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2.2. 时间复杂度
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0. 写在前面
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0. 写在前面
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0.1. 关于本书
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0.2. 如何使用本书
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1. 引言
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1. 引言
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1.1. 算法无处不在
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1.2. 算法是什么
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< li class = "md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_3" checked >
< label class = "md-nav__link" for = "__nav_3" id = "__nav_3_label" tabindex = "0" >
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2. 复杂度分析
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< label class = "md-nav__title" for = "__nav_3" >
< span class = "md-nav__icon md-icon" > < / span >
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2. 复杂度分析
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< / label >
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< li class = "md-nav__item" >
< a href = "../performance_evaluation/" class = "md-nav__link" >
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2.1. 算法效率评估
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< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
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2.2. 时间复杂度
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< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
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2.2. 时间复杂度
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< / a >
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< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#221" class = "md-nav__link" >
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2.2.1. 统计算法运行时间
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< a href = "#222" class = "md-nav__link" >
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2.2.2. 统计时间增长趋势
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< li class = "md-nav__item" >
< a href = "#223" class = "md-nav__link" >
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2.2.3. 函数渐近上界
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< a href = "#224" class = "md-nav__link" >
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2.2.4. 推算方法
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< / a >
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< nav class = "md-nav" aria-label = "2.2.4. 推算方法" >
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< a href = "#1" class = "md-nav__link" >
1) 统计操作数量
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< a href = "#2" class = "md-nav__link" >
2) 判断渐近上界
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< a href = "#225" class = "md-nav__link" >
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2.2.5. 常见类型
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< / a >
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< nav class = "md-nav" aria-label = "2.2.5. 常见类型" >
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< a href = "#o1" class = "md-nav__link" >
常数阶 \(O(1)\)
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< a href = "#on" class = "md-nav__link" >
线性阶 \(O(n)\)
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< a href = "#on2" class = "md-nav__link" >
平方阶 \(O(n^2)\)
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< a href = "#o2n" class = "md-nav__link" >
指数阶 \(O(2^n)\)
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< a href = "#olog-n" class = "md-nav__link" >
对数阶 \(O(\log n)\)
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< a href = "#on-log-n" class = "md-nav__link" >
线性对数阶 \(O(n \log n)\)
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< a href = "#on_1" class = "md-nav__link" >
阶乘阶 \(O(n!)\)
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< a href = "#226" class = "md-nav__link" >
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2.2.6. 最差、最佳、平均时间复杂度
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< li class = "md-nav__item" >
< a href = "../space_complexity/" class = "md-nav__link" >
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2.3. 空间复杂度
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< li class = "md-nav__item" >
< a href = "../space_time_tradeoff/" class = "md-nav__link" >
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2.4. 权衡时间与空间
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< li class = "md-nav__item" >
< a href = "../summary/" class = "md-nav__link" >
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2.5. 小结
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< label class = "md-nav__link" for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
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3. 数据结构简介
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< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
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3. 数据结构简介
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< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/data_and_memory/" class = "md-nav__link" >
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3.1. 数据与内存
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< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/classification_of_data_structure/" class = "md-nav__link" >
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3.2. 数据结构分类
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< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
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3.3. 小结
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< label class = "md-nav__link" for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
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4. 数组与链表
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< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
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4. 数组与链表
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
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4.1. 数组
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
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4.2. 链表
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
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4.3. 列表
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
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4.4. 小结
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< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_6" >
< label class = "md-nav__link" for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
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5. 栈与队列
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< label class = "md-nav__title" for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
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5. 栈与队列
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
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5.1. 栈
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
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5.2. 队列
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
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5.3. 双向队列
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
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5.4. 小结
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< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
< label class = "md-nav__link" for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
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6. 散列表
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_7_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
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6. 散列表
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
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6.1. 哈希表
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
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6.2. 哈希冲突处理
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
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6.3. 小结
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< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
< label class = "md-nav__link" for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
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7. 树
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
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7. 树
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
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7.1. 二叉树
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
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7.2. 二叉树遍历
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
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7.3. 二叉搜索树
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
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7.4. AVL 树 *
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
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7.5. 小结
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< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
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< label class = "md-nav__link" for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
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8. 堆
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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 >
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8. 堆
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
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8.1. 堆
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
8.2. 建堆操作 *
< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
8.3. 小结
< / a >
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< / ul >
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< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
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< label class = "md-nav__link" for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
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9. 图
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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 >
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9. 图
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
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9.1. 图
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
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9.2. 图基础操作
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
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9.3. 图的遍历
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< / a >
< / li >
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< li class = "md-nav__item" >
< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
9.4. 小结
< / a >
< / li >
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< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
< label class = "md-nav__link" for = "__nav_11" id = "__nav_11_label" tabindex = "0" >
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10. 查找算法
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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 >
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10. 查找算法
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/linear_search/" class = "md-nav__link" >
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10.1. 线性查找
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
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10.2. 二分查找
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/hashing_search/" class = "md-nav__link" >
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10.3. 哈希查找
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< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
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10.4. 小结
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< / a >
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< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
< label class = "md-nav__link" for = "__nav_12" id = "__nav_12_label" tabindex = "0" >
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11. 排序算法
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< span class = "md-nav__icon md-icon" > < / span >
< / label >
< 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 >
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11. 排序算法
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/intro_to_sort/" class = "md-nav__link" >
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11.1. 排序简介
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/bubble_sort/" class = "md-nav__link" >
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11.2. 冒泡排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/insertion_sort/" class = "md-nav__link" >
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11.3. 插入排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/quick_sort/" class = "md-nav__link" >
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11.4. 快速排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/merge_sort/" class = "md-nav__link" >
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11.5. 归并排序
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_sorting/summary/" class = "md-nav__link" >
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11.6. 小结
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< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
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< label class = "md-nav__link" for = "__nav_13" id = "__nav_13_label" tabindex = "0" >
12. 附录
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
12. 附录
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/installation/" class = "md-nav__link" >
12.1. 编程环境安装
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_appendix/contribution/" class = "md-nav__link" >
12.2. 一起参与创作
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_14" >
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< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_reference/" > 参考文献< / a >
< / div >
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< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_14_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_14" >
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< span class = "md-nav__icon md-icon" > < / span >
参考文献
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< / ul >
< / nav >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-sidebar md-sidebar--secondary" data-md-component = "sidebar" data-md-type = "toc" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#221" class = "md-nav__link" >
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2.2.1. 统计算法运行时间
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#222" class = "md-nav__link" >
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2.2.2. 统计时间增长趋势
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#223" class = "md-nav__link" >
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2.2.3. 函数渐近上界
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< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#224" class = "md-nav__link" >
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2.2.4. 推算方法
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< / a >
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< nav class = "md-nav" aria-label = "2.2.4. 推算方法" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#1" class = "md-nav__link" >
1) 统计操作数量
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#2" class = "md-nav__link" >
2) 判断渐近上界
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#225" class = "md-nav__link" >
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2.2.5. 常见类型
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< / a >
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< nav class = "md-nav" aria-label = "2.2.5. 常见类型" >
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< ul class = "md-nav__list" >
< li class = "md-nav__item" >
< a href = "#o1" class = "md-nav__link" >
常数阶 \(O(1)\)
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#on" class = "md-nav__link" >
线性阶 \(O(n)\)
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#on2" class = "md-nav__link" >
平方阶 \(O(n^2)\)
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#o2n" class = "md-nav__link" >
指数阶 \(O(2^n)\)
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#olog-n" class = "md-nav__link" >
对数阶 \(O(\log n)\)
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#on-log-n" class = "md-nav__link" >
线性对数阶 \(O(n \log n)\)
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#on_1" class = "md-nav__link" >
阶乘阶 \(O(n!)\)
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "#226" class = "md-nav__link" >
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2.2.6. 最差、最佳、平均时间复杂度
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< / a >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-content" data-md-component = "content" >
< article class = "md-content__inner md-typeset" >
< 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" >
< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z" / > < / svg >
< / a >
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< h1 id = "22" > 2.2. 时间复杂度< a class = "headerlink" href = "#22" title = "Permanent link" > ¶ < / a > < / h1 >
< h2 id = "221" > 2.2.1. 统计算法运行时间< a class = "headerlink" href = "#221" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 运行时间能够直观且准确地体现出算法的效率水平。如果我们想要 < strong > 准确预估一段代码的运行时间< / strong > ，该如何做呢？< / p >
< ol >
< li > 首先需要 < strong > 确定运行平台< / strong > ，包括硬件配置、编程语言、系统环境等，这些都会影响到代码的运行效率。< / li >
< li > 评估 < strong > 各种计算操作的所需运行时间< / strong > ，例如加法操作 < code > +< / code > 需要 1 ns ，乘法操作 < code > *< / code > 需要 10 ns ，打印操作需要 5 ns 等。< / li >
< li > 根据代码 < strong > 统计所有计算操作的数量< / strong > ，并将所有操作的执行时间求和，即可得到运行时间。< / li >
< / ol >
< p > 例如以下代码，输入数据大小为 < span class = "arithmatex" > \(n\)< / span > ，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 >
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:10" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > Java< / label > < label for = "__tabbed_1_2" > C++< / label > < label for = "__tabbed_1_3" > Python< / label > < label for = "__tabbed_1_4" > Go< / label > < label for = "__tabbed_1_5" > JavaScript< / label > < label for = "__tabbed_1_6" > TypeScript< / label > < label for = "__tabbed_1_7" > C< / label > < label for = "__tabbed_1_8" > C#< / label > < label for = "__tabbed_1_9" > Swift< / label > < label for = "__tabbed_1_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< 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 = "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-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / 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-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / 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-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / 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-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / 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-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / 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-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "p" > }< / 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 = "k" > def< / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "n" > a< / span > < span class = "o" > =< / span > < span class = "mi" > 2< / span > < span class = "c1" > # 1 ns< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / 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-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / 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-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "c1" > # 循环 n 次< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / 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-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / 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-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 = "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-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / 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-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / 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-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / 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-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 = "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-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / 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-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" > 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-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / 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-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 = "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-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 = "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-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 = "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-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / 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-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" > 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-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / 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-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / 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-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / 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-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / 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-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / 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-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "w" > < / span > < 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 = "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-6-3" name = "__codelineno-6-3" href = "#__codelineno-6-3" > < / 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-6-4" name = "__codelineno-6-4" href = "#__codelineno-6-4" > < / 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-6-5" name = "__codelineno-6-5" href = "#__codelineno-6-5" > < / 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-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 = "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-6-8" name = "__codelineno-6-8" href = "#__codelineno-6-8" > < / 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-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 = "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 >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / 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-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 1 ns< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / 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-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / 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-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < 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-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / 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-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / 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 >
