" href="#__codelineno-162-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-162-6" name="__codelineno-162-6" href="#__codelineno-162-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-162-7" name="__codelineno-162-7" href="#__codelineno-162-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-162-8" name="__codelineno-162-8" href="#__codelineno-162-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-162-9" name="__codelineno-162-9" href="#__codelineno-162-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-163-1" name="__codelineno-163-1" href="#__codelineno-163-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-163-2" name="__codelineno-163-2" href="#__codelineno-163-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-163-3" name="__codelineno-163-3" href="#__codelineno-163-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-163-4" name="__codelineno-163-4" href="#__codelineno-163-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">linearLogRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span>
|
||
<a id="__codelineno-163-5" name="__codelineno-163-5" href="#__codelineno-163-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-163-6" name="__codelineno-163-6" href="#__codelineno-163-6"></a><span class="w"> </span><span class="nx">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-163-7" name="__codelineno-163-7" href="#__codelineno-163-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-163-8" name="__codelineno-163-8" href="#__codelineno-163-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-163-9" name="__codelineno-163-9" href="#__codelineno-163-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-164-1" name="__codelineno-164-1" href="#__codelineno-164-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-164-2" name="__codelineno-164-2" href="#__codelineno-164-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="kt">num</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-164-3" name="__codelineno-164-3" href="#__codelineno-164-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-164-4" name="__codelineno-164-4" href="#__codelineno-164-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
|
||
<a id="__codelineno-164-5" name="__codelineno-164-5" href="#__codelineno-164-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-164-6" name="__codelineno-164-6" href="#__codelineno-164-6"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-164-7" name="__codelineno-164-7" href="#__codelineno-164-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-164-8" name="__codelineno-164-8" href="#__codelineno-164-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-164-9" name="__codelineno-164-9" href="#__codelineno-164-9"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-165-1" name="__codelineno-165-1" href="#__codelineno-165-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-165-2" name="__codelineno-165-2" href="#__codelineno-165-2"></a><span class="k">fn</span> <span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span>: <span class="kt">f32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-165-3" name="__codelineno-165-3" href="#__codelineno-165-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mf">1.0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-165-4" name="__codelineno-165-4" href="#__codelineno-165-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-165-5" name="__codelineno-165-5" href="#__codelineno-165-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-165-6" name="__codelineno-165-6" href="#__codelineno-165-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2.0</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span>
|
||
<a id="__codelineno-165-7" name="__codelineno-165-7" href="#__codelineno-165-7"></a><span class="w"> </span><span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2.0</span><span class="p">);</span>
|
||
<a id="__codelineno-165-8" name="__codelineno-165-8" href="#__codelineno-165-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-165-9" name="__codelineno-165-9" href="#__codelineno-165-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-165-10" name="__codelineno-165-10" href="#__codelineno-165-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-165-11" name="__codelineno-165-11" href="#__codelineno-165-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span>
|
||
<a id="__codelineno-165-12" name="__codelineno-165-12" href="#__codelineno-165-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-166-1" name="__codelineno-166-1" href="#__codelineno-166-1"></a><span class="cm">/* 线性对数阶 */</span>
|
||
<a id="__codelineno-166-2" name="__codelineno-166-2" href="#__codelineno-166-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-166-3" name="__codelineno-166-3" href="#__codelineno-166-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-166-4" name="__codelineno-166-4" href="#__codelineno-166-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-166-5" name="__codelineno-166-5" href="#__codelineno-166-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
|
||
<a id="__codelineno-166-6" name="__codelineno-166-6" href="#__codelineno-166-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-166-7" name="__codelineno-166-7" href="#__codelineno-166-7"></a><span class="w"> </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
|
||
<a id="__codelineno-166-8" name="__codelineno-166-8" href="#__codelineno-166-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-166-9" name="__codelineno-166-9" href="#__codelineno-166-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-166-10" name="__codelineno-166-10" href="#__codelineno-166-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-167-1" name="__codelineno-167-1" href="#__codelineno-167-1"></a><span class="c1">// 线性对数阶</span>
|
||
<a id="__codelineno-167-2" name="__codelineno-167-2" href="#__codelineno-167-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-167-3" name="__codelineno-167-3" href="#__codelineno-167-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-167-4" name="__codelineno-167-4" href="#__codelineno-167-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span>
|
||
<a id="__codelineno-167-5" name="__codelineno-167-5" href="#__codelineno-167-5"></a><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
|
||
<a id="__codelineno-167-6" name="__codelineno-167-6" href="#__codelineno-167-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">f32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-167-7" name="__codelineno-167-7" href="#__codelineno-167-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-167-8" name="__codelineno-167-8" href="#__codelineno-167-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-167-9" name="__codelineno-167-9" href="#__codelineno-167-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-167-10" name="__codelineno-167-10" href="#__codelineno-167-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-167-11" name="__codelineno-167-11" href="#__codelineno-167-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>图 2-13 展示了线性对数阶的生成方式。二叉树的每一层的操作总数都为 <span class="arithmatex">\(n\)</span> ，树共有 <span class="arithmatex">\(\log_2 n + 1\)</span> 层，因此时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span> 。</p>
|
||
<p><img alt="线性对数阶的时间复杂度" src="../time_complexity.assets/time_complexity_logarithmic_linear.png" /></p>
|
||
<p align="center"> 图 2-13 线性对数阶的时间复杂度 </p>
|
||
|
||
<p>主流排序算法的时间复杂度通常为 <span class="arithmatex">\(O(n \log n)\)</span> ，例如快速排序、归并排序、堆排序等。</p>
|
||
<h3 id="7-on">7. 阶乘阶 <span class="arithmatex">\(O(n!)\)</span><a class="headerlink" href="#7-on" title="Permanent link">¶</a></h3>
|
||
<p>阶乘阶对应数学上的“全排列”问题。给定 <span class="arithmatex">\(n\)</span> 个互不重复的元素，求其所有可能的排列方案，方案数量为：</p>
|
||
<div class="arithmatex">\[
|
||
n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
|
||
\]</div>
|
||