2023-03-03 21:53:57 +08:00
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / 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-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / 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-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / 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-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / 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-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / 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-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < 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 >
< / code > < / pre > < / div >
< / div >
< / div >
< / 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，我们不希望预估时间和运行平台绑定，毕竟算法需要跑在各式各样的平台之上。其次，我们很难获知每一种操作的运行时间，这为预估过程带来了极大的难度。< / p >
2023-02-24 18:46:22 +08:00
< h2 id = "222" > 2.2.2. 统计时间增长趋势< a class = "headerlink" href = "#222" title = "Permanent link" > ¶ < / a > < / h2 >
2023-02-08 14:54:41 +08:00
< p > 「时间复杂度分析」采取了不同的做法，其统计的不是算法运行时间，而是 < strong > 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，我们借助一个例子来理解。设输入数据大小为 < span class = "arithmatex" > \(n\)< / span > ，给定三个算法 < code > A< / code > , < code > B< / code > , < code > C< / code > 。< / 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 > 增大成线性增长。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，但运行时间仍与输入数据大小 < 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 >
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:10" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Java< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Python< / label > < label for = "__tabbed_2_4" > Go< / label > < label for = "__tabbed_2_5" > JavaScript< / label > < label for = "__tabbed_2_6" > TypeScript< / label > < label for = "__tabbed_2_7" > C< / label > < label for = "__tabbed_2_8" > C#< / label > < label for = "__tabbed_2_9" > Swift< / label > < label for = "__tabbed_2_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< 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" > // 算法 A 时间复杂度：常数阶< / 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_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-10-3" name = "__codelineno-10-3" href = "#__codelineno-10-3" > < / 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-10-4" name = "__codelineno-10-4" href = "#__codelineno-10-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-10-5" name = "__codelineno-10-5" href = "#__codelineno-10-5" > < / a > < span class = "c1" > // 算法 B 时间复杂度：线性阶< / span >
< a id = "__codelineno-10-6" name = "__codelineno-10-6" href = "#__codelineno-10-6" > < / 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-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 >
< a id = "__codelineno-10-8" name = "__codelineno-10-8" href = "#__codelineno-10-8" > < / 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-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 >
< a id = "__codelineno-10-11" name = "__codelineno-10-11" href = "#__codelineno-10-11" > < / a > < span class = "c1" > // 算法 C 时间复杂度：常数阶< / span >
< a id = "__codelineno-10-12" name = "__codelineno-10-12" href = "#__codelineno-10-12" > < / 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-10-13" name = "__codelineno-10-13" href = "#__codelineno-10-13" > < / 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-10-14" name = "__codelineno-10-14" href = "#__codelineno-10-14" > < / 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-10-15" name = "__codelineno-10-15" href = "#__codelineno-10-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-10-16" name = "__codelineno-10-16" href = "#__codelineno-10-16" > < / 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 > < span class = "c1" > // 算法 A 时间复杂度：常数阶< / span >
< a id = "__codelineno-11-2" name = "__codelineno-11-2" href = "#__codelineno-11-2" > < / 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-11-3" name = "__codelineno-11-3" href = "#__codelineno-11-3" > < / 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-11-4" name = "__codelineno-11-4" href = "#__codelineno-11-4" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-11-5" name = "__codelineno-11-5" href = "#__codelineno-11-5" > < / a > < span class = "c1" > // 算法 B 时间复杂度：线性阶< / span >
< a id = "__codelineno-11-6" name = "__codelineno-11-6" href = "#__codelineno-11-6" > < / 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-11-7" name = "__codelineno-11-7" href = "#__codelineno-11-7" > < / 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-11-8" name = "__codelineno-11-8" href = "#__codelineno-11-8" > < / 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-11-9" name = "__codelineno-11-9" href = "#__codelineno-11-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-10" name = "__codelineno-11-10" href = "#__codelineno-11-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-11-11" name = "__codelineno-11-11" href = "#__codelineno-11-11" > < / a > < span class = "c1" > // 算法 C 时间复杂度：常数阶< / span >
< a id = "__codelineno-11-12" name = "__codelineno-11-12" href = "#__codelineno-11-12" > < / 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-11-13" name = "__codelineno-11-13" href = "#__codelineno-11-13" > < / 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-11-14" name = "__codelineno-11-14" href = "#__codelineno-11-14" > < / 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-11-15" name = "__codelineno-11-15" href = "#__codelineno-11-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-11-16" name = "__codelineno-11-16" href = "#__codelineno-11-16" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< 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 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 >
< 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 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 >
< 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 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 >
< 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 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 = "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-13-3" name = "__codelineno-13-3" href = "#__codelineno-13-3" > < / 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-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 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 = "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-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 = "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-13-8" name = "__codelineno-13-8" href = "#__codelineno-13-8" > < / 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-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 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 = "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-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 = "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-13-14" name = "__codelineno-13-14" href = "#__codelineno-13-14" > < / 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-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 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 = "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-14-3" name = "__codelineno-14-3" href = "#__codelineno-14-3" > < / 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-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 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 = "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-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 = "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-14-8" name = "__codelineno-14-8" href = "#__codelineno-14-8" > < / 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-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 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 = "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-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 = "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-14-14" name = "__codelineno-14-14" href = "#__codelineno-14-14" > < / 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-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 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 = "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-15-3" name = "__codelineno-15-3" href = "#__codelineno-15-3" > < / 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-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 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 = "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-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 = "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-15-8" name = "__codelineno-15-8" href = "#__codelineno-15-8" > < / 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-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 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 = "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-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 = "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-15-14" name = "__codelineno-15-14" href = "#__codelineno-15-14" > < / 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-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 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 = "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-16-3" name = "__codelineno-16-3" href = "#__codelineno-16-3" > < / 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-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 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 = "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-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 = "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-16-8" name = "__codelineno-16-8" href = "#__codelineno-16-8" > < / 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-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 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 = "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-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 = "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-16-14" name = "__codelineno-16-14" href = "#__codelineno-16-14" > < / 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-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 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 = "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 >
< a id = "__codelineno-17-3" name = "__codelineno-17-3" href = "#__codelineno-17-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-17-4" name = "__codelineno-17-4" href = "#__codelineno-17-4" > < / 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-17-5" name = "__codelineno-17-5" href = "#__codelineno-17-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-6" name = "__codelineno-17-6" href = "#__codelineno-17-6" > < / a > < span class = "c1" > // 算法 B 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 = "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 >
< a id = "__codelineno-17-8" name = "__codelineno-17-8" href = "#__codelineno-17-8" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-17-9" name = "__codelineno-17-9" href = "#__codelineno-17-9" > < / 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 = "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-17-10" name = "__codelineno-17-10" href = "#__codelineno-17-10" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-17-11" name = "__codelineno-17-11" href = "#__codelineno-17-11" > < / 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-17-12" name = "__codelineno-17-12" href = "#__codelineno-17-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-17-13" name = "__codelineno-17-13" href = "#__codelineno-17-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-17-14" name = "__codelineno-17-14" href = "#__codelineno-17-14" > < / a > < span class = "c1" > // 算法 C 时间复杂度：常数阶< / span >
< a id = "__codelineno-17-15" name = "__codelineno-17-15" href = "#__codelineno-17-15" > < / 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 >
< a id = "__codelineno-17-16" name = "__codelineno-17-16" href = "#__codelineno-17-16" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-17-17" name = "__codelineno-17-17" href = "#__codelineno-17-17" > < / 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 = "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 >
< a id = "__codelineno-17-18" name = "__codelineno-17-18" href = "#__codelineno-17-18" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-17-19" name = "__codelineno-17-19" href = "#__codelineno-17-19" > < / 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-17-20" name = "__codelineno-17-20" href = "#__codelineno-17-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-17-21" name = "__codelineno-17-21" href = "#__codelineno-17-21" > < / 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 时间复杂度：常数阶< / span >
2023-03-03 21:53:57 +08:00
< a id = "__codelineno-18-2" name = "__codelineno-18-2" href = "#__codelineno-18-2" > < / 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 >
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< a id = "__codelineno-18-3" name = "__codelineno-18-3" href = "#__codelineno-18-3" > < / a > < span class = "bp" > print< / span > < span class = "p" > (< / span > < span class = "mi" > 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 >
< a id = "__codelineno-18-6" name = "__codelineno-18-6" href = "#__codelineno-18-6" > < / a > < span class = "c1" > // 算法 B 时间复杂度：线性阶< / span >
2023-03-03 21:53:57 +08:00
< a id = "__codelineno-18-7" name = "__codelineno-18-7" href = "#__codelineno-18-7" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-18-8" name = "__codelineno-18-8" href = "#__codelineno-18-8" > < / 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-18-9" name = "__codelineno-18-9" href = "#__codelineno-18-9" > < / a > < span class = "bp" > print< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / 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 = "p" > }< / span >
< a id = "__codelineno-18-12" name = "__codelineno-18-12" href = "#__codelineno-18-12" > < / a >
< a id = "__codelineno-18-13" name = "__codelineno-18-13" href = "#__codelineno-18-13" > < / a > < span class = "c1" > // 算法 C 时间复杂度：常数阶< / span >
2023-03-03 21:53:57 +08:00
< a id = "__codelineno-18-14" name = "__codelineno-18-14" href = "#__codelineno-18-14" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-18-15" name = "__codelineno-18-15" href = "#__codelineno-18-15" > < / 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-18-16" name = "__codelineno-18-16" href = "#__codelineno-18-16" > < / a > < span class = "bp" > print< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-18-17" name = "__codelineno-18-17" href = "#__codelineno-18-17" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-18-18" name = "__codelineno-18-18" href = "#__codelineno-18-18" > < / 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 >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-02-26 18:18:03 +08:00
< p > < img alt = "算法 A, B, C 的时间增长趋势" src = "../time_complexity.assets/time_complexity_simple_example.png" / > < / p >
2023-02-26 19:53:32 +08:00
< p align = "center" > Fig. 算法 A, B, C 的时间增长趋势 < / p >
2023-02-08 14:54:41 +08:00
< p > 相比直接统计算法运行时间，时间复杂度分析的做法有什么好处呢？以及有什么不足？< / p >
< p > < strong > 时间复杂度可以有效评估算法效率< / strong > 。算法 < code > B< / code > 运行时间的增长是线性的，在 < span class = "arithmatex" > \(n > 1\)< / span > 时慢于算法 < code > A< / code > ，在 < span class = "arithmatex" > \(n > 1000000\)< / span > 时慢于算法 < code > C< / code > 。实质上，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，这也正是时间增长趋势的含义。< / p >
< p > < strong > 时间复杂度的推算方法更加简便< / strong > 。在时间复杂度分析中，我们可以将统计「计算操作的运行时间」简化为统计「计算操作的数量」，这是因为，无论是运行平台还是计算操作类型，都与算法运行时间的增长趋势无关。因而，我们可以简单地将所有计算操作的执行时间统一看作是相同的“单位时间”，这样的简化做法大大降低了估算难度。< / p >
2023-02-27 03:45:08 +08:00
< p > < strong > 时间复杂度也存在一定的局限性< / strong > 。比如，虽然算法 < code > A< / code > 和 < code > C< / code > 的时间复杂度相同，但是实际的运行时间有非常大的差别。再比如，虽然算法 < code > B< / code > 比 < code > C< / code > 的时间复杂度要更高，但在输入数据大小 < span class = "arithmatex" > \(n\)< / span > 比较小时，算法 < code > B< / code > 是要明显优于算法 < code > C< / code > 的。对于以上情况，我们很难仅凭时间复杂度来判定算法效率高低。然而，即使存在这些问题，复杂度分析仍然是评判算法效率的最有效且常用的方法。< / p >
2023-02-24 18:46:22 +08:00
< h2 id = "223" > 2.2.3. 函数渐近上界< a class = "headerlink" href = "#223" title = "Permanent link" > ¶ < / a > < / h2 >
2023-02-08 14:54:41 +08:00
< p > 设算法「计算操作数量」为 < span class = "arithmatex" > \(T(n)\)< / span > ，其是一个关于输入数据大小 < span class = "arithmatex" > \(n\)< / span > 的函数。例如，以下算法的操作数量为< / p >
< div class = "arithmatex" > \[
T(n) = 3 + 2n
\]< / div >
< div class = "tabbed-set tabbed-alternate" data-tabs = "3:10" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_3_1" > Java< / label > < label for = "__tabbed_3_2" > C++< / label > < label for = "__tabbed_3_3" > Python< / label > < label for = "__tabbed_3_4" > Go< / label > < label for = "__tabbed_3_5" > JavaScript< / label > < label for = "__tabbed_3_6" > TypeScript< / label > < label for = "__tabbed_3_7" > C< / label > < label for = "__tabbed_3_8" > C#< / label > < label for = "__tabbed_3_9" > Swift< / label > < label for = "__tabbed_3_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< 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 = "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-20-2" name = "__codelineno-20-2" href = "#__codelineno-20-2" > < / 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-20-3" name = "__codelineno-20-3" href = "#__codelineno-20-3" > < / 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-20-4" name = "__codelineno-20-4" href = "#__codelineno-20-4" > < / 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-20-5" name = "__codelineno-20-5" href = "#__codelineno-20-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-20-6" name = "__codelineno-20-6" href = "#__codelineno-20-6" > < / 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（ ） < / span >
< a id = "__codelineno-20-7" name = "__codelineno-20-7" href = "#__codelineno-20-7" > < / 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-20-8" name = "__codelineno-20-8" href = "#__codelineno-20-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-20-9" name = "__codelineno-20-9" href = "#__codelineno-20-9" > < / 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 = "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-21-2" name = "__codelineno-21-2" href = "#__codelineno-21-2" > < / 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-21-3" name = "__codelineno-21-3" href = "#__codelineno-21-3" > < / 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-21-4" name = "__codelineno-21-4" href = "#__codelineno-21-4" > < / 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-21-5" name = "__codelineno-21-5" href = "#__codelineno-21-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-21-6" name = "__codelineno-21-6" href = "#__codelineno-21-6" > < / 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（ ） < / span >
< a id = "__codelineno-21-7" name = "__codelineno-21-7" href = "#__codelineno-21-7" > < / 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-21-8" name = "__codelineno-21-8" href = "#__codelineno-21-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-21-9" name = "__codelineno-21-9" href = "#__codelineno-21-9" > < / 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 = "k" > def< / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-22-2" name = "__codelineno-22-2" href = "#__codelineno-22-2" > < / a > < span class = "n" > a< / span > < span class = "o" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > # +1< / span >
< a id = "__codelineno-22-3" name = "__codelineno-22-3" href = "#__codelineno-22-3" > < / 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-22-4" name = "__codelineno-22-4" href = "#__codelineno-22-4" > < / 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-22-5" name = "__codelineno-22-5" href = "#__codelineno-22-5" > < / a > < span class = "c1" > # 循环 n 次< / span >
< a id = "__codelineno-22-6" name = "__codelineno-22-6" href = "#__codelineno-22-6" > < / 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-22-7" name = "__codelineno-22-7" href = "#__codelineno-22-7" > < / 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-23-1" name = "__codelineno-23-1" href = "#__codelineno-23-1" > < / 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-23-2" name = "__codelineno-23-2" href = "#__codelineno-23-2" > < / 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-23-3" name = "__codelineno-23-3" href = "#__codelineno-23-3" > < / 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-23-4" name = "__codelineno-23-4" href = "#__codelineno-23-4" > < / 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-23-5" name = "__codelineno-23-5" href = "#__codelineno-23-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-23-6" name = "__codelineno-23-6" href = "#__codelineno-23-6" > < / 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-23-7" name = "__codelineno-23-7" href = "#__codelineno-23-7" > < / 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-23-8" name = "__codelineno-23-8" href = "#__codelineno-23-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-23-9" name = "__codelineno-23-9" href = "#__codelineno-23-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-01 03:16:54 +08:00
< div class = "highlight" > < pre > < span > < / span > < code > < a id = "__codelineno-24-1" name = "__codelineno-24-1" href = "#__codelineno-24-1" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-24-2" name = "__codelineno-24-2" href = "#__codelineno-24-2" > < / 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-24-3" name = "__codelineno-24-3" href = "#__codelineno-24-3" > < / 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-24-4" name = "__codelineno-24-4" href = "#__codelineno-24-4" > < / 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-24-5" name = "__codelineno-24-5" href = "#__codelineno-24-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-24-6" name = "__codelineno-24-6" href = "#__codelineno-24-6" > < / 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（ ） < / span >
< a id = "__codelineno-24-7" name = "__codelineno-24-7" href = "#__codelineno-24-7" > < / 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-24-8" name = "__codelineno-24-8" href = "#__codelineno-24-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
2023-03-01 03:16:54 +08:00
< a id = "__codelineno-24-9" name = "__codelineno-24-9" href = "#__codelineno-24-9" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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 = "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-25-2" name = "__codelineno-25-2" href = "#__codelineno-25-2" > < / 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-25-3" name = "__codelineno-25-3" href = "#__codelineno-25-3" > < / 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-25-4" name = "__codelineno-25-4" href = "#__codelineno-25-4" > < / 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-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 = "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（ ） < / span >
< a id = "__codelineno-25-7" name = "__codelineno-25-7" href = "#__codelineno-25-7" > < / 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-25-8" name = "__codelineno-25-8" href = "#__codelineno-25-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
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< a id = "__codelineno-25-9" name = "__codelineno-25-9" href = "#__codelineno-25-9" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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（ ） < / span >
< a id = "__codelineno-26-7" name = "__codelineno-26-7" href = "#__codelineno-26-7" > < / 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-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 > < span class = "w" > < / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-01 03:16:54 +08:00
< 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 >
< a id = "__codelineno-27-2" name = "__codelineno-27-2" href = "#__codelineno-27-2" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-27-3" name = "__codelineno-27-3" href = "#__codelineno-27-3" > < / 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" > 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" > 1< / 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 = "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-27-6" name = "__codelineno-27-6" href = "#__codelineno-27-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-27-7" name = "__codelineno-27-7" href = "#__codelineno-27-7" > < / 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 = "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 = "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-27-10" name = "__codelineno-27-10" href = "#__codelineno-27-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-27-11" name = "__codelineno-27-11" href = "#__codelineno-27-11" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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 = "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-28-2" name = "__codelineno-28-2" href = "#__codelineno-28-2" > < / 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-28-3" name = "__codelineno-28-3" href = "#__codelineno-28-3" > < / 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-28-4" name = "__codelineno-28-4" href = "#__codelineno-28-4" > < / 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-28-5" name = "__codelineno-28-5" href = "#__codelineno-28-5" > < / a > < span class = "c1" > // 循环 n 次< / span >
< a id = "__codelineno-28-6" name = "__codelineno-28-6" href = "#__codelineno-28-6" > < / 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-28-7" name = "__codelineno-28-7" href = "#__codelineno-28-7" > < / 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-28-8" name = "__codelineno-28-8" href = "#__codelineno-28-8" > < / a > < 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 >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > < span class = "arithmatex" > \(T(n)\)< / span > 是个一次函数，说明时间增长趋势是线性的，因此易得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 > ，这个数学符号被称为「大 < span class = "arithmatex" > \(O\)< / span > 记号 Big-< span class = "arithmatex" > \(O\)< / span > Notation」， < span class = "arithmatex" > \(T(n)\)< / span > 的「渐近上界 asymptotic upper bound」。< / p >
< p > 我们要推算时间复杂度，本质上是在计算「操作数量函数 < span class = "arithmatex" > \(T(n)\)< / span > 」的渐近上界。下面我们先来看看函数渐近上界的数学定义。< / 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
$$
T(n) \leq c \cdot f(n)
$$
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
$$
T(n) = O(f(n))
$$< / p >
< / div >
2023-02-26 18:18:03 +08:00
< p > < img alt = "函数的渐近上界" src = "../time_complexity.assets/asymptotic_upper_bound.png" / > < / p >
2023-02-26 19:53:32 +08:00
< p align = "center" > Fig. 函数的渐近上界 < / p >
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< p > 本质上看，计算渐近上界就是在找一个函数 < span class = "arithmatex" > \(f(n)\)< / span > ， < strong > 使得在 < 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）< / strong > 。< / p >
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > 渐近上界的数学味儿有点重，如果你感觉没有完全理解，无需担心，因为在实际使用中我们只需要会推算即可，数学意义可以慢慢领悟。< / p >
< / div >
2023-02-24 18:46:22 +08:00
< h2 id = "224" > 2.2.4. 推算方法< a class = "headerlink" href = "#224" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 推算出 < span class = "arithmatex" > \(f(n)\)< / span > 后，我们就得到时间复杂度 < span class = "arithmatex" > \(O(f(n))\)< / span > 。那么，如何来确定渐近上界 < 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) 统计操作数量< a class = "headerlink" href = "#1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 对着代码，从上到下一行一行地计数即可。然而，< strong > 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，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偷懒技巧：< / p >
< ol >
< li > < strong > 跳过数量与 < span class = "arithmatex" > \(n\)< / span > 无关的操作< / strong > 。因为他们都是 < span class = "arithmatex" > \(T(n)\)< / span > 中的常数项，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、……，都可以化简记为 < span class = "arithmatex" > \(n\)< / span > 次，因为 < span class = "arithmatex" > \(n\)< / span > 前面的系数对时间复杂度也不产生影响。< / 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上述 < code > 1.< / code > 和 < code > 2.< / code > 技巧。< / li >
< / ol >
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< p > 以下示例展示了使用上述技巧前、后的统计结果。< / p >
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< 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 >
< p > 最终，两者都能推出相同的时间复杂度结果，即 < span class = "arithmatex" > \(O(n^2)\)< / span > 。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "4:10" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_4_1" > Java< / label > < label for = "__tabbed_4_2" > C++< / label > < label for = "__tabbed_4_3" > Python< / label > < label for = "__tabbed_4_4" > Go< / label > < label for = "__tabbed_4_5" > JavaScript< / label > < label for = "__tabbed_4_6" > TypeScript< / label > < label for = "__tabbed_4_7" > C< / label > < label for = "__tabbed_4_8" > C#< / label > < label for = "__tabbed_4_9" > Swift< / label > < label for = "__tabbed_4_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< 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 = "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-30-2" name = "__codelineno-30-2" href = "#__codelineno-30-2" > < / 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（ ） < / span >
< a id = "__codelineno-30-3" name = "__codelineno-30-3" href = "#__codelineno-30-3" > < / 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（ ） < / span >
< a id = "__codelineno-30-4" name = "__codelineno-30-4" href = "#__codelineno-30-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n（ ） < / span >
< a id = "__codelineno-30-5" name = "__codelineno-30-5" href = "#__codelineno-30-5" > < / 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-30-6" name = "__codelineno-30-6" href = "#__codelineno-30-6" > < / 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-30-7" name = "__codelineno-30-7" href = "#__codelineno-30-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-8" name = "__codelineno-30-8" href = "#__codelineno-30-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n*n（ ） < / span >
< a id = "__codelineno-30-9" name = "__codelineno-30-9" href = "#__codelineno-30-9" > < / 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-30-10" name = "__codelineno-30-10" href = "#__codelineno-30-10" > < / 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-30-11" name = "__codelineno-30-11" href = "#__codelineno-30-11" > < / 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-30-12" name = "__codelineno-30-12" href = "#__codelineno-30-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-13" name = "__codelineno-30-13" href = "#__codelineno-30-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-30-14" name = "__codelineno-30-14" href = "#__codelineno-30-14" > < / 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 = "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-31-2" name = "__codelineno-31-2" href = "#__codelineno-31-2" > < / 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（ ） < / span >
< a id = "__codelineno-31-3" name = "__codelineno-31-3" href = "#__codelineno-31-3" > < / 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（ ） < / span >
< a id = "__codelineno-31-4" name = "__codelineno-31-4" href = "#__codelineno-31-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n（ ） < / span >
< a id = "__codelineno-31-5" name = "__codelineno-31-5" href = "#__codelineno-31-5" > < / 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-31-6" name = "__codelineno-31-6" href = "#__codelineno-31-6" > < / 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-31-7" name = "__codelineno-31-7" href = "#__codelineno-31-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-8" name = "__codelineno-31-8" href = "#__codelineno-31-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n*n（ ） < / span >
< a id = "__codelineno-31-9" name = "__codelineno-31-9" href = "#__codelineno-31-9" > < / 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-31-10" name = "__codelineno-31-10" href = "#__codelineno-31-10" > < / 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-31-11" name = "__codelineno-31-11" href = "#__codelineno-31-11" > < / 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-31-12" name = "__codelineno-31-12" href = "#__codelineno-31-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-13" name = "__codelineno-31-13" href = "#__codelineno-31-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-31-14" name = "__codelineno-31-14" href = "#__codelineno-31-14" > < / 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 = "k" > def< / span > < span class = "nf" > algorithm< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-32-2" name = "__codelineno-32-2" href = "#__codelineno-32-2" > < / a > < span class = "n" > a< / span > < span class = "o" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > # +0（ ） < / span >
< a id = "__codelineno-32-3" name = "__codelineno-32-3" href = "#__codelineno-32-3" > < / 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（ ） < / span >
< a id = "__codelineno-32-4" name = "__codelineno-32-4" href = "#__codelineno-32-4" > < / a > < span class = "c1" > # +n（ ） < / span >
< a id = "__codelineno-32-5" name = "__codelineno-32-5" href = "#__codelineno-32-5" > < / 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-32-6" name = "__codelineno-32-6" href = "#__codelineno-32-6" > < / a > < span class = "nb" > print< / span > < span class = "p" > (< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-32-7" name = "__codelineno-32-7" href = "#__codelineno-32-7" > < / a > < span class = "c1" > # +n*n（ ） < / span >
< a id = "__codelineno-32-8" name = "__codelineno-32-8" href = "#__codelineno-32-8" > < / 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-32-9" name = "__codelineno-32-9" href = "#__codelineno-32-9" > < / 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-32-10" name = "__codelineno-32-10" href = "#__codelineno-32-10" > < / 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-33-1" name = "__codelineno-33-1" href = "#__codelineno-33-1" > < / 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-33-2" name = "__codelineno-33-2" href = "#__codelineno-33-2" > < / 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（ ） < / span >
< a id = "__codelineno-33-3" name = "__codelineno-33-3" href = "#__codelineno-33-3" > < / 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（ ） < / span >
< a id = "__codelineno-33-4" name = "__codelineno-33-4" href = "#__codelineno-33-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n（ ） < / span >
< a id = "__codelineno-33-5" name = "__codelineno-33-5" href = "#__codelineno-33-5" > < / 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-33-6" name = "__codelineno-33-6" href = "#__codelineno-33-6" > < / 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-33-7" name = "__codelineno-33-7" href = "#__codelineno-33-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-8" name = "__codelineno-33-8" href = "#__codelineno-33-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n*n（ ） < / span >
< a id = "__codelineno-33-9" name = "__codelineno-33-9" href = "#__codelineno-33-9" > < / 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-33-10" name = "__codelineno-33-10" href = "#__codelineno-33-10" > < / 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-33-11" name = "__codelineno-33-11" href = "#__codelineno-33-11" > < / 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-33-12" name = "__codelineno-33-12" href = "#__codelineno-33-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-13" name = "__codelineno-33-13" href = "#__codelineno-33-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-33-14" name = "__codelineno-33-14" href = "#__codelineno-33-14" > < / 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 = "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-34-2" name = "__codelineno-34-2" href = "#__codelineno-34-2" > < / 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（ ） < / span >
< a id = "__codelineno-34-3" name = "__codelineno-34-3" href = "#__codelineno-34-3" > < / 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（ ） < / span >
< a id = "__codelineno-34-4" name = "__codelineno-34-4" href = "#__codelineno-34-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n（ ） < / span >
< a id = "__codelineno-34-5" name = "__codelineno-34-5" href = "#__codelineno-34-5" > < / 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-34-6" name = "__codelineno-34-6" href = "#__codelineno-34-6" > < / 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-34-7" name = "__codelineno-34-7" href = "#__codelineno-34-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-8" name = "__codelineno-34-8" href = "#__codelineno-34-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n*n（ ） < / span >
< a id = "__codelineno-34-9" name = "__codelineno-34-9" href = "#__codelineno-34-9" > < / 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-34-10" name = "__codelineno-34-10" href = "#__codelineno-34-10" > < / 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-34-11" name = "__codelineno-34-11" href = "#__codelineno-34-11" > < / 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-34-12" name = "__codelineno-34-12" href = "#__codelineno-34-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-13" name = "__codelineno-34-13" href = "#__codelineno-34-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-34-14" name = "__codelineno-34-14" href = "#__codelineno-34-14" > < / a > < span class = "p" > }< / 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 > < 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-35-2" name = "__codelineno-35-2" href = "#__codelineno-35-2" > < / 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（ ） < / span >
< a id = "__codelineno-35-3" name = "__codelineno-35-3" href = "#__codelineno-35-3" > < / 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（ ） < / span >
< a id = "__codelineno-35-4" name = "__codelineno-35-4" href = "#__codelineno-35-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n（ ） < / span >
< a id = "__codelineno-35-5" name = "__codelineno-35-5" href = "#__codelineno-35-5" > < / 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-35-6" name = "__codelineno-35-6" href = "#__codelineno-35-6" > < / 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-35-7" name = "__codelineno-35-7" href = "#__codelineno-35-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-35-8" name = "__codelineno-35-8" href = "#__codelineno-35-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n*n（ ） < / span >
< a id = "__codelineno-35-9" name = "__codelineno-35-9" href = "#__codelineno-35-9" > < / 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-35-10" name = "__codelineno-35-10" href = "#__codelineno-35-10" > < / 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-35-11" name = "__codelineno-35-11" href = "#__codelineno-35-11" > < / 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-35-12" name = "__codelineno-35-12" href = "#__codelineno-35-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-35-13" name = "__codelineno-35-13" href = "#__codelineno-35-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-35-14" name = "__codelineno-35-14" href = "#__codelineno-35-14" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< 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 = "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-36-2" name = "__codelineno-36-2" href = "#__codelineno-36-2" > < / 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（ ） < / span >
< a id = "__codelineno-36-3" name = "__codelineno-36-3" href = "#__codelineno-36-3" > < / 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（ ） < / span >
< a id = "__codelineno-36-4" name = "__codelineno-36-4" href = "#__codelineno-36-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n（ ） < / span >
< a id = "__codelineno-36-5" name = "__codelineno-36-5" href = "#__codelineno-36-5" > < / 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-36-6" name = "__codelineno-36-6" href = "#__codelineno-36-6" > < / 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-36-7" name = "__codelineno-36-7" href = "#__codelineno-36-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-8" name = "__codelineno-36-8" href = "#__codelineno-36-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n*n（ ） < / span >
< a id = "__codelineno-36-9" name = "__codelineno-36-9" href = "#__codelineno-36-9" > < / 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-36-10" name = "__codelineno-36-10" href = "#__codelineno-36-10" > < / 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-36-11" name = "__codelineno-36-11" href = "#__codelineno-36-11" > < / 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-36-12" name = "__codelineno-36-12" href = "#__codelineno-36-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-13" name = "__codelineno-36-13" href = "#__codelineno-36-13" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-36-14" name = "__codelineno-36-14" href = "#__codelineno-36-14" > < / a > < 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 = "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 >