<p>阶乘通常使用递归实现。如图 2-14 和以下代码所示，第一层分裂出 <span class="arithmatex">\(n\)</span> 个，第二层分裂出 <span class="arithmatex">\(n - 1\)</span> 个，以此类推，直至第 <span class="arithmatex">\(n\)</span> 层时停止分裂：</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="15:12"><input checked="checked" id="__tabbed_15_1" name="__tabbed_15" type="radio" /><input id="__tabbed_15_2" name="__tabbed_15" type="radio" /><input id="__tabbed_15_3" name="__tabbed_15" type="radio" /><input id="__tabbed_15_4" name="__tabbed_15" type="radio" /><input id="__tabbed_15_5" name="__tabbed_15" type="radio" /><input id="__tabbed_15_6" name="__tabbed_15" type="radio" /><input id="__tabbed_15_7" name="__tabbed_15" type="radio" /><input id="__tabbed_15_8" name="__tabbed_15" type="radio" /><input id="__tabbed_15_9" name="__tabbed_15" type="radio" /><input id="__tabbed_15_10" name="__tabbed_15" type="radio" /><input id="__tabbed_15_11" name="__tabbed_15" type="radio" /><input id="__tabbed_15_12" name="__tabbed_15" type="radio" /><div class="tabbed-labels"><label for="__tabbed_15_1">Python</label><label for="__tabbed_15_2">C++</label><label for="__tabbed_15_3">Java</label><label for="__tabbed_15_4">C#</label><label for="__tabbed_15_5">Go</label><label for="__tabbed_15_6">Swift</label><label for="__tabbed_15_7">JS</label><label for="__tabbed_15_8">TS</label><label for="__tabbed_15_9">Dart</label><label for="__tabbed_15_10">Rust</label><label for="__tabbed_15_11">C</label><label for="__tabbed_15_12">Zig</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-168-1" name="__codelineno-168-1" href="#__codelineno-168-1"></a><span class="k">def</span> <span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-168-2" name="__codelineno-168-2" href="#__codelineno-168-2"></a><span class="w"> </span><span class="sd">"""阶乘阶（递归实现）"""</span>
|
||
<a id="__codelineno-168-3" name="__codelineno-168-3" href="#__codelineno-168-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
|
||
<a id="__codelineno-168-4" name="__codelineno-168-4" href="#__codelineno-168-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||
<a id="__codelineno-168-5" name="__codelineno-168-5" href="#__codelineno-168-5"></a> <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-168-6" name="__codelineno-168-6" href="#__codelineno-168-6"></a> <span class="c1"># 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-168-7" name="__codelineno-168-7" href="#__codelineno-168-7"></a> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
|
||
<a id="__codelineno-168-8" name="__codelineno-168-8" href="#__codelineno-168-8"></a> <span class="n">count</span> <span class="o">+=</span> <span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-168-9" name="__codelineno-168-9" href="#__codelineno-168-9"></a> <span class="k">return</span> <span class="n">count</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-169-1" name="__codelineno-169-1" href="#__codelineno-169-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-169-2" name="__codelineno-169-2" href="#__codelineno-169-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-169-3" name="__codelineno-169-3" href="#__codelineno-169-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-169-4" name="__codelineno-169-4" href="#__codelineno-169-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-169-5" name="__codelineno-169-5" href="#__codelineno-169-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-169-6" name="__codelineno-169-6" href="#__codelineno-169-6"></a><span class="w"> </span><span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-169-7" name="__codelineno-169-7" href="#__codelineno-169-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-169-8" name="__codelineno-169-8" href="#__codelineno-169-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-169-9" name="__codelineno-169-9" href="#__codelineno-169-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-169-10" name="__codelineno-169-10" href="#__codelineno-169-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-169-11" name="__codelineno-169-11" href="#__codelineno-169-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-170-1" name="__codelineno-170-1" href="#__codelineno-170-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-170-2" name="__codelineno-170-2" href="#__codelineno-170-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-170-3" name="__codelineno-170-3" href="#__codelineno-170-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-170-4" name="__codelineno-170-4" href="#__codelineno-170-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-170-5" name="__codelineno-170-5" href="#__codelineno-170-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-170-6" name="__codelineno-170-6" href="#__codelineno-170-6"></a><span class="w"> </span><span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-170-7" name="__codelineno-170-7" href="#__codelineno-170-7"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-170-8" name="__codelineno-170-8" href="#__codelineno-170-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-170-9" name="__codelineno-170-9" href="#__codelineno-170-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-170-10" name="__codelineno-170-10" href="#__codelineno-170-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-170-11" name="__codelineno-170-11" href="#__codelineno-170-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-171-1" name="__codelineno-171-1" href="#__codelineno-171-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-171-2" name="__codelineno-171-2" href="#__codelineno-171-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-171-3" name="__codelineno-171-3" href="#__codelineno-171-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-171-4" name="__codelineno-171-4" href="#__codelineno-171-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-171-5" name="__codelineno-171-5" href="#__codelineno-171-5"></a><span class="w"> </span><span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-171-6" name="__codelineno-171-6" href="#__codelineno-171-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-171-7" name="__codelineno-171-7" href="#__codelineno-171-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||
<a id="__codelineno-171-8" name="__codelineno-171-8" href="#__codelineno-171-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-171-9" name="__codelineno-171-9" href="#__codelineno-171-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-171-10" name="__codelineno-171-10" href="#__codelineno-171-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-172-1" name="__codelineno-172-1" href="#__codelineno-172-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-172-2" name="__codelineno-172-2" href="#__codelineno-172-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-172-3" name="__codelineno-172-3" href="#__codelineno-172-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-172-4" name="__codelineno-172-4" href="#__codelineno-172-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-172-5" name="__codelineno-172-5" href="#__codelineno-172-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-172-6" name="__codelineno-172-6" href="#__codelineno-172-6"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
|
||
<a id="__codelineno-172-7" name="__codelineno-172-7" href="#__codelineno-172-7"></a><span class="w"> </span><span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-172-8" name="__codelineno-172-8" href="#__codelineno-172-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-172-9" name="__codelineno-172-9" href="#__codelineno-172-9"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-172-10" name="__codelineno-172-10" href="#__codelineno-172-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-172-11" name="__codelineno-172-11" href="#__codelineno-172-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span>
|
||
<a id="__codelineno-172-12" name="__codelineno-172-12" href="#__codelineno-172-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-173-1" name="__codelineno-173-1" href="#__codelineno-173-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-173-2" name="__codelineno-173-2" href="#__codelineno-173-2"></a><span class="kd">func</span> <span class="nf">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-173-3" name="__codelineno-173-3" href="#__codelineno-173-3"></a> <span class="k">if</span> <span class="n">n</span> <span class="p">==</span> <span class="mi">0</span> <span class="p">{</span>
|
||
<a id="__codelineno-173-4" name="__codelineno-173-4" href="#__codelineno-173-4"></a> <span class="k">return</span> <span class="mi">1</span>
|
||
<a id="__codelineno-173-5" name="__codelineno-173-5" href="#__codelineno-173-5"></a> <span class="p">}</span>
|
||
<a id="__codelineno-173-6" name="__codelineno-173-6" href="#__codelineno-173-6"></a> <span class="kd">var</span> <span class="nv">count</span> <span class="p">=</span> <span class="mi">0</span>
|
||
<a id="__codelineno-173-7" name="__codelineno-173-7" href="#__codelineno-173-7"></a> <span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-173-8" name="__codelineno-173-8" href="#__codelineno-173-8"></a> <span class="k">for</span> <span class="kc">_</span> <span class="k">in</span> <span class="mi">0</span> <span class="p">..</span><span class="o"><</span> <span class="n">n</span> <span class="p">{</span>
|
||
<a id="__codelineno-173-9" name="__codelineno-173-9" href="#__codelineno-173-9"></a> <span class="bp">count</span> <span class="o">+=</span> <span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-173-10" name="__codelineno-173-10" href="#__codelineno-173-10"></a> <span class="p">}</span>
|
||
<a id="__codelineno-173-11" name="__codelineno-173-11" href="#__codelineno-173-11"></a> <span class="k">return</span> <span class="bp">count</span>
|
||
<a id="__codelineno-173-12" name="__codelineno-173-12" href="#__codelineno-173-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-174-1" name="__codelineno-174-1" href="#__codelineno-174-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-174-2" name="__codelineno-174-2" href="#__codelineno-174-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-174-3" name="__codelineno-174-3" href="#__codelineno-174-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-174-4" name="__codelineno-174-4" href="#__codelineno-174-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-174-5" name="__codelineno-174-5" href="#__codelineno-174-5"></a><span class="w"> </span><span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-174-6" name="__codelineno-174-6" href="#__codelineno-174-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-174-7" name="__codelineno-174-7" href="#__codelineno-174-7"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||
<a id="__codelineno-174-8" name="__codelineno-174-8" href="#__codelineno-174-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-174-9" name="__codelineno-174-9" href="#__codelineno-174-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-174-10" name="__codelineno-174-10" href="#__codelineno-174-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-175-1" name="__codelineno-175-1" href="#__codelineno-175-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-175-2" name="__codelineno-175-2" href="#__codelineno-175-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-175-3" name="__codelineno-175-3" href="#__codelineno-175-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-175-4" name="__codelineno-175-4" href="#__codelineno-175-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
|
||
<a id="__codelineno-175-5" name="__codelineno-175-5" href="#__codelineno-175-5"></a><span class="w"> </span><span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-175-6" name="__codelineno-175-6" href="#__codelineno-175-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-175-7" name="__codelineno-175-7" href="#__codelineno-175-7"></a><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">factorialRecur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
|
||
<a id="__codelineno-175-8" name="__codelineno-175-8" href="#__codelineno-175-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-175-9" name="__codelineno-175-9" href="#__codelineno-175-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">count</span><span class="p">;</span>
|
||
<a id="__codelineno-175-10" name="__codelineno-175-10" href="#__codelineno-175-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-176-1" name="__codelineno-176-1" href="#__codelineno-176-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-176-2" name="__codelineno-176-2" href="#__codelineno-176-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-176-3" name="__codelineno-176-3" href="#__codelineno-176-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-176-4" name="__codelineno-176-4" href="#__codelineno-176-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
|
||
<a id="__codelineno-176-5" name="__codelineno-176-5" href="#__codelineno-176-5"></a><span class="w"> </span><span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-176-6" name="__codelineno-176-6" href="#__codelineno-176-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-176-7" name="__codelineno-176-7" href="#__codelineno-176-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
||
<a id="__codelineno-176-8" name="__codelineno-176-8" href="#__codelineno-176-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-176-9" name="__codelineno-176-9" href="#__codelineno-176-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-176-10" name="__codelineno-176-10" href="#__codelineno-176-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-177-1" name="__codelineno-177-1" href="#__codelineno-177-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-177-2" name="__codelineno-177-2" href="#__codelineno-177-2"></a><span class="k">fn</span> <span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
|
||
<a id="__codelineno-177-3" name="__codelineno-177-3" href="#__codelineno-177-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-177-4" name="__codelineno-177-4" href="#__codelineno-177-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-177-5" name="__codelineno-177-5" href="#__codelineno-177-5"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-177-6" name="__codelineno-177-6" href="#__codelineno-177-6"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-177-7" name="__codelineno-177-7" href="#__codelineno-177-7"></a><span class="w"> </span><span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-177-8" name="__codelineno-177-8" href="#__codelineno-177-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-177-9" name="__codelineno-177-9" href="#__codelineno-177-9"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-177-10" name="__codelineno-177-10" href="#__codelineno-177-10"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-177-11" name="__codelineno-177-11" href="#__codelineno-177-11"></a><span class="w"> </span><span class="n">count</span>
|
||
<a id="__codelineno-177-12" name="__codelineno-177-12" href="#__codelineno-177-12"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-178-1" name="__codelineno-178-1" href="#__codelineno-178-1"></a><span class="cm">/* 阶乘阶（递归实现） */</span>
|
||
<a id="__codelineno-178-2" name="__codelineno-178-2" href="#__codelineno-178-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-178-3" name="__codelineno-178-3" href="#__codelineno-178-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
|
||
<a id="__codelineno-178-4" name="__codelineno-178-4" href="#__codelineno-178-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-178-5" name="__codelineno-178-5" href="#__codelineno-178-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-178-6" name="__codelineno-178-6" href="#__codelineno-178-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-178-7" name="__codelineno-178-7" href="#__codelineno-178-7"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-178-8" name="__codelineno-178-8" href="#__codelineno-178-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-178-9" name="__codelineno-178-9" href="#__codelineno-178-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-178-10" name="__codelineno-178-10" href="#__codelineno-178-10"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-179-1" name="__codelineno-179-1" href="#__codelineno-179-1"></a><span class="c1">// 阶乘阶（递归实现）</span>
|
||
<a id="__codelineno-179-2" name="__codelineno-179-2" href="#__codelineno-179-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-179-3" name="__codelineno-179-3" href="#__codelineno-179-3"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-179-4" name="__codelineno-179-4" href="#__codelineno-179-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-179-5" name="__codelineno-179-5" href="#__codelineno-179-5"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
|
||
<a id="__codelineno-179-6" name="__codelineno-179-6" href="#__codelineno-179-6"></a><span class="w"> </span><span class="c1">// 从 1 个分裂出 n 个</span>
|
||
<a id="__codelineno-179-7" name="__codelineno-179-7" href="#__codelineno-179-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-179-8" name="__codelineno-179-8" href="#__codelineno-179-8"></a><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-179-9" name="__codelineno-179-9" href="#__codelineno-179-9"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-179-10" name="__codelineno-179-10" href="#__codelineno-179-10"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
|
||
<a id="__codelineno-179-11" name="__codelineno-179-11" href="#__codelineno-179-11"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p><img alt="阶乘阶的时间复杂度" src="../time_complexity.assets/time_complexity_factorial.png" /></p>
|
||
<p align="center"> 图 2-14 阶乘阶的时间复杂度 </p>
|
||
|
||
<p>请注意，因为当 <span class="arithmatex">\(n \geq 4\)</span> 时恒有 <span class="arithmatex">\(n! > 2^n\)</span> ，所以阶乘阶比指数阶增长得更快，在 <span class="arithmatex">\(n\)</span> 较大时也是不可接受的。</p>
|
||
<h2 id="235">2.3.5 最差、最佳、平均时间复杂度<a class="headerlink" href="#235" title="Permanent link">¶</a></h2>
|
||