< a id = "__codelineno-37-2" name = "__codelineno-37-2" href = "#__codelineno-37-2" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-37-3" name = "__codelineno-37-3" href = "#__codelineno-37-3" > < / 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" > 1< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // +0（ ） < / span >
< a id = "__codelineno-37-4" name = "__codelineno-37-4" href = "#__codelineno-37-4" > < / 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 = "n" > n< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // +0（ ） < / span >
< a id = "__codelineno-37-5" name = "__codelineno-37-5" href = "#__codelineno-37-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // +n（ ） < / span >
< a id = "__codelineno-37-6" name = "__codelineno-37-6" href = "#__codelineno-37-6" > < / 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 = "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 >
< 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 = "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-37-9" name = "__codelineno-37-9" href = "#__codelineno-37-9" > < / a > < 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 = "c1" > // +n*n（ ） < / span >
< a id = "__codelineno-37-11" name = "__codelineno-37-11" href = "#__codelineno-37-11" > < / 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 >
< 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 = "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 >
< a id = "__codelineno-37-14" name = "__codelineno-37-14" href = "#__codelineno-37-14" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-37-15" name = "__codelineno-37-15" href = "#__codelineno-37-15" > < / 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-37-16" name = "__codelineno-37-16" href = "#__codelineno-37-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-17" name = "__codelineno-37-17" href = "#__codelineno-37-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-37-18" name = "__codelineno-37-18" href = "#__codelineno-37-18" > < / 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 = "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-38-2" name = "__codelineno-38-2" href = "#__codelineno-38-2" > < / a > < span class = "kd" > var< / span > < span class = "nv" > a< / span > < span class = "p" > =< / span > < span class = "mi" > 1< / span > < span class = "c1" > // +0（ ） < / span >
< a id = "__codelineno-38-3" name = "__codelineno-38-3" href = "#__codelineno-38-3" > < / 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（ ） < / span >
< a id = "__codelineno-38-4" name = "__codelineno-38-4" href = "#__codelineno-38-4" > < / a > < span class = "c1" > // +n（ ） < / span >
< a id = "__codelineno-38-5" name = "__codelineno-38-5" href = "#__codelineno-38-5" > < / 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-38-6" name = "__codelineno-38-6" href = "#__codelineno-38-6" > < / a > < span class = "bp" > print< / 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 = "p" > }< / span >
< a id = "__codelineno-38-8" name = "__codelineno-38-8" href = "#__codelineno-38-8" > < / a > < span class = "c1" > // +n*n（ ） < / span >
< a id = "__codelineno-38-9" name = "__codelineno-38-9" href = "#__codelineno-38-9" > < / 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-38-10" name = "__codelineno-38-10" href = "#__codelineno-38-10" > < / 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-38-11" name = "__codelineno-38-11" href = "#__codelineno-38-11" > < / a > < span class = "bp" > print< / 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 = "p" > }< / span >
< a id = "__codelineno-38-13" name = "__codelineno-38-13" href = "#__codelineno-38-13" > < / a > < 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 >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "2" > 2) 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，最高阶的项将处于主导作用，其它项的影响都可以被忽略。< / p >
< p > 以下表格给出了一些例子，其中有一些夸张的值，是想要向大家强调 < strong > 系数无法撼动阶数< / strong > 这一结论。在 < span class = "arithmatex" > \(n\)< / span > 趋于无穷大时，这些常数都是“浮云”。< / 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 >
2023-02-24 18:46:22 +08:00
< h2 id = "225" > 2.2.5. 常见类型< a class = "headerlink" href = "#225" title = "Permanent link" > ¶ < / a > < / h2 >
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< p > 设输入数据大小为 < span class = "arithmatex" > \(n\)< / span > ，常见的时间复杂度类型有（从低到高排列）< / 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 >
2023-02-26 18:18:03 +08:00
< p > < img alt = "时间复杂度的常见类型" src = "../time_complexity.assets/time_complexity_common_types.png" / > < / p >
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< p align = "center" > Fig. 时间复杂度的常见类型 < / p >
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< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > 部分示例代码需要一些前置知识，包括数组、递归算法等。如果遇到看不懂的地方无需担心，可以在学习完后面章节后再来复习，现阶段先聚焦在理解时间复杂度含义和推算方法上。< / p >
< / div >
< h3 id = "o1" > 常数阶 < span class = "arithmatex" > \(O(1)\)< / span > < a class = "headerlink" href = "#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 > 对于以下算法，无论操作数量 < code > size< / code > 有多大，只要与数据大小 < span class = "arithmatex" > \(n\)< / span > 无关，时间复杂度就仍为 < span class = "arithmatex" > \(O(1)\)< / span > 。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "5:10" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_5_1" > Java< / label > < label for = "__tabbed_5_2" > C++< / label > < label for = "__tabbed_5_3" > Python< / label > < label for = "__tabbed_5_4" > Go< / label > < label for = "__tabbed_5_5" > JavaScript< / label > < label for = "__tabbed_5_6" > TypeScript< / label > < label for = "__tabbed_5_7" > C< / label > < label for = "__tabbed_5_8" > C#< / label > < label for = "__tabbed_5_9" > Swift< / label > < label for = "__tabbed_5_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-40-1" name = "__codelineno-40-1" href = "#__codelineno-40-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-40-2" name = "__codelineno-40-2" href = "#__codelineno-40-2" > < / 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-40-3" name = "__codelineno-40-3" href = "#__codelineno-40-3" > < / 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-40-4" name = "__codelineno-40-4" href = "#__codelineno-40-4" > < / 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-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 = "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-40-6" name = "__codelineno-40-6" href = "#__codelineno-40-6" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-40-8" name = "__codelineno-40-8" href = "#__codelineno-40-8" > < / a > < span class = "p" > }< / 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-41-1" name = "__codelineno-41-1" href = "#__codelineno-41-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-41-2" name = "__codelineno-41-2" href = "#__codelineno-41-2" > < / 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-41-3" name = "__codelineno-41-3" href = "#__codelineno-41-3" > < / 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-41-4" name = "__codelineno-41-4" href = "#__codelineno-41-4" > < / 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-41-5" name = "__codelineno-41-5" href = "#__codelineno-41-5" > < / 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-41-6" name = "__codelineno-41-6" href = "#__codelineno-41-6" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-41-7" name = "__codelineno-41-7" href = "#__codelineno-41-7" > < / 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-41-8" name = "__codelineno-41-8" href = "#__codelineno-41-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-42-1" name = "__codelineno-42-1" href = "#__codelineno-42-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > constant< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-42-2" name = "__codelineno-42-2" href = "#__codelineno-42-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 常数阶 " " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-42-3" name = "__codelineno-42-3" href = "#__codelineno-42-3" > < / a > < span class = "n" > count< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-42-4" name = "__codelineno-42-4" href = "#__codelineno-42-4" > < / a > < span class = "n" > size< / span > < span class = "o" > =< / span > < span class = "mi" > 100000< / span >
< a id = "__codelineno-42-5" name = "__codelineno-42-5" href = "#__codelineno-42-5" > < / 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-42-6" name = "__codelineno-42-6" href = "#__codelineno-42-6" > < / a > < span class = "n" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-42-7" name = "__codelineno-42-7" href = "#__codelineno-42-7" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-43-1" name = "__codelineno-43-1" href = "#__codelineno-43-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-43-2" name = "__codelineno-43-2" href = "#__codelineno-43-2" > < / 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-43-3" name = "__codelineno-43-3" href = "#__codelineno-43-3" > < / 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-43-4" name = "__codelineno-43-4" href = "#__codelineno-43-4" > < / 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-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 = "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 >
2023-02-09 04:43:20 +08:00
< a id = "__codelineno-43-6" name = "__codelineno-43-6" href = "#__codelineno-43-6" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / span >
2023-02-08 14:54:41 +08:00
< 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > count< / span >
< a id = "__codelineno-43-9" name = "__codelineno-43-9" href = "#__codelineno-43-9" > < / 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-44-1" name = "__codelineno-44-1" href = "#__codelineno-44-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-44-2" name = "__codelineno-44-2" href = "#__codelineno-44-2" > < / 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-44-3" name = "__codelineno-44-3" href = "#__codelineno-44-3" > < / 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-44-4" name = "__codelineno-44-4" href = "#__codelineno-44-4" > < / 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-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 = "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-44-6" name = "__codelineno-44-6" href = "#__codelineno-44-6" > < / 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-44-7" name = "__codelineno-44-7" href = "#__codelineno-44-7" > < / 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-45-1" name = "__codelineno-45-1" href = "#__codelineno-45-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-45-2" name = "__codelineno-45-2" href = "#__codelineno-45-2" > < / 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-45-3" name = "__codelineno-45-3" href = "#__codelineno-45-3" > < / 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-45-4" name = "__codelineno-45-4" href = "#__codelineno-45-4" > < / 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-45-5" name = "__codelineno-45-5" href = "#__codelineno-45-5" > < / 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-45-6" name = "__codelineno-45-6" href = "#__codelineno-45-6" > < / 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-45-7" name = "__codelineno-45-7" href = "#__codelineno-45-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-46-1" name = "__codelineno-46-1" href = "#__codelineno-46-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > constant< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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-47-1" name = "__codelineno-47-1" href = "#__codelineno-47-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-47-2" name = "__codelineno-47-2" href = "#__codelineno-47-2" > < / 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 >
< a id = "__codelineno-47-3" name = "__codelineno-47-3" href = "#__codelineno-47-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-47-4" name = "__codelineno-47-4" href = "#__codelineno-47-4" > < / 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-47-5" name = "__codelineno-47-5" href = "#__codelineno-47-5" > < / 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-47-6" name = "__codelineno-47-6" href = "#__codelineno-47-6" > < / 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" > 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-47-7" name = "__codelineno-47-7" href = "#__codelineno-47-7" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-47-8" name = "__codelineno-47-8" href = "#__codelineno-47-8" > < / 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-47-9" name = "__codelineno-47-9" href = "#__codelineno-47-9" > < / 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-48-1" name = "__codelineno-48-1" href = "#__codelineno-48-1" > < / a > < span class = "cm" > /* 常数阶 */< / span >
< a id = "__codelineno-48-2" name = "__codelineno-48-2" href = "#__codelineno-48-2" > < / 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-48-3" name = "__codelineno-48-3" href = "#__codelineno-48-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > count< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
2023-02-08 20:30:33 +08:00
< a id = "__codelineno-48-4" name = "__codelineno-48-4" href = "#__codelineno-48-4" > < / a > < span class = "kd" > let< / span > < span class = "nv" > size< / span > < span class = "p" > =< / span > < span class = "mi" > 100_000< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-48-5" name = "__codelineno-48-5" href = "#__codelineno-48-5" > < / 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-48-6" name = "__codelineno-48-6" href = "#__codelineno-48-6" > < / a > < span class = "bp" > 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 = "p" > }< / span >
< a id = "__codelineno-48-8" name = "__codelineno-48-8" href = "#__codelineno-48-8" > < / a > < span class = "k" > return< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-48-9" name = "__codelineno-48-9" href = "#__codelineno-48-9" > < / 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-49-1" name = "__codelineno-49-1" href = "#__codelineno-49-1" > < / a > < span class = "c1" > // 常数阶< / span >
< a id = "__codelineno-49-2" name = "__codelineno-49-2" href = "#__codelineno-49-2" > < / 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-49-3" name = "__codelineno-49-3" href = "#__codelineno-49-3" > < / 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-49-4" name = "__codelineno-49-4" href = "#__codelineno-49-4" > < / 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-49-5" name = "__codelineno-49-5" href = "#__codelineno-49-5" > < / 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-49-6" name = "__codelineno-49-6" href = "#__codelineno-49-6" > < / 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-49-7" name = "__codelineno-49-7" href = "#__codelineno-49-7" > < / 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-49-8" name = "__codelineno-49-8" href = "#__codelineno-49-8" > < / 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-49-9" name = "__codelineno-49-9" href = "#__codelineno-49-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-49-10" name = "__codelineno-49-10" href = "#__codelineno-49-10" > < / 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-49-11" name = "__codelineno-49-11" href = "#__codelineno-49-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "on" > 线性阶 < span class = "arithmatex" > \(O(n)\)< / span > < a class = "headerlink" href = "#on" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 线性阶的操作数量相对输入数据大小成线性级别增长。线性阶常出现于单层循环。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "6:10" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_6_1" > Java< / label > < label for = "__tabbed_6_2" > C++< / label > < label for = "__tabbed_6_3" > Python< / label > < label for = "__tabbed_6_4" > Go< / label > < label for = "__tabbed_6_5" > JavaScript< / label > < label for = "__tabbed_6_6" > TypeScript< / label > < label for = "__tabbed_6_7" > C< / label > < label for = "__tabbed_6_8" > C#< / label > < label for = "__tabbed_6_9" > Swift< / label > < label for = "__tabbed_6_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< 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" > /* 线性阶 */< / 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" > 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-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 = "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-50-5" name = "__codelineno-50-5" href = "#__codelineno-50-5" > < / a > < span class = "w" > < / span > < span class = "n" > count< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-50-7" name = "__codelineno-50-7" href = "#__codelineno-50-7" > < / a > < span class = "p" > }< / 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-51-1" name = "__codelineno-51-1" href = "#__codelineno-51-1" > < / a > < span class = "cm" > /* 线性阶 */< / 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" > 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-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 = "mi" > 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 = "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-51-5" name = "__codelineno-51-5" href = "#__codelineno-51-5" > < / a > < span class = "w" > < / span > < span class = "n" > count< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-51-7" name = "__codelineno-51-7" href = "#__codelineno-51-7" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-52-1" name = "__codelineno-52-1" href = "#__codelineno-52-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > linear< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-52-2" name = "__codelineno-52-2" href = "#__codelineno-52-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 线性阶 " " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-52-3" name = "__codelineno-52-3" href = "#__codelineno-52-3" > < / a > < span class = "n" > count< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-52-4" name = "__codelineno-52-4" href = "#__codelineno-52-4" > < / 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-52-5" name = "__codelineno-52-5" href = "#__codelineno-52-5" > < / a > < span class = "n" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-52-6" name = "__codelineno-52-6" href = "#__codelineno-52-6" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-53-1" name = "__codelineno-53-1" href = "#__codelineno-53-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-53-2" name = "__codelineno-53-2" href = "#__codelineno-53-2" > < / 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-53-3" name = "__codelineno-53-3" href = "#__codelineno-53-3" > < / 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-53-4" name = "__codelineno-53-4" href = "#__codelineno-53-4" > < / 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-53-5" name = "__codelineno-53-5" href = "#__codelineno-53-5" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-53-6" name = "__codelineno-53-6" href = "#__codelineno-53-6" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-53-7" name = "__codelineno-53-7" href = "#__codelineno-53-7" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > count< / span >
< a id = "__codelineno-53-8" name = "__codelineno-53-8" href = "#__codelineno-53-8" > < / 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-54-1" name = "__codelineno-54-1" href = "#__codelineno-54-1" > < / a > < span class = "cm" > /* 线性阶 */< / 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" > 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-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 = "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-54-5" name = "__codelineno-54-5" href = "#__codelineno-54-5" > < / 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-54-6" name = "__codelineno-54-6" href = "#__codelineno-54-6" > < / 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-55-1" name = "__codelineno-55-1" href = "#__codelineno-55-1" > < / a > < span class = "cm" > /* 线性阶 */< / 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" > 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-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 = "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-55-5" name = "__codelineno-55-5" href = "#__codelineno-55-5" > < / 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-55-6" name = "__codelineno-55-6" href = "#__codelineno-55-6" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-56-1" name = "__codelineno-56-1" href = "#__codelineno-56-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > linear< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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-57-1" name = "__codelineno-57-1" href = "#__codelineno-57-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-57-2" name = "__codelineno-57-2" href = "#__codelineno-57-2" > < / 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 >
< a id = "__codelineno-57-3" name = "__codelineno-57-3" href = "#__codelineno-57-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-57-4" name = "__codelineno-57-4" href = "#__codelineno-57-4" > < / 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-57-5" name = "__codelineno-57-5" href = "#__codelineno-57-5" > < / 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 >
< a id = "__codelineno-57-6" name = "__codelineno-57-6" href = "#__codelineno-57-6" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-57-8" name = "__codelineno-57-8" href = "#__codelineno-57-8" > < / 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-58-1" name = "__codelineno-58-1" href = "#__codelineno-58-1" > < / a > < span class = "cm" > /* 线性阶 */< / span >