<p><strong>算法的时间效率往往不是固定的，而是与输入数据的分布有关</strong>。假设输入一个长度为 <span class="arithmatex">\(n\)</span> 的数组 <code>nums</code> ，其中 <code>nums</code> 由从 <span class="arithmatex">\(1\)</span> 至 <span class="arithmatex">\(n\)</span> 的数字组成，每个数字只出现一次；但元素顺序是随机打乱的，任务目标是返回元素 <span class="arithmatex">\(1\)</span> 的索引。我们可以得出以下结论。</p>
|
||
<ul>
|
||
<li>当 <code>nums = [?, ?, ..., 1]</code> ，即当末尾元素是 <span class="arithmatex">\(1\)</span> 时，需要完整遍历数组，<strong>达到最差时间复杂度 <span class="arithmatex">\(O(n)\)</span></strong> 。</li>
|
||
<li>当 <code>nums = [1, ?, ?, ...]</code> ，即当首个元素为 <span class="arithmatex">\(1\)</span> 时，无论数组多长都不需要继续遍历，<strong>达到最佳时间复杂度 <span class="arithmatex">\(\Omega(1)\)</span></strong> 。</li>
|
||
</ul>
|
||
<p>“最差时间复杂度”对应函数渐近上界，使用大 <span class="arithmatex">\(O\)</span> 记号表示。相应地，“最佳时间复杂度”对应函数渐近下界，用 <span class="arithmatex">\(\Omega\)</span> 记号表示：</p>
|
||
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|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.py</span><pre><span></span><code><a id="__codelineno-180-1" name="__codelineno-180-1" href="#__codelineno-180-1"></a><span class="k">def</span> <span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
|
||
<a id="__codelineno-180-2" name="__codelineno-180-2" href="#__codelineno-180-2"></a><span class="w"> </span><span class="sd">"""生成一个数组，元素为: 1, 2, ..., n ，顺序被打乱"""</span>
|
||
<a id="__codelineno-180-3" name="__codelineno-180-3" href="#__codelineno-180-3"></a> <span class="c1"># 生成数组 nums =: 1, 2, 3, ..., n</span>
|
||
<a id="__codelineno-180-4" name="__codelineno-180-4" href="#__codelineno-180-4"></a> <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
|
||
<a id="__codelineno-180-5" name="__codelineno-180-5" href="#__codelineno-180-5"></a> <span class="c1"># 随机打乱数组元素</span>
|
||
<a id="__codelineno-180-6" name="__codelineno-180-6" href="#__codelineno-180-6"></a> <span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
|
||
<a id="__codelineno-180-7" name="__codelineno-180-7" href="#__codelineno-180-7"></a> <span class="k">return</span> <span class="n">nums</span>
|
||
<a id="__codelineno-180-8" name="__codelineno-180-8" href="#__codelineno-180-8"></a>
|
||
<a id="__codelineno-180-9" name="__codelineno-180-9" href="#__codelineno-180-9"></a><span class="k">def</span> <span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
|
||
<a id="__codelineno-180-10" name="__codelineno-180-10" href="#__codelineno-180-10"></a><span class="w"> </span><span class="sd">"""查找数组 nums 中数字 1 所在索引"""</span>
|
||
<a id="__codelineno-180-11" name="__codelineno-180-11" href="#__codelineno-180-11"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
|
||
<a id="__codelineno-180-12" name="__codelineno-180-12" href="#__codelineno-180-12"></a> <span class="c1"># 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-180-13" name="__codelineno-180-13" href="#__codelineno-180-13"></a> <span class="c1"># 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-180-14" name="__codelineno-180-14" href="#__codelineno-180-14"></a> <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
|
||
<a id="__codelineno-180-15" name="__codelineno-180-15" href="#__codelineno-180-15"></a> <span class="k">return</span> <span class="n">i</span>
|
||
<a id="__codelineno-180-16" name="__codelineno-180-16" href="#__codelineno-180-16"></a> <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-181-1" name="__codelineno-181-1" href="#__codelineno-181-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-181-2" name="__codelineno-181-2" href="#__codelineno-181-2"></a><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-181-3" name="__codelineno-181-3" href="#__codelineno-181-3"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
|
||
<a id="__codelineno-181-4" name="__codelineno-181-4" href="#__codelineno-181-4"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-181-5" name="__codelineno-181-5" href="#__codelineno-181-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-181-6" name="__codelineno-181-6" href="#__codelineno-181-6"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-181-7" name="__codelineno-181-7" href="#__codelineno-181-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-181-8" name="__codelineno-181-8" href="#__codelineno-181-8"></a><span class="w"> </span><span class="c1">// 使用系统时间生成随机种子</span>
|
||
<a id="__codelineno-181-9" name="__codelineno-181-9" href="#__codelineno-181-9"></a><span class="w"> </span><span class="kt">unsigned</span><span class="w"> </span><span class="n">seed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">chrono</span><span class="o">::</span><span class="n">system_clock</span><span class="o">::</span><span class="n">now</span><span class="p">().</span><span class="n">time_since_epoch</span><span class="p">().</span><span class="n">count</span><span class="p">();</span>
|
||
<a id="__codelineno-181-10" name="__codelineno-181-10" href="#__codelineno-181-10"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-181-11" name="__codelineno-181-11" href="#__codelineno-181-11"></a><span class="w"> </span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">default_random_engine</span><span class="p">(</span><span class="n">seed</span><span class="p">));</span>
|
||
<a id="__codelineno-181-12" name="__codelineno-181-12" href="#__codelineno-181-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
|
||
<a id="__codelineno-181-13" name="__codelineno-181-13" href="#__codelineno-181-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-181-14" name="__codelineno-181-14" href="#__codelineno-181-14"></a>
|
||
<a id="__codelineno-181-15" name="__codelineno-181-15" href="#__codelineno-181-15"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-181-16" name="__codelineno-181-16" href="#__codelineno-181-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">findOne</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-181-17" name="__codelineno-181-17" href="#__codelineno-181-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-181-18" name="__codelineno-181-18" href="#__codelineno-181-18"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-181-19" name="__codelineno-181-19" href="#__codelineno-181-19"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-181-20" name="__codelineno-181-20" href="#__codelineno-181-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-181-21" name="__codelineno-181-21" href="#__codelineno-181-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-181-22" name="__codelineno-181-22" href="#__codelineno-181-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-181-23" name="__codelineno-181-23" href="#__codelineno-181-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
|
||
<a id="__codelineno-181-24" name="__codelineno-181-24" href="#__codelineno-181-24"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.java</span><pre><span></span><code><a id="__codelineno-182-1" name="__codelineno-182-1" href="#__codelineno-182-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-182-2" name="__codelineno-182-2" href="#__codelineno-182-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-182-3" name="__codelineno-182-3" href="#__codelineno-182-3"></a><span class="w"> </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-182-4" name="__codelineno-182-4" href="#__codelineno-182-4"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-182-5" name="__codelineno-182-5" href="#__codelineno-182-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-182-6" name="__codelineno-182-6" href="#__codelineno-182-6"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-182-7" name="__codelineno-182-7" href="#__codelineno-182-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-182-8" name="__codelineno-182-8" href="#__codelineno-182-8"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-182-9" name="__codelineno-182-9" href="#__codelineno-182-9"></a><span class="w"> </span><span class="n">Collections</span><span class="p">.</span><span class="na">shuffle</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">nums</span><span class="p">));</span>
|
||
<a id="__codelineno-182-10" name="__codelineno-182-10" href="#__codelineno-182-10"></a><span class="w"> </span><span class="c1">// Integer[] -> int[]</span>
|
||
<a id="__codelineno-182-11" name="__codelineno-182-11" href="#__codelineno-182-11"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-182-12" name="__codelineno-182-12" href="#__codelineno-182-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-182-13" name="__codelineno-182-13" href="#__codelineno-182-13"></a><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
|
||
<a id="__codelineno-182-14" name="__codelineno-182-14" href="#__codelineno-182-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-182-15" name="__codelineno-182-15" href="#__codelineno-182-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
||
<a id="__codelineno-182-16" name="__codelineno-182-16" href="#__codelineno-182-16"></a><span class="p">}</span>
|
||
<a id="__codelineno-182-17" name="__codelineno-182-17" href="#__codelineno-182-17"></a>
|
||
<a id="__codelineno-182-18" name="__codelineno-182-18" href="#__codelineno-182-18"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-182-19" name="__codelineno-182-19" href="#__codelineno-182-19"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-182-20" name="__codelineno-182-20" href="#__codelineno-182-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-182-21" name="__codelineno-182-21" href="#__codelineno-182-21"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-182-22" name="__codelineno-182-22" href="#__codelineno-182-22"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-182-23" name="__codelineno-182-23" href="#__codelineno-182-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-182-24" name="__codelineno-182-24" href="#__codelineno-182-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-182-25" name="__codelineno-182-25" href="#__codelineno-182-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-182-26" name="__codelineno-182-26" href="#__codelineno-182-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-182-27" name="__codelineno-182-27" href="#__codelineno-182-27"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.cs</span><pre><span></span><code><a id="__codelineno-183-1" name="__codelineno-183-1" href="#__codelineno-183-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-183-2" name="__codelineno-183-2" href="#__codelineno-183-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-183-3" name="__codelineno-183-3" href="#__codelineno-183-3"></a><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
|
||
<a id="__codelineno-183-4" name="__codelineno-183-4" href="#__codelineno-183-4"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-183-5" name="__codelineno-183-5" href="#__codelineno-183-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-183-6" name="__codelineno-183-6" href="#__codelineno-183-6"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-183-7" name="__codelineno-183-7" href="#__codelineno-183-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-183-8" name="__codelineno-183-8" href="#__codelineno-183-8"></a>
|
||
<a id="__codelineno-183-9" name="__codelineno-183-9" href="#__codelineno-183-9"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-183-10" name="__codelineno-183-10" href="#__codelineno-183-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-183-11" name="__codelineno-183-11" href="#__codelineno-183-11"></a><span class="w"> </span><span class="kt">var</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Random</span><span class="p">().</span><span class="n">Next</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">);</span>
|
||
<a id="__codelineno-183-12" name="__codelineno-183-12" href="#__codelineno-183-12"></a><span class="w"> </span><span class="kt">var</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
||
<a id="__codelineno-183-13" name="__codelineno-183-13" href="#__codelineno-183-13"></a><span class="w"> </span><span class="kt">var</span><span class="w"> </span><span class="n">ran</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
|
||
<a id="__codelineno-183-14" name="__codelineno-183-14" href="#__codelineno-183-14"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ran</span><span class="p">;</span>
|
||
<a id="__codelineno-183-15" name="__codelineno-183-15" href="#__codelineno-183-15"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
|
||
<a id="__codelineno-183-16" name="__codelineno-183-16" href="#__codelineno-183-16"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-183-17" name="__codelineno-183-17" href="#__codelineno-183-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
|
||
<a id="__codelineno-183-18" name="__codelineno-183-18" href="#__codelineno-183-18"></a><span class="p">}</span>
|
||
<a id="__codelineno-183-19" name="__codelineno-183-19" href="#__codelineno-183-19"></a>
|
||
<a id="__codelineno-183-20" name="__codelineno-183-20" href="#__codelineno-183-20"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-183-21" name="__codelineno-183-21" href="#__codelineno-183-21"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-183-22" name="__codelineno-183-22" href="#__codelineno-183-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-183-23" name="__codelineno-183-23" href="#__codelineno-183-23"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-183-24" name="__codelineno-183-24" href="#__codelineno-183-24"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-183-25" name="__codelineno-183-25" href="#__codelineno-183-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
|
||
<a id="__codelineno-183-26" name="__codelineno-183-26" href="#__codelineno-183-26"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-183-27" name="__codelineno-183-27" href="#__codelineno-183-27"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-183-28" name="__codelineno-183-28" href="#__codelineno-183-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-183-29" name="__codelineno-183-29" href="#__codelineno-183-29"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.go</span><pre><span></span><code><a id="__codelineno-184-1" name="__codelineno-184-1" href="#__codelineno-184-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-184-2" name="__codelineno-184-2" href="#__codelineno-184-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">randomNumbers</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-184-3" name="__codelineno-184-3" href="#__codelineno-184-3"></a><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span>
|
||
<a id="__codelineno-184-4" name="__codelineno-184-4" href="#__codelineno-184-4"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-184-5" name="__codelineno-184-5" href="#__codelineno-184-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-184-6" name="__codelineno-184-6" href="#__codelineno-184-6"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
||
<a id="__codelineno-184-7" name="__codelineno-184-7" href="#__codelineno-184-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-184-8" name="__codelineno-184-8" href="#__codelineno-184-8"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-184-9" name="__codelineno-184-9" href="#__codelineno-184-9"></a><span class="w"> </span><span class="nx">rand</span><span class="p">.</span><span class="nx">Shuffle</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">),</span><span class="w"> </span><span class="kd">func</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-184-10" name="__codelineno-184-10" href="#__codelineno-184-10"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
|
||
<a id="__codelineno-184-11" name="__codelineno-184-11" href="#__codelineno-184-11"></a><span class="w"> </span><span class="p">})</span>
|
||
<a id="__codelineno-184-12" name="__codelineno-184-12" href="#__codelineno-184-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span>
|
||
<a id="__codelineno-184-13" name="__codelineno-184-13" href="#__codelineno-184-13"></a><span class="p">}</span>
|
||
<a id="__codelineno-184-14" name="__codelineno-184-14" href="#__codelineno-184-14"></a>
|
||
<a id="__codelineno-184-15" name="__codelineno-184-15" href="#__codelineno-184-15"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-184-16" name="__codelineno-184-16" href="#__codelineno-184-16"></a><span class="kd">func</span><span class="w"> </span><span class="nx">findOne</span><span class="p">(</span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-184-17" name="__codelineno-184-17" href="#__codelineno-184-17"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-184-18" name="__codelineno-184-18" href="#__codelineno-184-18"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-184-19" name="__codelineno-184-19" href="#__codelineno-184-19"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-184-20" name="__codelineno-184-20" href="#__codelineno-184-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-184-21" name="__codelineno-184-21" href="#__codelineno-184-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span>
|
||
<a id="__codelineno-184-22" name="__codelineno-184-22" href="#__codelineno-184-22"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-184-23" name="__codelineno-184-23" href="#__codelineno-184-23"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-184-24" name="__codelineno-184-24" href="#__codelineno-184-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