< a id = "__codelineno-58-2" name = "__codelineno-58-2" href = "#__codelineno-58-2" > < / 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-58-3" name = "__codelineno-58-3" href = "#__codelineno-58-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > count< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-58-4" name = "__codelineno-58-4" href = "#__codelineno-58-4" > < / 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-58-5" name = "__codelineno-58-5" href = "#__codelineno-58-5" > < / a > < span class = "bp" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-58-6" name = "__codelineno-58-6" href = "#__codelineno-58-6" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-58-7" name = "__codelineno-58-7" href = "#__codelineno-58-7" > < / a > < span class = "k" > return< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-58-8" name = "__codelineno-58-8" href = "#__codelineno-58-8" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
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< 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" > // 线性阶< / 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" > 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-59-3" name = "__codelineno-59-3" href = "#__codelineno-59-3" > < / 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-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" > 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-59-5" name = "__codelineno-59-5" href = "#__codelineno-59-5" > < / 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-59-6" name = "__codelineno-59-6" href = "#__codelineno-59-6" > < / 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-59-7" name = "__codelineno-59-7" href = "#__codelineno-59-7" > < / a > < 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-59-9" name = "__codelineno-59-9" href = "#__codelineno-59-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
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< p > 「遍历数组」和「遍历链表」等操作，时间复杂度都为 < 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 = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > < strong > 数据大小 < span class = "arithmatex" > \(n\)< / span > 是根据输入数据的类型来确定的< / strong > 。比如，在上述示例中，我们直接将 < span class = "arithmatex" > \(n\)< / span > 看作输入数据大小；以下遍历数组示例中，数据大小 < span class = "arithmatex" > \(n\)< / span > 为数组的长度。< / p >
< / div >
< div class = "tabbed-set tabbed-alternate" data-tabs = "7:10" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_7_1" > Java< / label > < label for = "__tabbed_7_2" > C++< / label > < label for = "__tabbed_7_3" > Python< / label > < label for = "__tabbed_7_4" > Go< / label > < label for = "__tabbed_7_5" > JavaScript< / label > < label for = "__tabbed_7_6" > TypeScript< / label > < label for = "__tabbed_7_7" > C< / label > < label for = "__tabbed_7_8" > C#< / label > < label for = "__tabbed_7_9" > Swift< / label > < label for = "__tabbed_7_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-60-1" name = "__codelineno-60-1" href = "#__codelineno-60-1" > < / a > < span class = "cm" > /* 线性阶（遍历数组） */< / span >
< a id = "__codelineno-60-2" name = "__codelineno-60-2" href = "#__codelineno-60-2" > < / 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-60-3" name = "__codelineno-60-3" href = "#__codelineno-60-3" > < / 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-60-4" name = "__codelineno-60-4" href = "#__codelineno-60-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环次数与数组长度成正比< / span >
< a id = "__codelineno-60-5" name = "__codelineno-60-5" href = "#__codelineno-60-5" > < / 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-60-6" name = "__codelineno-60-6" href = "#__codelineno-60-6" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-60-7" name = "__codelineno-60-7" href = "#__codelineno-60-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-60-8" name = "__codelineno-60-8" href = "#__codelineno-60-8" > < / 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-60-9" name = "__codelineno-60-9" href = "#__codelineno-60-9" > < / a > < span class = "p" > }< / 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（遍历数组） */< / 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" > 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 = "n" > nums< / 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 = "c1" > // 循环次数与数组长度成正比< / span >
< a id = "__codelineno-61-5" name = "__codelineno-61-5" href = "#__codelineno-61-5" > < / 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-61-6" name = "__codelineno-61-6" href = "#__codelineno-61-6" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-61-7" name = "__codelineno-61-7" href = "#__codelineno-61-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-61-8" name = "__codelineno-61-8" href = "#__codelineno-61-8" > < / 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-61-9" name = "__codelineno-61-9" href = "#__codelineno-61-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-62-1" name = "__codelineno-62-1" href = "#__codelineno-62-1" > < / 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 >
< a id = "__codelineno-62-2" name = "__codelineno-62-2" href = "#__codelineno-62-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 线性阶（遍历数组）" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-62-3" name = "__codelineno-62-3" href = "#__codelineno-62-3" > < / a > < span class = "n" > count< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-62-4" name = "__codelineno-62-4" href = "#__codelineno-62-4" > < / a > < span class = "c1" > # 循环次数与数组长度成正比< / span >
< a id = "__codelineno-62-5" name = "__codelineno-62-5" href = "#__codelineno-62-5" > < / 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-62-6" name = "__codelineno-62-6" href = "#__codelineno-62-6" > < / a > < span class = "n" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-62-7" name = "__codelineno-62-7" href = "#__codelineno-62-7" > < / 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.go< / 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（遍历数组） */< / span >
< a id = "__codelineno-63-2" name = "__codelineno-63-2" href = "#__codelineno-63-2" > < / 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-63-3" name = "__codelineno-63-3" href = "#__codelineno-63-3" > < / 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-63-4" name = "__codelineno-63-4" href = "#__codelineno-63-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环次数与数组长度成正比< / span >
< a id = "__codelineno-63-5" name = "__codelineno-63-5" href = "#__codelineno-63-5" > < / 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-63-6" name = "__codelineno-63-6" href = "#__codelineno-63-6" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-63-7" name = "__codelineno-63-7" href = "#__codelineno-63-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-63-8" name = "__codelineno-63-8" href = "#__codelineno-63-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > count< / span >
< a id = "__codelineno-63-9" name = "__codelineno-63-9" href = "#__codelineno-63-9" > < / 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-64-1" name = "__codelineno-64-1" href = "#__codelineno-64-1" > < / a > < span class = "cm" > /* 线性阶（遍历数组） */< / span >
< a id = "__codelineno-64-2" name = "__codelineno-64-2" href = "#__codelineno-64-2" > < / 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-64-3" name = "__codelineno-64-3" href = "#__codelineno-64-3" > < / 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-64-4" name = "__codelineno-64-4" href = "#__codelineno-64-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环次数与数组长度成正比< / span >
< a id = "__codelineno-64-5" name = "__codelineno-64-5" href = "#__codelineno-64-5" > < / 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-64-6" name = "__codelineno-64-6" href = "#__codelineno-64-6" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-64-8" name = "__codelineno-64-8" href = "#__codelineno-64-8" > < / 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-64-9" name = "__codelineno-64-9" href = "#__codelineno-64-9" > < / 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-65-1" name = "__codelineno-65-1" href = "#__codelineno-65-1" > < / a > < span class = "cm" > /* 线性阶（遍历数组） */< / span >
< a id = "__codelineno-65-2" name = "__codelineno-65-2" href = "#__codelineno-65-2" > < / 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-65-3" name = "__codelineno-65-3" href = "#__codelineno-65-3" > < / 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-65-4" name = "__codelineno-65-4" href = "#__codelineno-65-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环次数与数组长度成正比< / span >
< a id = "__codelineno-65-5" name = "__codelineno-65-5" href = "#__codelineno-65-5" > < / 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-65-6" name = "__codelineno-65-6" href = "#__codelineno-65-6" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-65-7" name = "__codelineno-65-7" href = "#__codelineno-65-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-65-8" name = "__codelineno-65-8" href = "#__codelineno-65-8" > < / 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-65-9" name = "__codelineno-65-9" href = "#__codelineno-65-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-66-1" name = "__codelineno-66-1" href = "#__codelineno-66-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > arrayTraversal< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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-67-1" name = "__codelineno-67-1" href = "#__codelineno-67-1" > < / a > < span class = "cm" > /* 线性阶（遍历数组） */< / span >
< a id = "__codelineno-67-2" name = "__codelineno-67-2" href = "#__codelineno-67-2" > < / 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 >
< a id = "__codelineno-67-3" name = "__codelineno-67-3" href = "#__codelineno-67-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-67-4" name = "__codelineno-67-4" href = "#__codelineno-67-4" > < / 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-67-5" name = "__codelineno-67-5" href = "#__codelineno-67-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环次数与数组长度成正比< / span >
2023-02-08 22:16:28 +08:00
< a id = "__codelineno-67-6" name = "__codelineno-67-6" href = "#__codelineno-67-6" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-67-7" name = "__codelineno-67-7" href = "#__codelineno-67-7" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-67-8" name = "__codelineno-67-8" href = "#__codelineno-67-8" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-67-9" name = "__codelineno-67-9" href = "#__codelineno-67-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-67-10" name = "__codelineno-67-10" href = "#__codelineno-67-10" > < / 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-67-11" name = "__codelineno-67-11" href = "#__codelineno-67-11" > < / 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-68-1" name = "__codelineno-68-1" href = "#__codelineno-68-1" > < / a > < span class = "cm" > /* 线性阶（遍历数组） */< / span >
< a id = "__codelineno-68-2" name = "__codelineno-68-2" href = "#__codelineno-68-2" > < / 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-68-3" name = "__codelineno-68-3" href = "#__codelineno-68-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > count< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-68-4" name = "__codelineno-68-4" href = "#__codelineno-68-4" > < / a > < span class = "c1" > // 循环次数与数组长度成正比< / span >
< a id = "__codelineno-68-5" name = "__codelineno-68-5" href = "#__codelineno-68-5" > < / 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-68-6" name = "__codelineno-68-6" href = "#__codelineno-68-6" > < / a > < span class = "bp" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-68-7" name = "__codelineno-68-7" href = "#__codelineno-68-7" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-68-8" name = "__codelineno-68-8" href = "#__codelineno-68-8" > < / a > < span class = "k" > return< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-68-9" name = "__codelineno-68-9" href = "#__codelineno-68-9" > < / 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-69-1" name = "__codelineno-69-1" href = "#__codelineno-69-1" > < / a > < span class = "c1" > // 线性阶（遍历数组）< / span >
< a id = "__codelineno-69-2" name = "__codelineno-69-2" href = "#__codelineno-69-2" > < / 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-69-3" name = "__codelineno-69-3" href = "#__codelineno-69-3" > < / 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-69-4" name = "__codelineno-69-4" href = "#__codelineno-69-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 循环次数与数组长度成正比< / span >
< a id = "__codelineno-69-5" name = "__codelineno-69-5" href = "#__codelineno-69-5" > < / 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-69-6" name = "__codelineno-69-6" href = "#__codelineno-69-6" > < / 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-69-7" name = "__codelineno-69-7" href = "#__codelineno-69-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-69-8" name = "__codelineno-69-8" href = "#__codelineno-69-8" > < / 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-69-9" name = "__codelineno-69-9" href = "#__codelineno-69-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "on2" > 平方阶 < span class = "arithmatex" > \(O(n^2)\)< / span > < a class = "headerlink" href = "#on2" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 平方阶的操作数量相对输入数据大小成平方级别增长。平方阶常出现于嵌套循环，外层循环和内层循环都为 < span class = "arithmatex" > \(O(n)\)< / span > ，总体为 < span class = "arithmatex" > \(O(n^2)\)< / span > 。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "8:10" > < input checked = "checked" id = "__tabbed_8_1" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_2" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_3" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_4" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_5" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_6" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_7" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_8" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_9" name = "__tabbed_8" type = "radio" / > < input id = "__tabbed_8_10" name = "__tabbed_8" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_8_1" > Java< / label > < label for = "__tabbed_8_2" > C++< / label > < label for = "__tabbed_8_3" > Python< / label > < label for = "__tabbed_8_4" > Go< / label > < label for = "__tabbed_8_5" > JavaScript< / label > < label for = "__tabbed_8_6" > TypeScript< / label > < label for = "__tabbed_8_7" > C< / label > < label for = "__tabbed_8_8" > C#< / label > < label for = "__tabbed_8_9" > Swift< / label > < label for = "__tabbed_8_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-70-1" name = "__codelineno-70-1" href = "#__codelineno-70-1" > < / a > < span class = "cm" > /* 平方阶 */< / 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" > 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-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 = "c1" > // 循环次数与数组长度成平方关系< / span >
< a id = "__codelineno-70-5" name = "__codelineno-70-5" href = "#__codelineno-70-5" > < / 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-70-6" name = "__codelineno-70-6" href = "#__codelineno-70-6" > < / 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-70-7" name = "__codelineno-70-7" href = "#__codelineno-70-7" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-70-8" name = "__codelineno-70-8" href = "#__codelineno-70-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-70-9" name = "__codelineno-70-9" href = "#__codelineno-70-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-70-10" name = "__codelineno-70-10" href = "#__codelineno-70-10" > < / 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-70-11" name = "__codelineno-70-11" href = "#__codelineno-70-11" > < / a > < span class = "p" > }< / 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-71-1" name = "__codelineno-71-1" href = "#__codelineno-71-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-71-2" name = "__codelineno-71-2" href = "#__codelineno-71-2" > < / 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-71-3" name = "__codelineno-71-3" href = "#__codelineno-71-3" > < / 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-71-4" name = "__codelineno-71-4" href = "#__codelineno-71-4" > < / 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-71-5" name = "__codelineno-71-5" href = "#__codelineno-71-5" > < / 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-71-6" name = "__codelineno-71-6" href = "#__codelineno-71-6" > < / 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-71-7" name = "__codelineno-71-7" href = "#__codelineno-71-7" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-71-9" name = "__codelineno-71-9" href = "#__codelineno-71-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-71-10" name = "__codelineno-71-10" href = "#__codelineno-71-10" > < / 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-71-11" name = "__codelineno-71-11" href = "#__codelineno-71-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< 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" > quadratic< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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" > " " " 平方阶 " " " < / span >
2023-02-08 14:54:41 +08:00
< 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平方关系< / span >
< a id = "__codelineno-72-5" name = "__codelineno-72-5" href = "#__codelineno-72-5" > < / 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-72-6" name = "__codelineno-72-6" href = "#__codelineno-72-6" > < / 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-72-7" name = "__codelineno-72-7" href = "#__codelineno-72-7" > < / a > < span class = "n" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-72-8" name = "__codelineno-72-8" href = "#__codelineno-72-8" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-73-1" name = "__codelineno-73-1" href = "#__codelineno-73-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-73-2" name = "__codelineno-73-2" href = "#__codelineno-73-2" > < / 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-73-3" name = "__codelineno-73-3" href = "#__codelineno-73-3" > < / 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-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平方关系< / 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 = "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-73-6" name = "__codelineno-73-6" href = "#__codelineno-73-6" > < / 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-73-7" name = "__codelineno-73-7" href = "#__codelineno-73-7" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-73-8" name = "__codelineno-73-8" href = "#__codelineno-73-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-73-9" name = "__codelineno-73-9" href = "#__codelineno-73-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-73-10" name = "__codelineno-73-10" href = "#__codelineno-73-10" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > count< / span >
< a id = "__codelineno-73-11" name = "__codelineno-73-11" href = "#__codelineno-73-11" > < / 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-74-1" name = "__codelineno-74-1" href = "#__codelineno-74-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-74-2" name = "__codelineno-74-2" href = "#__codelineno-74-2" > < / 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-74-3" name = "__codelineno-74-3" href = "#__codelineno-74-3" > < / 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-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平方关系< / 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 = "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-74-6" name = "__codelineno-74-6" href = "#__codelineno-74-6" > < / 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-74-7" name = "__codelineno-74-7" href = "#__codelineno-74-7" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-74-9" name = "__codelineno-74-9" href = "#__codelineno-74-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-74-10" name = "__codelineno-74-10" href = "#__codelineno-74-10" > < / 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-74-11" name = "__codelineno-74-11" href = "#__codelineno-74-11" > < / 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-75-1" name = "__codelineno-75-1" href = "#__codelineno-75-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-75-2" name = "__codelineno-75-2" href = "#__codelineno-75-2" > < / 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-75-3" name = "__codelineno-75-3" href = "#__codelineno-75-3" > < / 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-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平方关系< / span >
< a id = "__codelineno-75-5" name = "__codelineno-75-5" href = "#__codelineno-75-5" > < / 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-75-6" name = "__codelineno-75-6" href = "#__codelineno-75-6" > < / 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-75-7" name = "__codelineno-75-7" href = "#__codelineno-75-7" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-75-9" name = "__codelineno-75-9" href = "#__codelineno-75-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-75-10" name = "__codelineno-75-10" href = "#__codelineno-75-10" > < / 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-75-11" name = "__codelineno-75-11" href = "#__codelineno-75-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-76-1" name = "__codelineno-76-1" href = "#__codelineno-76-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > quadratic< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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-77-1" name = "__codelineno-77-1" href = "#__codelineno-77-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-77-2" name = "__codelineno-77-2" href = "#__codelineno-77-2" > < / 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 >