|
||
<a id="__codelineno-184-25" name="__codelineno-184-25" href="#__codelineno-184-25"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.swift</span><pre><span></span><code><a id="__codelineno-185-1" name="__codelineno-185-1" href="#__codelineno-185-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-185-2" name="__codelineno-185-2" href="#__codelineno-185-2"></a><span class="kd">func</span> <span class="nf">randomNumbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">{</span>
|
||
<a id="__codelineno-185-3" name="__codelineno-185-3" href="#__codelineno-185-3"></a> <span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-185-4" name="__codelineno-185-4" href="#__codelineno-185-4"></a> <span class="kd">var</span> <span class="nv">nums</span> <span class="p">=</span> <span class="nb">Array</span><span class="p">(</span><span class="mi">1</span> <span class="p">...</span> <span class="n">n</span><span class="p">)</span>
|
||
<a id="__codelineno-185-5" name="__codelineno-185-5" href="#__codelineno-185-5"></a> <span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-185-6" name="__codelineno-185-6" href="#__codelineno-185-6"></a> <span class="n">nums</span><span class="p">.</span><span class="n">shuffle</span><span class="p">()</span>
|
||
<a id="__codelineno-185-7" name="__codelineno-185-7" href="#__codelineno-185-7"></a> <span class="k">return</span> <span class="n">nums</span>
|
||
<a id="__codelineno-185-8" name="__codelineno-185-8" href="#__codelineno-185-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-185-9" name="__codelineno-185-9" href="#__codelineno-185-9"></a>
|
||
<a id="__codelineno-185-10" name="__codelineno-185-10" href="#__codelineno-185-10"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-185-11" name="__codelineno-185-11" href="#__codelineno-185-11"></a><span class="kd">func</span> <span class="nf">findOne</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">])</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
|
||
<a id="__codelineno-185-12" name="__codelineno-185-12" href="#__codelineno-185-12"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="n">nums</span><span class="p">.</span><span class="bp">indices</span> <span class="p">{</span>
|
||
<a id="__codelineno-185-13" name="__codelineno-185-13" href="#__codelineno-185-13"></a> <span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-185-14" name="__codelineno-185-14" href="#__codelineno-185-14"></a> <span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-185-15" name="__codelineno-185-15" href="#__codelineno-185-15"></a> <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="p">==</span> <span class="mi">1</span> <span class="p">{</span>
|
||
<a id="__codelineno-185-16" name="__codelineno-185-16" href="#__codelineno-185-16"></a> <span class="k">return</span> <span class="n">i</span>
|
||
<a id="__codelineno-185-17" name="__codelineno-185-17" href="#__codelineno-185-17"></a> <span class="p">}</span>
|
||
<a id="__codelineno-185-18" name="__codelineno-185-18" href="#__codelineno-185-18"></a> <span class="p">}</span>
|
||
<a id="__codelineno-185-19" name="__codelineno-185-19" href="#__codelineno-185-19"></a> <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
|
||
<a id="__codelineno-185-20" name="__codelineno-185-20" href="#__codelineno-185-20"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.js</span><pre><span></span><code><a id="__codelineno-186-1" name="__codelineno-186-1" href="#__codelineno-186-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-186-2" name="__codelineno-186-2" href="#__codelineno-186-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">randomNumbers</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-186-3" name="__codelineno-186-3" href="#__codelineno-186-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
|
||
<a id="__codelineno-186-4" name="__codelineno-186-4" href="#__codelineno-186-4"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-186-5" name="__codelineno-186-5" href="#__codelineno-186-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-186-6" name="__codelineno-186-6" href="#__codelineno-186-6"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-186-7" name="__codelineno-186-7" href="#__codelineno-186-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-186-8" name="__codelineno-186-8" href="#__codelineno-186-8"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-186-9" name="__codelineno-186-9" href="#__codelineno-186-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-186-10" name="__codelineno-186-10" href="#__codelineno-186-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">));</span>
|
||
<a id="__codelineno-186-11" name="__codelineno-186-11" href="#__codelineno-186-11"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
|
||
<a id="__codelineno-186-12" name="__codelineno-186-12" href="#__codelineno-186-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">];</span>
|
||
<a id="__codelineno-186-13" name="__codelineno-186-13" href="#__codelineno-186-13"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span>
|
||
<a id="__codelineno-186-14" name="__codelineno-186-14" href="#__codelineno-186-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-186-15" name="__codelineno-186-15" href="#__codelineno-186-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span><span class="p">;</span>
|
||
<a id="__codelineno-186-16" name="__codelineno-186-16" href="#__codelineno-186-16"></a><span class="p">}</span>
|
||
<a id="__codelineno-186-17" name="__codelineno-186-17" href="#__codelineno-186-17"></a>
|
||
<a id="__codelineno-186-18" name="__codelineno-186-18" href="#__codelineno-186-18"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-186-19" name="__codelineno-186-19" href="#__codelineno-186-19"></a><span class="kd">function</span><span class="w"> </span><span class="nx">findOne</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-186-20" name="__codelineno-186-20" href="#__codelineno-186-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-186-21" name="__codelineno-186-21" href="#__codelineno-186-21"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-186-22" name="__codelineno-186-22" href="#__codelineno-186-22"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-186-23" name="__codelineno-186-23" href="#__codelineno-186-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-186-24" name="__codelineno-186-24" href="#__codelineno-186-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
|
||
<a id="__codelineno-186-25" name="__codelineno-186-25" href="#__codelineno-186-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-186-26" name="__codelineno-186-26" href="#__codelineno-186-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-186-27" name="__codelineno-186-27" href="#__codelineno-186-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-186-28" name="__codelineno-186-28" href="#__codelineno-186-28"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.ts</span><pre><span></span><code><a id="__codelineno-187-1" name="__codelineno-187-1" href="#__codelineno-187-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-187-2" name="__codelineno-187-2" href="#__codelineno-187-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">randomNumbers</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-187-3" name="__codelineno-187-3" href="#__codelineno-187-3"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span>
|
||
<a id="__codelineno-187-4" name="__codelineno-187-4" href="#__codelineno-187-4"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-187-5" name="__codelineno-187-5" href="#__codelineno-187-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-187-6" name="__codelineno-187-6" href="#__codelineno-187-6"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-187-7" name="__codelineno-187-7" href="#__codelineno-187-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-187-8" name="__codelineno-187-8" href="#__codelineno-187-8"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-187-9" name="__codelineno-187-9" href="#__codelineno-187-9"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-187-10" name="__codelineno-187-10" href="#__codelineno-187-10"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">(</span><span class="nb">Math</span><span class="p">.</span><span class="nx">random</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">));</span>
|
||
<a id="__codelineno-187-11" name="__codelineno-187-11" href="#__codelineno-187-11"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
|
||