< a id = "__codelineno-77-3" name = "__codelineno-77-3" href = "#__codelineno-77-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-77-4" name = "__codelineno-77-4" href = "#__codelineno-77-4" > < / 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-77-5" name = "__codelineno-77-5" href = "#__codelineno-77-5" > < / 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-77-6" name = "__codelineno-77-6" href = "#__codelineno-77-6" > < / 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 >
< a id = "__codelineno-77-7" name = "__codelineno-77-7" href = "#__codelineno-77-7" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-77-8" name = "__codelineno-77-8" href = "#__codelineno-77-8" > < / 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 >
< a id = "__codelineno-77-9" name = "__codelineno-77-9" href = "#__codelineno-77-9" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-77-10" name = "__codelineno-77-10" href = "#__codelineno-77-10" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-77-11" name = "__codelineno-77-11" href = "#__codelineno-77-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-77-12" name = "__codelineno-77-12" href = "#__codelineno-77-12" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-77-13" name = "__codelineno-77-13" href = "#__codelineno-77-13" > < / 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-77-14" name = "__codelineno-77-14" href = "#__codelineno-77-14" > < / 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-78-1" name = "__codelineno-78-1" href = "#__codelineno-78-1" > < / a > < span class = "cm" > /* 平方阶 */< / span >
< a id = "__codelineno-78-2" name = "__codelineno-78-2" href = "#__codelineno-78-2" > < / 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-78-3" name = "__codelineno-78-3" href = "#__codelineno-78-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > count< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-78-4" name = "__codelineno-78-4" href = "#__codelineno-78-4" > < / a > < span class = "c1" > // 循环次数与数组长度成平方关系< / span >
< a id = "__codelineno-78-5" name = "__codelineno-78-5" href = "#__codelineno-78-5" > < / 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-78-6" name = "__codelineno-78-6" href = "#__codelineno-78-6" > < / 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-78-7" name = "__codelineno-78-7" href = "#__codelineno-78-7" > < / a > < span class = "bp" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-78-8" name = "__codelineno-78-8" href = "#__codelineno-78-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-9" name = "__codelineno-78-9" href = "#__codelineno-78-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-78-10" name = "__codelineno-78-10" href = "#__codelineno-78-10" > < / a > < span class = "k" > return< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-78-11" name = "__codelineno-78-11" href = "#__codelineno-78-11" > < / 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-79-1" name = "__codelineno-79-1" href = "#__codelineno-79-1" > < / a > < span class = "c1" > // 平方阶< / span >
< a id = "__codelineno-79-2" name = "__codelineno-79-2" href = "#__codelineno-79-2" > < / 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-79-3" name = "__codelineno-79-3" href = "#__codelineno-79-3" > < / 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-79-4" name = "__codelineno-79-4" href = "#__codelineno-79-4" > < / 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-79-5" name = "__codelineno-79-5" href = "#__codelineno-79-5" > < / 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-79-6" name = "__codelineno-79-6" href = "#__codelineno-79-6" > < / 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-79-7" name = "__codelineno-79-7" href = "#__codelineno-79-7" > < / 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-79-8" name = "__codelineno-79-8" href = "#__codelineno-79-8" > < / 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-79-9" name = "__codelineno-79-9" href = "#__codelineno-79-9" > < / 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-79-10" name = "__codelineno-79-10" href = "#__codelineno-79-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-79-11" name = "__codelineno-79-11" href = "#__codelineno-79-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-79-12" name = "__codelineno-79-12" href = "#__codelineno-79-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "p" > ;< / span >
2023-02-09 22:55:35 +08:00
< a id = "__codelineno-79-13" name = "__codelineno-79-13" href = "#__codelineno-79-13" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-02-26 18:18:03 +08:00
< p > < img alt = "常数阶、线性阶、平方阶的时间复杂度" src = "../time_complexity.assets/time_complexity_constant_linear_quadratic.png" / > < / p >
2023-02-26 19:53:32 +08:00
< p align = "center" > Fig. 常数阶、线性阶、平方阶的时间复杂度 < / p >
2023-02-08 14:54:41 +08:00
< p > 以「冒泡排序」为例，外层循环 < span class = "arithmatex" > \(n - 1\)< / span > 次，内层循环 < span class = "arithmatex" > \(n-1, n-2, \cdots, 2, 1\)< / span > 次，平均为 < span class = "arithmatex" > \(\frac{n}{2}\)< / span > 次，因此时间复杂度为 < span class = "arithmatex" > \(O(n^2)\)< / span > 。< / p >
< div class = "arithmatex" > \[
O((n - 1) \frac{n}{2}) = O(n^2)
\]< / div >
< div class = "tabbed-set tabbed-alternate" data-tabs = "9:10" > < input checked = "checked" id = "__tabbed_9_1" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_2" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_3" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_4" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_5" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_6" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_7" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_8" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_9" name = "__tabbed_9" type = "radio" / > < input id = "__tabbed_9_10" name = "__tabbed_9" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_9_1" > Java< / label > < label for = "__tabbed_9_2" > C++< / label > < label for = "__tabbed_9_3" > Python< / label > < label for = "__tabbed_9_4" > Go< / label > < label for = "__tabbed_9_5" > JavaScript< / label > < label for = "__tabbed_9_6" > TypeScript< / label > < label for = "__tabbed_9_7" > C< / label > < label for = "__tabbed_9_8" > C#< / label > < label for = "__tabbed_9_9" > Swift< / label > < label for = "__tabbed_9_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-80-1" name = "__codelineno-80-1" href = "#__codelineno-80-1" > < / a > < span class = "cm" > /* 平方阶（冒泡排序） */< / 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 = "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-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 = "mi" > 0< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 计数器< / span >
< a id = "__codelineno-80-4" name = "__codelineno-80-4" href = "#__codelineno-80-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 外循环：待排序元素数量为 n-1, n-2, ..., 1< / 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 = "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-80-6" name = "__codelineno-80-6" href = "#__codelineno-80-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 内循环：冒泡操作< / span >
< a id = "__codelineno-80-7" name = "__codelineno-80-7" href = "#__codelineno-80-7" > < / 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-80-8" name = "__codelineno-80-8" href = "#__codelineno-80-8" > < / 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-80-9" name = "__codelineno-80-9" href = "#__codelineno-80-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换 nums[j] 与 nums[j + 1]< / span >
< a id = "__codelineno-80-10" name = "__codelineno-80-10" href = "#__codelineno-80-10" > < / 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-80-11" name = "__codelineno-80-11" href = "#__codelineno-80-11" > < / 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-80-12" name = "__codelineno-80-12" href = "#__codelineno-80-12" > < / 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-80-13" name = "__codelineno-80-13" href = "#__codelineno-80-13" > < / 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-80-14" name = "__codelineno-80-14" href = "#__codelineno-80-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-80-15" name = "__codelineno-80-15" href = "#__codelineno-80-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-80-16" name = "__codelineno-80-16" href = "#__codelineno-80-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-80-17" name = "__codelineno-80-17" href = "#__codelineno-80-17" > < / 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-80-18" name = "__codelineno-80-18" href = "#__codelineno-80-18" > < / a > < span class = "p" > }< / 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-81-1" name = "__codelineno-81-1" href = "#__codelineno-81-1" > < / a > < span class = "cm" > /* 平方阶（冒泡排序） */< / span >
< a id = "__codelineno-81-2" name = "__codelineno-81-2" href = "#__codelineno-81-2" > < / 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 = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / 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 = "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-81-4" name = "__codelineno-81-4" href = "#__codelineno-81-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 外循环：待排序元素数量为 n-1, n-2, ..., 1< / 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 = "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-81-6" name = "__codelineno-81-6" href = "#__codelineno-81-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 内循环：冒泡操作< / span >
< a id = "__codelineno-81-7" name = "__codelineno-81-7" href = "#__codelineno-81-7" > < / 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-81-8" name = "__codelineno-81-8" href = "#__codelineno-81-8" > < / 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-81-9" name = "__codelineno-81-9" href = "#__codelineno-81-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换 nums[j] 与 nums[j + 1]< / span >
< a id = "__codelineno-81-10" name = "__codelineno-81-10" href = "#__codelineno-81-10" > < / 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-81-11" name = "__codelineno-81-11" href = "#__codelineno-81-11" > < / 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-81-12" name = "__codelineno-81-12" href = "#__codelineno-81-12" > < / 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-81-13" name = "__codelineno-81-13" href = "#__codelineno-81-13" > < / 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-81-14" name = "__codelineno-81-14" href = "#__codelineno-81-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-81-15" name = "__codelineno-81-15" href = "#__codelineno-81-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-81-16" name = "__codelineno-81-16" href = "#__codelineno-81-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-81-17" name = "__codelineno-81-17" href = "#__codelineno-81-17" > < / 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-81-18" name = "__codelineno-81-18" href = "#__codelineno-81-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-82-1" name = "__codelineno-82-1" href = "#__codelineno-82-1" > < / 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 >
< a id = "__codelineno-82-2" name = "__codelineno-82-2" href = "#__codelineno-82-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 平方阶（冒泡排序）" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-82-3" name = "__codelineno-82-3" href = "#__codelineno-82-3" > < / 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-82-4" name = "__codelineno-82-4" href = "#__codelineno-82-4" > < / a > < span class = "c1" > # 外循环：待排序元素数量为 n-1, n-2, ..., 1< / span >
< a id = "__codelineno-82-5" name = "__codelineno-82-5" href = "#__codelineno-82-5" > < / 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-82-6" name = "__codelineno-82-6" href = "#__codelineno-82-6" > < / a > < span class = "c1" > # 内循环：冒泡操作< / span >
< a id = "__codelineno-82-7" name = "__codelineno-82-7" href = "#__codelineno-82-7" > < / 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-82-8" name = "__codelineno-82-8" href = "#__codelineno-82-8" > < / 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-82-9" name = "__codelineno-82-9" href = "#__codelineno-82-9" > < / a > < span class = "c1" > # 交换 nums[j] 与 nums[j + 1]< / span >
< a id = "__codelineno-82-10" name = "__codelineno-82-10" href = "#__codelineno-82-10" > < / a > < span class = "n" > tmp< / 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-82-11" name = "__codelineno-82-11" href = "#__codelineno-82-11" > < / 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-82-12" name = "__codelineno-82-12" href = "#__codelineno-82-12" > < / 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-82-13" name = "__codelineno-82-13" href = "#__codelineno-82-13" > < / 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-82-14" name = "__codelineno-82-14" href = "#__codelineno-82-14" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-83-1" name = "__codelineno-83-1" href = "#__codelineno-83-1" > < / a > < span class = "cm" > /* 平方阶（冒泡排序） */< / span >
< a id = "__codelineno-83-2" name = "__codelineno-83-2" href = "#__codelineno-83-2" > < / 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-83-3" name = "__codelineno-83-3" href = "#__codelineno-83-3" > < / 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-83-4" name = "__codelineno-83-4" href = "#__codelineno-83-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 外循环：待排序元素数量为 n-1, n-2, ..., 1< / 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 = "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-83-6" name = "__codelineno-83-6" href = "#__codelineno-83-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 内循环：冒泡操作< / span >
< a id = "__codelineno-83-7" name = "__codelineno-83-7" href = "#__codelineno-83-7" > < / 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-83-8" name = "__codelineno-83-8" href = "#__codelineno-83-8" > < / 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-83-9" name = "__codelineno-83-9" href = "#__codelineno-83-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换 nums[j] 与 nums[j + 1]< / span >
< a id = "__codelineno-83-10" name = "__codelineno-83-10" href = "#__codelineno-83-10" > < / 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-83-11" name = "__codelineno-83-11" href = "#__codelineno-83-11" > < / 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-83-12" name = "__codelineno-83-12" href = "#__codelineno-83-12" > < / 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-83-13" name = "__codelineno-83-13" href = "#__codelineno-83-13" > < / 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-83-14" name = "__codelineno-83-14" href = "#__codelineno-83-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-83-15" name = "__codelineno-83-15" href = "#__codelineno-83-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-83-16" name = "__codelineno-83-16" href = "#__codelineno-83-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-83-17" name = "__codelineno-83-17" href = "#__codelineno-83-17" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > count< / span >
< a id = "__codelineno-83-18" name = "__codelineno-83-18" href = "#__codelineno-83-18" > < / 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-84-1" name = "__codelineno-84-1" href = "#__codelineno-84-1" > < / a > < span class = "cm" > /* 平方阶（冒泡排序） */< / span >
< a id = "__codelineno-84-2" name = "__codelineno-84-2" href = "#__codelineno-84-2" > < / 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-84-3" name = "__codelineno-84-3" href = "#__codelineno-84-3" > < / 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-84-4" name = "__codelineno-84-4" href = "#__codelineno-84-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 外循环：待排序元素数量为 n-1, n-2, ..., 1< / span >
< a id = "__codelineno-84-5" name = "__codelineno-84-5" href = "#__codelineno-84-5" > < / 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-84-6" name = "__codelineno-84-6" href = "#__codelineno-84-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 内循环：冒泡操作< / span >
< a id = "__codelineno-84-7" name = "__codelineno-84-7" href = "#__codelineno-84-7" > < / 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-84-8" name = "__codelineno-84-8" href = "#__codelineno-84-8" > < / 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-84-9" name = "__codelineno-84-9" href = "#__codelineno-84-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换 nums[j] 与 nums[j + 1]< / span >
< a id = "__codelineno-84-10" name = "__codelineno-84-10" href = "#__codelineno-84-10" > < / 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-84-11" name = "__codelineno-84-11" href = "#__codelineno-84-11" > < / 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-84-12" name = "__codelineno-84-12" href = "#__codelineno-84-12" > < / 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-84-13" name = "__codelineno-84-13" href = "#__codelineno-84-13" > < / 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-84-14" name = "__codelineno-84-14" href = "#__codelineno-84-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-84-15" name = "__codelineno-84-15" href = "#__codelineno-84-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-84-16" name = "__codelineno-84-16" href = "#__codelineno-84-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-84-17" name = "__codelineno-84-17" href = "#__codelineno-84-17" > < / 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-84-18" name = "__codelineno-84-18" href = "#__codelineno-84-18" > < / 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-85-1" name = "__codelineno-85-1" href = "#__codelineno-85-1" > < / a > < span class = "cm" > /* 平方阶（冒泡排序） */< / span >
< a id = "__codelineno-85-2" name = "__codelineno-85-2" href = "#__codelineno-85-2" > < / 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-85-3" name = "__codelineno-85-3" href = "#__codelineno-85-3" > < / 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-85-4" name = "__codelineno-85-4" href = "#__codelineno-85-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 外循环：待排序元素数量为 n-1, n-2, ..., 1< / 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 = "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-85-6" name = "__codelineno-85-6" href = "#__codelineno-85-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 内循环：冒泡操作< / span >
< a id = "__codelineno-85-7" name = "__codelineno-85-7" href = "#__codelineno-85-7" > < / 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-85-8" name = "__codelineno-85-8" href = "#__codelineno-85-8" > < / 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-85-9" name = "__codelineno-85-9" href = "#__codelineno-85-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换 nums[j] 与 nums[j + 1]< / span >
< a id = "__codelineno-85-10" name = "__codelineno-85-10" href = "#__codelineno-85-10" > < / 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-85-11" name = "__codelineno-85-11" href = "#__codelineno-85-11" > < / 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-85-12" name = "__codelineno-85-12" href = "#__codelineno-85-12" > < / 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-85-13" name = "__codelineno-85-13" href = "#__codelineno-85-13" > < / 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-85-14" name = "__codelineno-85-14" href = "#__codelineno-85-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-85-15" name = "__codelineno-85-15" href = "#__codelineno-85-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-85-16" name = "__codelineno-85-16" href = "#__codelineno-85-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-85-17" name = "__codelineno-85-17" href = "#__codelineno-85-17" > < / 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-85-18" name = "__codelineno-85-18" href = "#__codelineno-85-18" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-86-1" name = "__codelineno-86-1" href = "#__codelineno-86-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > bubbleSort< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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（冒泡排序） */< / 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" > 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 >
< a id = "__codelineno-87-3" name = "__codelineno-87-3" href = "#__codelineno-87-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-87-4" name = "__codelineno-87-4" href = "#__codelineno-87-4" > < / 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 > < span class = "w" > < / span > < span class = "c1" > // 计数器< / span >
< a id = "__codelineno-87-5" name = "__codelineno-87-5" href = "#__codelineno-87-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 外循环：待排序元素数量为 n-1, n-2, ..., 1< / 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" > 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 >
< a id = "__codelineno-87-7" name = "__codelineno-87-7" href = "#__codelineno-87-7" > < / a > < span class = "w" > < / 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 = "c1" > // 内循环：冒泡操作< / span >
< a id = "__codelineno-87-9" name = "__codelineno-87-9" href = "#__codelineno-87-9" > < / 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" > 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 >
< a id = "__codelineno-87-10" name = "__codelineno-87-10" href = "#__codelineno-87-10" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-87-11" name = "__codelineno-87-11" href = "#__codelineno-87-11" > < / 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 >
< a id = "__codelineno-87-12" name = "__codelineno-87-12" href = "#__codelineno-87-12" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-87-13" name = "__codelineno-87-13" href = "#__codelineno-87-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换 nums[j] 与 nums[j + 1]< / span >
< a id = "__codelineno-87-14" name = "__codelineno-87-14" href = "#__codelineno-87-14" > < / 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-87-15" name = "__codelineno-87-15" href = "#__codelineno-87-15" > < / 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-87-16" name = "__codelineno-87-16" href = "#__codelineno-87-16" > < / 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-87-17" name = "__codelineno-87-17" href = "#__codelineno-87-17" > < / 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-87-18" name = "__codelineno-87-18" href = "#__codelineno-87-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-87-19" name = "__codelineno-87-19" href = "#__codelineno-87-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-87-20" name = "__codelineno-87-20" href = "#__codelineno-87-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-87-21" name = "__codelineno-87-21" href = "#__codelineno-87-21" > < / 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-87-22" name = "__codelineno-87-22" href = "#__codelineno-87-22" > < / 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-88-1" name = "__codelineno-88-1" href = "#__codelineno-88-1" > < / a > < span class = "cm" > /* 平方阶（冒泡排序） */< / span >
< a id = "__codelineno-88-2" name = "__codelineno-88-2" href = "#__codelineno-88-2" > < / 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-88-3" name = "__codelineno-88-3" href = "#__codelineno-88-3" > < / 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-88-4" name = "__codelineno-88-4" href = "#__codelineno-88-4" > < / a > < span class = "c1" > // 外循环：待排序元素数量为 n-1, n-2, ..., 1< / span >
< a id = "__codelineno-88-5" name = "__codelineno-88-5" href = "#__codelineno-88-5" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "n" > sequence< / span > < span class = "p" > (< / span > < span class = "bp" > first< / 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" > next< / span > < span class = "p" > :< / span > < span class = "p" > {< / span > < span class = "nv" > $0< / span > < span class = "o" > > < / span > < span class = "mi" > 0< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ?< / span > < span class = "nv" > $0< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span > < span class = "kc" > nil< / span > < span class = "p" > })< / span > < span class = "p" > {< / span >
< a id = "__codelineno-88-6" name = "__codelineno-88-6" href = "#__codelineno-88-6" > < / a > < span class = "c1" > // 内循环：冒泡操作< / span >
< a id = "__codelineno-88-7" name = "__codelineno-88-7" href = "#__codelineno-88-7" > < / 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-88-8" name = "__codelineno-88-8" href = "#__codelineno-88-8" > < / 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-88-9" name = "__codelineno-88-9" href = "#__codelineno-88-9" > < / a > < span class = "c1" > // 交换 nums[j] 与 nums[j + 1]< / span >
< a id = "__codelineno-88-10" name = "__codelineno-88-10" href = "#__codelineno-88-10" > < / 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-88-11" name = "__codelineno-88-11" href = "#__codelineno-88-11" > < / 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-88-12" name = "__codelineno-88-12" href = "#__codelineno-88-12" > < / 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-88-13" name = "__codelineno-88-13" href = "#__codelineno-88-13" > < / 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-88-14" name = "__codelineno-88-14" href = "#__codelineno-88-14" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-88-15" name = "__codelineno-88-15" href = "#__codelineno-88-15" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-88-16" name = "__codelineno-88-16" href = "#__codelineno-88-16" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-88-17" name = "__codelineno-88-17" href = "#__codelineno-88-17" > < / a > < span class = "k" > return< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-88-18" name = "__codelineno-88-18" href = "#__codelineno-88-18" > < / 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-89-1" name = "__codelineno-89-1" href = "#__codelineno-89-1" > < / a > < span class = "c1" > // 平方阶（冒泡排序）< / span >
< a id = "__codelineno-89-2" name = "__codelineno-89-2" href = "#__codelineno-89-2" > < / 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-89-3" name = "__codelineno-89-3" href = "#__codelineno-89-3" > < / 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-89-4" name = "__codelineno-89-4" href = "#__codelineno-89-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 外循环：待排序元素数量为 n-1, n-2, ..., 1< / span >
< a id = "__codelineno-89-5" name = "__codelineno-89-5" href = "#__codelineno-89-5" > < / 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" > @intCast< / span > < span class = "p" > (< / span > < span class = "kt" > i32< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > len< / span > < span class = "w" > < / 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-89-6" name = "__codelineno-89-6" href = "#__codelineno-89-6" > < / 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-89-7" name = "__codelineno-89-7" href = "#__codelineno-89-7" > < / 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-89-8" name = "__codelineno-89-8" href = "#__codelineno-89-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 内循环：冒泡操作< / span >
< a id = "__codelineno-89-9" name = "__codelineno-89-9" href = "#__codelineno-89-9" > < / 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-89-10" name = "__codelineno-89-10" href = "#__codelineno-89-10" > < / 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-89-11" name = "__codelineno-89-11" href = "#__codelineno-89-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 交换 nums[j] 与 nums[j + 1]< / span >
< a id = "__codelineno-89-12" name = "__codelineno-89-12" href = "#__codelineno-89-12" > < / 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-89-13" name = "__codelineno-89-13" href = "#__codelineno-89-13" > < / 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-89-14" name = "__codelineno-89-14" href = "#__codelineno-89-14" > < / 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-89-15" name = "__codelineno-89-15" href = "#__codelineno-89-15" > < / 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-89-16" name = "__codelineno-89-16" href = "#__codelineno-89-16" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-89-17" name = "__codelineno-89-17" href = "#__codelineno-89-17" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-89-18" name = "__codelineno-89-18" href = "#__codelineno-89-18" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-89-19" name = "__codelineno-89-19" href = "#__codelineno-89-19" > < / 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-89-20" name = "__codelineno-89-20" href = "#__codelineno-89-20" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "o2n" > 指数阶 < span class = "arithmatex" > \(O(2^n)\)< / span > < a class = "headerlink" href = "#o2n" title = "Permanent link" > ¶ < / a > < / h3 >
< div class = "admonition note" >
< p class = "admonition-title" > Note< / p >
< p > 生物学科中的“细胞分裂”即是指数阶增长：初始状态为 < span class = "arithmatex" > \(1\)< / span > 个细胞，分裂一轮后为 < span class = "arithmatex" > \(2\)< / span > 个，分裂两轮后为 < span class = "arithmatex" > \(4\)< / span > 个，……，分裂 < span class = "arithmatex" > \(n\)< / span > 轮后有 < span class = "arithmatex" > \(2^n\)< / span > 个细胞。< / p >
< / div >
< p > 指数阶增长得非常快，在实际应用中一般是不能被接受的。若一个问题使用「暴力枚举」求解的时间复杂度是 < span class = "arithmatex" > \(O(2^n)\)< / span > ，那么一般都需要使用「动态规划」或「贪心算法」等算法来求解。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "10:10" > < input checked = "checked" id = "__tabbed_10_1" name = "__tabbed_10" type = "radio" / > < input id = "__tabbed_10_2" name = "__tabbed_10" type = "radio" / > < input id = "__tabbed_10_3" name = "__tabbed_10" type = "radio" / > < input id = "__tabbed_10_4" name = "__tabbed_10" type = "radio" / > < input id = "__tabbed_10_5" name = "__tabbed_10" type = "radio" / > < input id = "__tabbed_10_6" name = "__tabbed_10" type = "radio" / > < input id = "__tabbed_10_7" name = "__tabbed_10" type = "radio" / > < input id = "__tabbed_10_8" name = "__tabbed_10" type = "radio" / > < input id = "__tabbed_10_9" name = "__tabbed_10" type = "radio" / > < input id = "__tabbed_10_10" name = "__tabbed_10" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_10_1" > Java< / label > < label for = "__tabbed_10_2" > C++< / label > < label for = "__tabbed_10_3" > Python< / label > < label for = "__tabbed_10_4" > Go< / label > < label for = "__tabbed_10_5" > JavaScript< / label > < label for = "__tabbed_10_6" > TypeScript< / label > < label for = "__tabbed_10_7" > C< / label > < label for = "__tabbed_10_8" > C#< / label > < label for = "__tabbed_10_9" > Swift< / label > < label for = "__tabbed_10_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-90-1" name = "__codelineno-90-1" href = "#__codelineno-90-1" > < / a > < span class = "cm" > /* 指数阶（循环实现） */< / span >
< a id = "__codelineno-90-2" name = "__codelineno-90-2" href = "#__codelineno-90-2" > < / 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-90-3" name = "__codelineno-90-3" href = "#__codelineno-90-3" > < / 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-90-4" name = "__codelineno-90-4" href = "#__codelineno-90-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)< / 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 = "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-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 = "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-90-7" name = "__codelineno-90-7" href = "#__codelineno-90-7" > < / a > < span class = "w" > < / span > < span class = "n" > 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 = "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-90-10" name = "__codelineno-90-10" href = "#__codelineno-90-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-90-11" name = "__codelineno-90-11" href = "#__codelineno-90-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1< / span >
< a id = "__codelineno-90-12" name = "__codelineno-90-12" href = "#__codelineno-90-12" > < / 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-90-13" name = "__codelineno-90-13" href = "#__codelineno-90-13" > < / a > < span class = "p" > }< / 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-91-1" name = "__codelineno-91-1" href = "#__codelineno-91-1" > < / a > < span class = "cm" > /* 指数阶（循环实现） */< / span >
< a id = "__codelineno-91-2" name = "__codelineno-91-2" href = "#__codelineno-91-2" > < / 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-91-3" name = "__codelineno-91-3" href = "#__codelineno-91-3" > < / 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-91-4" name = "__codelineno-91-4" href = "#__codelineno-91-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)< / 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 = "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-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 = "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-91-7" name = "__codelineno-91-7" href = "#__codelineno-91-7" > < / a > < span class = "w" > < / span > < span class = "n" > 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 = "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-91-10" name = "__codelineno-91-10" href = "#__codelineno-91-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-91-11" name = "__codelineno-91-11" href = "#__codelineno-91-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1< / span >
< a id = "__codelineno-91-12" name = "__codelineno-91-12" href = "#__codelineno-91-12" > < / 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-91-13" name = "__codelineno-91-13" href = "#__codelineno-91-13" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-92-1" name = "__codelineno-92-1" href = "#__codelineno-92-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > exponential< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-92-2" name = "__codelineno-92-2" href = "#__codelineno-92-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 指数阶（循环实现）" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-92-3" name = "__codelineno-92-3" href = "#__codelineno-92-3" > < / a > < span class = "n" > count< / span > < span class = "p" > ,< / span > < span class = "n" > base< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-92-4" name = "__codelineno-92-4" href = "#__codelineno-92-4" > < / a > < span class = "c1" > # cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)< / span >
< a id = "__codelineno-92-5" name = "__codelineno-92-5" href = "#__codelineno-92-5" > < / 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" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-92-6" name = "__codelineno-92-6" href = "#__codelineno-92-6" > < / 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" > base< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-92-7" name = "__codelineno-92-7" href = "#__codelineno-92-7" > < / a > < span class = "n" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-92-8" name = "__codelineno-92-8" href = "#__codelineno-92-8" > < / a > < span class = "n" > base< / span > < span class = "o" > *=< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-92-9" name = "__codelineno-92-9" href = "#__codelineno-92-9" > < / a > < span class = "c1" > # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1< / span >
< a id = "__codelineno-92-10" name = "__codelineno-92-10" href = "#__codelineno-92-10" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-93-1" name = "__codelineno-93-1" href = "#__codelineno-93-1" > < / a > < span class = "cm" > /* 指数阶（循环实现）*/< / span >
< a id = "__codelineno-93-2" name = "__codelineno-93-2" href = "#__codelineno-93-2" > < / 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-93-3" name = "__codelineno-93-3" href = "#__codelineno-93-3" > < / 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-93-4" name = "__codelineno-93-4" href = "#__codelineno-93-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)< / 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 = "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-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 = "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-93-7" name = "__codelineno-93-7" href = "#__codelineno-93-7" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / 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 = "nx" > base< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-93-10" name = "__codelineno-93-10" href = "#__codelineno-93-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-93-11" name = "__codelineno-93-11" href = "#__codelineno-93-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1< / span >
< a id = "__codelineno-93-12" name = "__codelineno-93-12" href = "#__codelineno-93-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > count< / span >
< a id = "__codelineno-93-13" name = "__codelineno-93-13" href = "#__codelineno-93-13" > < / 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-94-1" name = "__codelineno-94-1" href = "#__codelineno-94-1" > < / a > < span class = "cm" > /* 指数阶（循环实现） */< / span >
< a id = "__codelineno-94-2" name = "__codelineno-94-2" href = "#__codelineno-94-2" > < / 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-94-3" name = "__codelineno-94-3" href = "#__codelineno-94-3" > < / 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-94-4" name = "__codelineno-94-4" href = "#__codelineno-94-4" > < / 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-94-5" name = "__codelineno-94-5" href = "#__codelineno-94-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)< / 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 = "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-94-7" name = "__codelineno-94-7" href = "#__codelineno-94-7" > < / 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-94-8" name = "__codelineno-94-8" href = "#__codelineno-94-8" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / 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 = "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-94-11" name = "__codelineno-94-11" href = "#__codelineno-94-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-94-12" name = "__codelineno-94-12" href = "#__codelineno-94-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1< / span >
< a id = "__codelineno-94-13" name = "__codelineno-94-13" href = "#__codelineno-94-13" > < / 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-94-14" name = "__codelineno-94-14" href = "#__codelineno-94-14" > < / 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-95-1" name = "__codelineno-95-1" href = "#__codelineno-95-1" > < / a > < span class = "cm" > /* 指数阶（循环实现） */< / span >
< a id = "__codelineno-95-2" name = "__codelineno-95-2" href = "#__codelineno-95-2" > < / 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-95-3" name = "__codelineno-95-3" href = "#__codelineno-95-3" > < / 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-95-4" name = "__codelineno-95-4" href = "#__codelineno-95-4" > < / 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-95-5" name = "__codelineno-95-5" href = "#__codelineno-95-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)< / span >
< a id = "__codelineno-95-6" name = "__codelineno-95-6" href = "#__codelineno-95-6" > < / 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-95-7" name = "__codelineno-95-7" href = "#__codelineno-95-7" > < / 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-95-8" name = "__codelineno-95-8" href = "#__codelineno-95-8" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-95-10" name = "__codelineno-95-10" href = "#__codelineno-95-10" > < / 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-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 = "c1" > // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1< / span >
< a id = "__codelineno-95-13" name = "__codelineno-95-13" href = "#__codelineno-95-13" > < / 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-95-14" name = "__codelineno-95-14" href = "#__codelineno-95-14" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-96-1" name = "__codelineno-96-1" href = "#__codelineno-96-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > exponential< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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-97-1" name = "__codelineno-97-1" href = "#__codelineno-97-1" > < / a > < span class = "cm" > /* 指数阶（循环实现） */< / 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" > exponential< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-97-3" name = "__codelineno-97-3" href = "#__codelineno-97-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-97-4" name = "__codelineno-97-4" href = "#__codelineno-97-4" > < / 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 > < 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-97-5" name = "__codelineno-97-5" href = "#__codelineno-97-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)< / span >
< a id = "__codelineno-97-6" name = "__codelineno-97-6" href = "#__codelineno-97-6" > < / 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 >
< a id = "__codelineno-97-7" name = "__codelineno-97-7" href = "#__codelineno-97-7" > < / a > < 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" > 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 >
< a id = "__codelineno-97-9" name = "__codelineno-97-9" href = "#__codelineno-97-9" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-97-10" name = "__codelineno-97-10" href = "#__codelineno-97-10" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-97-12" name = "__codelineno-97-12" href = "#__codelineno-97-12" > < / a > < span class = "w" > < / span > < span class = "n" > bas< / span > < span class = "w" > < / span > < span class = "o" > *=< / span > < span class = "w" > < / span > < span class = "m" > 2< / 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 = "p" > }< / span >
< a id = "__codelineno-97-14" name = "__codelineno-97-14" href = "#__codelineno-97-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1< / span >
< a id = "__codelineno-97-15" name = "__codelineno-97-15" href = "#__codelineno-97-15" > < / 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-97-16" name = "__codelineno-97-16" href = "#__codelineno-97-16" > < / 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-98-1" name = "__codelineno-98-1" href = "#__codelineno-98-1" > < / a > < span class = "cm" > /* 指数阶（循环实现） */< / span >
< a id = "__codelineno-98-2" name = "__codelineno-98-2" href = "#__codelineno-98-2" > < / 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-98-3" name = "__codelineno-98-3" href = "#__codelineno-98-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > count< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-98-4" name = "__codelineno-98-4" href = "#__codelineno-98-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > base< / span > < span class = "p" > =< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-98-5" name = "__codelineno-98-5" href = "#__codelineno-98-5" > < / a > < span class = "c1" > // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)< / span >
< a id = "__codelineno-98-6" name = "__codelineno-98-6" href = "#__codelineno-98-6" > < / 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-98-7" name = "__codelineno-98-7" href = "#__codelineno-98-7" > < / 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-98-8" name = "__codelineno-98-8" href = "#__codelineno-98-8" > < / a > < span class = "bp" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-98-9" name = "__codelineno-98-9" href = "#__codelineno-98-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-98-10" name = "__codelineno-98-10" href = "#__codelineno-98-10" > < / a > < span class = "n" > base< / span > < span class = "o" > *=< / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-98-11" name = "__codelineno-98-11" href = "#__codelineno-98-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-98-12" name = "__codelineno-98-12" href = "#__codelineno-98-12" > < / a > < span class = "c1" > // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1< / span >