<a id="__codelineno-187-12" name="__codelineno-187-12" href="#__codelineno-187-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">];</span>
|
||
<a id="__codelineno-187-13" name="__codelineno-187-13" href="#__codelineno-187-13"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">temp</span><span class="p">;</span>
|
||
<a id="__codelineno-187-14" name="__codelineno-187-14" href="#__codelineno-187-14"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-187-15" name="__codelineno-187-15" href="#__codelineno-187-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">nums</span><span class="p">;</span>
|
||
<a id="__codelineno-187-16" name="__codelineno-187-16" href="#__codelineno-187-16"></a><span class="p">}</span>
|
||
<a id="__codelineno-187-17" name="__codelineno-187-17" href="#__codelineno-187-17"></a>
|
||
<a id="__codelineno-187-18" name="__codelineno-187-18" href="#__codelineno-187-18"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-187-19" name="__codelineno-187-19" href="#__codelineno-187-19"></a><span class="kd">function</span><span class="w"> </span><span class="nx">findOne</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-187-20" name="__codelineno-187-20" href="#__codelineno-187-20"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-187-21" name="__codelineno-187-21" href="#__codelineno-187-21"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-187-22" name="__codelineno-187-22" href="#__codelineno-187-22"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-187-23" name="__codelineno-187-23" href="#__codelineno-187-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-187-24" name="__codelineno-187-24" href="#__codelineno-187-24"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
|
||
<a id="__codelineno-187-25" name="__codelineno-187-25" href="#__codelineno-187-25"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-187-26" name="__codelineno-187-26" href="#__codelineno-187-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-187-27" name="__codelineno-187-27" href="#__codelineno-187-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mf">1</span><span class="p">;</span>
|
||
<a id="__codelineno-187-28" name="__codelineno-187-28" href="#__codelineno-187-28"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.dart</span><pre><span></span><code><a id="__codelineno-188-1" name="__codelineno-188-1" href="#__codelineno-188-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-188-2" name="__codelineno-188-2" href="#__codelineno-188-2"></a><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-188-3" name="__codelineno-188-3" href="#__codelineno-188-3"></a><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
|
||
<a id="__codelineno-188-4" name="__codelineno-188-4" href="#__codelineno-188-4"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-188-5" name="__codelineno-188-5" href="#__codelineno-188-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-188-6" name="__codelineno-188-6" href="#__codelineno-188-6"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-188-7" name="__codelineno-188-7" href="#__codelineno-188-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-188-8" name="__codelineno-188-8" href="#__codelineno-188-8"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-188-9" name="__codelineno-188-9" href="#__codelineno-188-9"></a><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">shuffle</span><span class="p">();</span>
|
||
<a id="__codelineno-188-10" name="__codelineno-188-10" href="#__codelineno-188-10"></a>
|
||
<a id="__codelineno-188-11" name="__codelineno-188-11" href="#__codelineno-188-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
|
||
<a id="__codelineno-188-12" name="__codelineno-188-12" href="#__codelineno-188-12"></a><span class="p">}</span>
|
||
<a id="__codelineno-188-13" name="__codelineno-188-13" href="#__codelineno-188-13"></a>
|
||
<a id="__codelineno-188-14" name="__codelineno-188-14" href="#__codelineno-188-14"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-188-15" name="__codelineno-188-15" href="#__codelineno-188-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">findOne</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-188-16" name="__codelineno-188-16" href="#__codelineno-188-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-188-17" name="__codelineno-188-17" href="#__codelineno-188-17"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-188-18" name="__codelineno-188-18" href="#__codelineno-188-18"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-188-19" name="__codelineno-188-19" href="#__codelineno-188-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-188-20" name="__codelineno-188-20" href="#__codelineno-188-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-188-21" name="__codelineno-188-21" href="#__codelineno-188-21"></a>
|
||
<a id="__codelineno-188-22" name="__codelineno-188-22" href="#__codelineno-188-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="m">1</span><span class="p">;</span>
|
||
<a id="__codelineno-188-23" name="__codelineno-188-23" href="#__codelineno-188-23"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.rs</span><pre><span></span><code><a id="__codelineno-189-1" name="__codelineno-189-1" href="#__codelineno-189-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-189-2" name="__codelineno-189-2" href="#__codelineno-189-2"></a><span class="k">fn</span> <span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-> <span class="nb">Vec</span><span class="o"><</span><span class="kt">i32</span><span class="o">></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-189-3" name="__codelineno-189-3" href="#__codelineno-189-3"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-189-4" name="__codelineno-189-4" href="#__codelineno-189-4"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">1</span><span class="o">..=</span><span class="n">n</span><span class="p">).</span><span class="n">collect</span>::<span class="o"><</span><span class="nb">Vec</span><span class="o"><</span><span class="kt">i32</span><span class="o">>></span><span class="p">();</span>
|
||
<a id="__codelineno-189-5" name="__codelineno-189-5" href="#__codelineno-189-5"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-189-6" name="__codelineno-189-6" href="#__codelineno-189-6"></a><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">shuffle</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="n">thread_rng</span><span class="p">());</span>
|
||
<a id="__codelineno-189-7" name="__codelineno-189-7" href="#__codelineno-189-7"></a><span class="w"> </span><span class="n">nums</span>
|
||
<a id="__codelineno-189-8" name="__codelineno-189-8" href="#__codelineno-189-8"></a><span class="p">}</span>
|
||
<a id="__codelineno-189-9" name="__codelineno-189-9" href="#__codelineno-189-9"></a>
|
||
<a id="__codelineno-189-10" name="__codelineno-189-10" href="#__codelineno-189-10"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-189-11" name="__codelineno-189-11" href="#__codelineno-189-11"></a><span class="k">fn</span> <span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span>: <span class="kp">&</span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span>-> <span class="nb">Option</span><span class="o"><</span><span class="kt">usize</span><span class="o">></span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-189-12" name="__codelineno-189-12" href="#__codelineno-189-12"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-189-13" name="__codelineno-189-13" href="#__codelineno-189-13"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-189-14" name="__codelineno-189-14" href="#__codelineno-189-14"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-189-15" name="__codelineno-189-15" href="#__codelineno-189-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-189-16" name="__codelineno-189-16" href="#__codelineno-189-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-189-17" name="__codelineno-189-17" href="#__codelineno-189-17"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-189-18" name="__codelineno-189-18" href="#__codelineno-189-18"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-189-19" name="__codelineno-189-19" href="#__codelineno-189-19"></a><span class="w"> </span><span class="nb">None</span>
|
||
<a id="__codelineno-189-20" name="__codelineno-189-20" href="#__codelineno-189-20"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.c</span><pre><span></span><code><a id="__codelineno-190-1" name="__codelineno-190-1" href="#__codelineno-190-1"></a><span class="cm">/* 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱 */</span>
|
||
<a id="__codelineno-190-2" name="__codelineno-190-2" href="#__codelineno-190-2"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-190-3" name="__codelineno-190-3" href="#__codelineno-190-3"></a><span class="w"> </span><span class="c1">// 分配堆区内存（创建一维可变长数组：数组中元素数量为 n ，元素类型为 int ）</span>
|
||
<a id="__codelineno-190-4" name="__codelineno-190-4" href="#__codelineno-190-4"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">));</span>
|
||
<a id="__codelineno-190-5" name="__codelineno-190-5" href="#__codelineno-190-5"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-190-6" name="__codelineno-190-6" href="#__codelineno-190-6"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-190-7" name="__codelineno-190-7" href="#__codelineno-190-7"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-190-8" name="__codelineno-190-8" href="#__codelineno-190-8"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-190-9" name="__codelineno-190-9" href="#__codelineno-190-9"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-190-10" name="__codelineno-190-10" href="#__codelineno-190-10"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-190-11" name="__codelineno-190-11" href="#__codelineno-190-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">()</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
|
||
<a id="__codelineno-190-12" name="__codelineno-190-12" href="#__codelineno-190-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
|
||
<a id="__codelineno-190-13" name="__codelineno-190-13" href="#__codelineno-190-13"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
|
||
<a id="__codelineno-190-14" name="__codelineno-190-14" href="#__codelineno-190-14"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
|
||
<a id="__codelineno-190-15" name="__codelineno-190-15" href="#__codelineno-190-15"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-190-16" name="__codelineno-190-16" href="#__codelineno-190-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
|
||
<a id="__codelineno-190-17" name="__codelineno-190-17" href="#__codelineno-190-17"></a><span class="p">}</span>
|
||
<a id="__codelineno-190-18" name="__codelineno-190-18" href="#__codelineno-190-18"></a>
|
||
<a id="__codelineno-190-19" name="__codelineno-190-19" href="#__codelineno-190-19"></a><span class="cm">/* 查找数组 nums 中数字 1 所在索引 */</span>
|
||
<a id="__codelineno-190-20" name="__codelineno-190-20" href="#__codelineno-190-20"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-190-21" name="__codelineno-190-21" href="#__codelineno-190-21"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-190-22" name="__codelineno-190-22" href="#__codelineno-190-22"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-190-23" name="__codelineno-190-23" href="#__codelineno-190-23"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-190-24" name="__codelineno-190-24" href="#__codelineno-190-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
|
||
<a id="__codelineno-190-25" name="__codelineno-190-25" href="#__codelineno-190-25"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
|
||
<a id="__codelineno-190-26" name="__codelineno-190-26" href="#__codelineno-190-26"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-190-27" name="__codelineno-190-27" href="#__codelineno-190-27"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
|
||
<a id="__codelineno-190-28" name="__codelineno-190-28" href="#__codelineno-190-28"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">worst_best_time_complexity.zig</span><pre><span></span><code><a id="__codelineno-191-1" name="__codelineno-191-1" href="#__codelineno-191-1"></a><span class="c1">// 生成一个数组，元素为 { 1, 2, ..., n }，顺序被打乱</span>
|
||
<a id="__codelineno-191-2" name="__codelineno-191-2" href="#__codelineno-191-2"></a><span class="kr">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">randomNumbers</span><span class="p">(</span><span class="kr">comptime</span><span class="w"> </span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-191-3" name="__codelineno-191-3" href="#__codelineno-191-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">nums</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">undefined</span><span class="p">;</span>
|
||
<a id="__codelineno-191-4" name="__codelineno-191-4" href="#__codelineno-191-4"></a><span class="w"> </span><span class="c1">// 生成数组 nums = { 1, 2, 3, ..., n }</span>
|
||
<a id="__codelineno-191-5" name="__codelineno-191-5" href="#__codelineno-191-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="o">|*</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-191-6" name="__codelineno-191-6" href="#__codelineno-191-6"></a><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="o">*</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">@intCast</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-191-7" name="__codelineno-191-7" href="#__codelineno-191-7"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-191-8" name="__codelineno-191-8" href="#__codelineno-191-8"></a><span class="w"> </span><span class="c1">// 随机打乱数组元素</span>
|
||
<a id="__codelineno-191-9" name="__codelineno-191-9" href="#__codelineno-191-9"></a><span class="w"> </span><span class="kr">const</span><span class="w"> </span><span class="n">rand</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">crypto</span><span class="p">.</span><span class="n">random</span><span class="p">;</span>
|
||
<a id="__codelineno-191-10" name="__codelineno-191-10" href="#__codelineno-191-10"></a><span class="w"> </span><span class="n">rand</span><span class="p">.</span><span class="n">shuffle</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="o">&</span><span class="n">nums</span><span class="p">);</span>
|
||
<a id="__codelineno-191-11" name="__codelineno-191-11" href="#__codelineno-191-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
|
||
<a id="__codelineno-191-12" name="__codelineno-191-12" href="#__codelineno-191-12"></a><span class="p">}</span>
|
||
<a id="__codelineno-191-13" name="__codelineno-191-13" href="#__codelineno-191-13"></a>
|
||
<a id="__codelineno-191-14" name="__codelineno-191-14" href="#__codelineno-191-14"></a><span class="c1">// 查找数组 nums 中数字 1 所在索引</span>
|
||
<a id="__codelineno-191-15" name="__codelineno-191-15" href="#__codelineno-191-15"></a><span class="kr">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">findOne</span><span class="p">(</span><span class="n">nums</span><span class="o">:</span><span class="w"> </span><span class="p">[]</span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-191-16" name="__codelineno-191-16" href="#__codelineno-191-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
|
||
<a id="__codelineno-191-17" name="__codelineno-191-17" href="#__codelineno-191-17"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组头部时，达到最佳时间复杂度 O(1)</span>
|
||
<a id="__codelineno-191-18" name="__codelineno-191-18" href="#__codelineno-191-18"></a><span class="w"> </span><span class="c1">// 当元素 1 在数组尾部时，达到最差时间复杂度 O(n)</span>
|
||
<a id="__codelineno-191-19" name="__codelineno-191-19" href="#__codelineno-191-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">@intCast</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
|
||
<a id="__codelineno-191-20" name="__codelineno-191-20" href="#__codelineno-191-20"></a><span class="w"> </span><span class="p">}</span>
|
||
<a id="__codelineno-191-21" name="__codelineno-191-21" href="#__codelineno-191-21"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
|
||
<a id="__codelineno-191-22" name="__codelineno-191-22" href="#__codelineno-191-22"></a><span class="p">}</span>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>值得说明的是，我们在实际中很少使用最佳时间复杂度，因为通常只有在很小概率下才能达到，可能会带来一定的误导性。<strong>而最差时间复杂度更为实用，因为它给出了一个效率安全值</strong>，让我们可以放心地使用算法。</p>
|
||
<p>从上述示例可以看出，最差或最佳时间复杂度只出现于“特殊的数据分布”，这些情况的出现概率可能很小，并不能真实地反映算法运行效率。相比之下，<strong>平均时间复杂度可以体现算法在随机输入数据下的运行效率</strong>，用 <span class="arithmatex">\(\Theta\)</span> 记号来表示。</p>
|
||
<p>对于部分算法，我们可以简单地推算出随机数据分布下的平均情况。比如上述示例，由于输入数组是被打乱的，因此元素 <span class="arithmatex">\(1\)</span> 出现在任意索引的概率都是相等的，那么算法的平均循环次数就是数组长度的一半 <span class="arithmatex">\(n / 2\)</span> ，平均时间复杂度为 <span class="arithmatex">\(\Theta(n / 2) = \Theta(n)\)</span> 。</p>
|
||
<p>但对于较为复杂的算法，计算平均时间复杂度往往是比较困难的，因为很难分析出在数据分布下的整体数学期望。在这种情况下，我们通常使用最差时间复杂度作为算法效率的评判标准。</p>
|
||
<div class="admonition question">
|
||
<p class="admonition-title">为什么很少看到 <span class="arithmatex">\(\Theta\)</span> 符号？</p>
|
||
<p>可能由于 <span class="arithmatex">\(O\)</span> 符号过于朗朗上口，我们常常使用它来表示平均时间复杂度。但从严格意义上看，这种做法并不规范。在本书和其他资料中，若遇到类似“平均时间复杂度 <span class="arithmatex">\(O(n)\)</span>”的表述，请将其直接理解为 <span class="arithmatex">\(\Theta(n)\)</span> 。</p>
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