< a id = "__codelineno-98-13" name = "__codelineno-98-13" href = "#__codelineno-98-13" > < / a > < span class = "k" > return< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-98-14" name = "__codelineno-98-14" href = "#__codelineno-98-14" > < / 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-99-1" name = "__codelineno-99-1" href = "#__codelineno-99-1" > < / a > < span class = "c1" > // 指数阶（循环实现）< / span >
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< a id = "__codelineno-99-2" name = "__codelineno-99-2" href = "#__codelineno-99-2" > < / 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 >
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< a id = "__codelineno-99-3" name = "__codelineno-99-3" href = "#__codelineno-99-3" > < / 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-99-4" name = "__codelineno-99-4" href = "#__codelineno-99-4" > < / 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-99-5" name = "__codelineno-99-5" href = "#__codelineno-99-5" > < / 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-99-6" name = "__codelineno-99-6" href = "#__codelineno-99-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // cell 每轮一分为二，形成数列 1, 2, 4, 8, ..., 2^(n-1)< / span >
< a id = "__codelineno-99-7" name = "__codelineno-99-7" href = "#__codelineno-99-7" > < / 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-99-8" name = "__codelineno-99-8" href = "#__codelineno-99-8" > < / 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-99-9" name = "__codelineno-99-9" href = "#__codelineno-99-9" > < / 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-99-10" name = "__codelineno-99-10" href = "#__codelineno-99-10" > < / 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-99-11" name = "__codelineno-99-11" href = "#__codelineno-99-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-99-12" name = "__codelineno-99-12" href = "#__codelineno-99-12" > < / 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-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 = "c1" > // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1< / 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 >
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< a id = "__codelineno-99-16" name = "__codelineno-99-16" href = "#__codelineno-99-16" > < / a > < span class = "p" > }< / span >
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< / code > < / pre > < / div >
< / div >
< / div >
< / div >
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< p > < img alt = "指数阶的时间复杂度" src = "../time_complexity.assets/time_complexity_exponential.png" / > < / p >
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< p align = "center" > Fig. 指数阶的时间复杂度 < / p >
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< p > 在实际算法中，指数阶常出现于递归函数。例如以下代码，不断地一分为二，分裂 < span class = "arithmatex" > \(n\)< / span > 次后停止。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "11:10" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_11_1" > Java< / label > < label for = "__tabbed_11_2" > C++< / label > < label for = "__tabbed_11_3" > Python< / label > < label for = "__tabbed_11_4" > Go< / label > < label for = "__tabbed_11_5" > JavaScript< / label > < label for = "__tabbed_11_6" > TypeScript< / label > < label for = "__tabbed_11_7" > C< / label > < label for = "__tabbed_11_8" > C#< / label > < label for = "__tabbed_11_9" > Swift< / label > < label for = "__tabbed_11_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-100-1" name = "__codelineno-100-1" href = "#__codelineno-100-1" > < / a > < span class = "cm" > /* 指数阶（递归实现） */< / span >
< a id = "__codelineno-100-2" name = "__codelineno-100-2" href = "#__codelineno-100-2" > < / 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-100-3" name = "__codelineno-100-3" href = "#__codelineno-100-3" > < / 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-100-4" name = "__codelineno-100-4" href = "#__codelineno-100-4" > < / 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-100-5" name = "__codelineno-100-5" href = "#__codelineno-100-5" > < / a > < span class = "p" > }< / 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-101-1" name = "__codelineno-101-1" href = "#__codelineno-101-1" > < / a > < span class = "cm" > /* 指数阶（递归实现） */< / span >
< a id = "__codelineno-101-2" name = "__codelineno-101-2" href = "#__codelineno-101-2" > < / 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-101-3" name = "__codelineno-101-3" href = "#__codelineno-101-3" > < / 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-101-4" name = "__codelineno-101-4" href = "#__codelineno-101-4" > < / 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-101-5" name = "__codelineno-101-5" href = "#__codelineno-101-5" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< 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-102-1" name = "__codelineno-102-1" href = "#__codelineno-102-1" > < / 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 >
< a id = "__codelineno-102-2" name = "__codelineno-102-2" href = "#__codelineno-102-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 指数阶（递归实现）" " " < / span >
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< a id = "__codelineno-102-3" name = "__codelineno-102-3" href = "#__codelineno-102-3" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-102-4" name = "__codelineno-102-4" href = "#__codelineno-102-4" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-103-1" name = "__codelineno-103-1" href = "#__codelineno-103-1" > < / a > < span class = "cm" > /* 指数阶（递归实现）*/< / span >
< a id = "__codelineno-103-2" name = "__codelineno-103-2" href = "#__codelineno-103-2" > < / 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-103-3" name = "__codelineno-103-3" href = "#__codelineno-103-3" > < / 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-103-4" name = "__codelineno-103-4" href = "#__codelineno-103-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-103-5" name = "__codelineno-103-5" href = "#__codelineno-103-5" > < / a > < 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 = "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-103-7" name = "__codelineno-103-7" href = "#__codelineno-103-7" > < / 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-104-1" name = "__codelineno-104-1" href = "#__codelineno-104-1" > < / a > < span class = "cm" > /* 指数阶（递归实现） */< / span >
< a id = "__codelineno-104-2" name = "__codelineno-104-2" href = "#__codelineno-104-2" > < / 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-104-3" name = "__codelineno-104-3" href = "#__codelineno-104-3" > < / 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-104-4" name = "__codelineno-104-4" href = "#__codelineno-104-4" > < / 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-104-5" name = "__codelineno-104-5" href = "#__codelineno-104-5" > < / 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-105-1" name = "__codelineno-105-1" href = "#__codelineno-105-1" > < / a > < span class = "cm" > /* 指数阶（递归实现） */< / span >
< a id = "__codelineno-105-2" name = "__codelineno-105-2" href = "#__codelineno-105-2" > < / 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-105-3" name = "__codelineno-105-3" href = "#__codelineno-105-3" > < / 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-105-4" name = "__codelineno-105-4" href = "#__codelineno-105-4" > < / 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-105-5" name = "__codelineno-105-5" href = "#__codelineno-105-5" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< 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 = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > expRecur< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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-107-1" name = "__codelineno-107-1" href = "#__codelineno-107-1" > < / a > < span class = "cm" > /* 指数阶（递归实现） */< / span >
< a id = "__codelineno-107-2" name = "__codelineno-107-2" href = "#__codelineno-107-2" > < / 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 >
< a id = "__codelineno-107-3" name = "__codelineno-107-3" href = "#__codelineno-107-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-107-4" name = "__codelineno-107-4" href = "#__codelineno-107-4" > < / 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-107-5" name = "__codelineno-107-5" href = "#__codelineno-107-5" > < / 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-107-6" name = "__codelineno-107-6" href = "#__codelineno-107-6" > < / 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-108-1" name = "__codelineno-108-1" href = "#__codelineno-108-1" > < / a > < span class = "cm" > /* 指数阶（递归实现） */< / span >
< a id = "__codelineno-108-2" name = "__codelineno-108-2" href = "#__codelineno-108-2" > < / 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-108-3" name = "__codelineno-108-3" href = "#__codelineno-108-3" > < / 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-108-4" name = "__codelineno-108-4" href = "#__codelineno-108-4" > < / a > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-108-5" name = "__codelineno-108-5" href = "#__codelineno-108-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-108-6" name = "__codelineno-108-6" href = "#__codelineno-108-6" > < / 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-108-7" name = "__codelineno-108-7" href = "#__codelineno-108-7" > < / 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-109-1" name = "__codelineno-109-1" href = "#__codelineno-109-1" > < / a > < span class = "c1" > // 指数阶（递归实现）< / span >
2023-02-09 22:55:35 +08:00
< a id = "__codelineno-109-2" name = "__codelineno-109-2" href = "#__codelineno-109-2" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-109-3" name = "__codelineno-109-3" href = "#__codelineno-109-3" > < / 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-109-4" name = "__codelineno-109-4" href = "#__codelineno-109-4" > < / 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-109-5" name = "__codelineno-109-5" href = "#__codelineno-109-5" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "olog-n" > 对数阶 < span class = "arithmatex" > \(O(\log n)\)< / span > < a class = "headerlink" href = "#olog-n" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 对数阶与指数阶正好相反，后者反映“每轮增加到两倍的情况”，而前者反映“每轮缩减到一半的情况”。对数阶仅次于常数阶，时间增长得很慢，是理想的时间复杂度。< / p >
< p > 对数阶常出现于「二分查找」和「分治算法」中，体现“一分为多”、“化繁为简”的算法思想。< / p >
< p > 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 >
< div class = "tabbed-set tabbed-alternate" data-tabs = "12:10" > < input checked = "checked" id = "__tabbed_12_1" name = "__tabbed_12" type = "radio" / > < input id = "__tabbed_12_2" name = "__tabbed_12" type = "radio" / > < input id = "__tabbed_12_3" name = "__tabbed_12" type = "radio" / > < input id = "__tabbed_12_4" name = "__tabbed_12" type = "radio" / > < input id = "__tabbed_12_5" name = "__tabbed_12" type = "radio" / > < input id = "__tabbed_12_6" name = "__tabbed_12" type = "radio" / > < input id = "__tabbed_12_7" name = "__tabbed_12" type = "radio" / > < input id = "__tabbed_12_8" name = "__tabbed_12" type = "radio" / > < input id = "__tabbed_12_9" name = "__tabbed_12" type = "radio" / > < input id = "__tabbed_12_10" name = "__tabbed_12" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_12_1" > Java< / label > < label for = "__tabbed_12_2" > C++< / label > < label for = "__tabbed_12_3" > Python< / label > < label for = "__tabbed_12_4" > Go< / label > < label for = "__tabbed_12_5" > JavaScript< / label > < label for = "__tabbed_12_6" > TypeScript< / label > < label for = "__tabbed_12_7" > C< / label > < label for = "__tabbed_12_8" > C#< / label > < label for = "__tabbed_12_9" > Swift< / label > < label for = "__tabbed_12_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< 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" > /* 对数阶（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" > 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-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 >
< a id = "__codelineno-110-4" name = "__codelineno-110-4" href = "#__codelineno-110-4" > < / 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-110-5" name = "__codelineno-110-5" href = "#__codelineno-110-5" > < / 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-110-6" name = "__codelineno-110-6" href = "#__codelineno-110-6" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-110-8" name = "__codelineno-110-8" href = "#__codelineno-110-8" > < / 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-110-9" name = "__codelineno-110-9" href = "#__codelineno-110-9" > < / a > < span class = "p" > }< / 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-111-1" name = "__codelineno-111-1" href = "#__codelineno-111-1" > < / a > < span class = "cm" > /* 对数阶（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" > 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-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 = "mi" > 0< / 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 = "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-111-5" name = "__codelineno-111-5" href = "#__codelineno-111-5" > < / 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-111-6" name = "__codelineno-111-6" href = "#__codelineno-111-6" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-111-8" name = "__codelineno-111-8" href = "#__codelineno-111-8" > < / 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-111-9" name = "__codelineno-111-9" href = "#__codelineno-111-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-112-1" name = "__codelineno-112-1" href = "#__codelineno-112-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > logarithmic< / span > < span class = "p" > (< / span > < span class = "n" > n< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-112-2" name = "__codelineno-112-2" href = "#__codelineno-112-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 对数阶（循环实现）" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-112-3" name = "__codelineno-112-3" href = "#__codelineno-112-3" > < / a > < span class = "n" > count< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-112-4" name = "__codelineno-112-4" href = "#__codelineno-112-4" > < / 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-112-5" name = "__codelineno-112-5" href = "#__codelineno-112-5" > < / 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-112-6" name = "__codelineno-112-6" href = "#__codelineno-112-6" > < / a > < span class = "n" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-112-7" name = "__codelineno-112-7" href = "#__codelineno-112-7" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-113-1" name = "__codelineno-113-1" href = "#__codelineno-113-1" > < / a > < span class = "cm" > /* 对数阶（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 = "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-113-3" name = "__codelineno-113-3" href = "#__codelineno-113-3" > < / 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-113-4" name = "__codelineno-113-4" href = "#__codelineno-113-4" > < / 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-113-5" name = "__codelineno-113-5" href = "#__codelineno-113-5" > < / 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-113-6" name = "__codelineno-113-6" href = "#__codelineno-113-6" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-113-7" name = "__codelineno-113-7" href = "#__codelineno-113-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-113-8" name = "__codelineno-113-8" href = "#__codelineno-113-8" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > count< / span >
< a id = "__codelineno-113-9" name = "__codelineno-113-9" href = "#__codelineno-113-9" > < / 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-114-1" name = "__codelineno-114-1" href = "#__codelineno-114-1" > < / a > < span class = "cm" > /* 对数阶（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" > 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-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 = "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-114-5" name = "__codelineno-114-5" href = "#__codelineno-114-5" > < / 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-114-6" name = "__codelineno-114-6" href = "#__codelineno-114-6" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-114-8" name = "__codelineno-114-8" href = "#__codelineno-114-8" > < / 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-114-9" name = "__codelineno-114-9" href = "#__codelineno-114-9" > < / 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-115-1" name = "__codelineno-115-1" href = "#__codelineno-115-1" > < / a > < span class = "cm" > /* 对数阶（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" > 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-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 = "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-115-5" name = "__codelineno-115-5" href = "#__codelineno-115-5" > < / 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-115-6" name = "__codelineno-115-6" href = "#__codelineno-115-6" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / 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 = "p" > }< / span >
< a id = "__codelineno-115-8" name = "__codelineno-115-8" href = "#__codelineno-115-8" > < / 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-115-9" name = "__codelineno-115-9" href = "#__codelineno-115-9" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-116-1" name = "__codelineno-116-1" href = "#__codelineno-116-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > logarithmic< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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-117-1" name = "__codelineno-117-1" href = "#__codelineno-117-1" > < / a > < span class = "cm" > /* 对数阶（循环实现） */< / span >
< a id = "__codelineno-117-2" name = "__codelineno-117-2" href = "#__codelineno-117-2" > < / 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 >
< a id = "__codelineno-117-3" name = "__codelineno-117-3" href = "#__codelineno-117-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-117-4" name = "__codelineno-117-4" href = "#__codelineno-117-4" > < / 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-117-5" name = "__codelineno-117-5" href = "#__codelineno-117-5" > < / 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 >
< a id = "__codelineno-117-6" name = "__codelineno-117-6" href = "#__codelineno-117-6" > < / a > < 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 = "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-117-8" name = "__codelineno-117-8" href = "#__codelineno-117-8" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-117-11" name = "__codelineno-117-11" href = "#__codelineno-117-11" > < / 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-118-1" name = "__codelineno-118-1" href = "#__codelineno-118-1" > < / a > < span class = "cm" > /* 对数阶（循环实现） */< / span >
2023-03-03 21:53:57 +08:00
< a id = "__codelineno-118-2" name = "__codelineno-118-2" href = "#__codelineno-118-2" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-118-3" name = "__codelineno-118-3" href = "#__codelineno-118-3" > < / a > < span class = "kd" > var< / span > < span class = "nv" > count< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-118-4" name = "__codelineno-118-4" href = "#__codelineno-118-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > n< / span > < span class = "p" > =< / span > < span class = "n" > n< / span >
< a id = "__codelineno-118-5" name = "__codelineno-118-5" href = "#__codelineno-118-5" > < / 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-118-6" name = "__codelineno-118-6" href = "#__codelineno-118-6" > < / 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-118-7" name = "__codelineno-118-7" href = "#__codelineno-118-7" > < / a > < span class = "bp" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-118-8" name = "__codelineno-118-8" href = "#__codelineno-118-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-118-9" name = "__codelineno-118-9" href = "#__codelineno-118-9" > < / a > < span class = "k" > return< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-118-10" name = "__codelineno-118-10" href = "#__codelineno-118-10" > < / 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-119-1" name = "__codelineno-119-1" href = "#__codelineno-119-1" > < / a > < span class = "c1" > // 对数阶（循环实现）< / span >
2023-02-09 22:55:35 +08:00
< 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" > 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-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" > 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-119-5" name = "__codelineno-119-5" href = "#__codelineno-119-5" > < / 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-119-6" name = "__codelineno-119-6" href = "#__codelineno-119-6" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-119-7" name = "__codelineno-119-7" href = "#__codelineno-119-7" > < / 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-119-8" name = "__codelineno-119-8" href = "#__codelineno-119-8" > < / 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-119-9" name = "__codelineno-119-9" href = "#__codelineno-119-9" > < / a > < 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 = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-119-11" name = "__codelineno-119-11" href = "#__codelineno-119-11" > < / a > < span class = "p" > }< / span >
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< p > < img alt = "对数阶的时间复杂度" src = "../time_complexity.assets/time_complexity_logarithmic.png" / > < / p >
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< p align = "center" > Fig. 对数阶的时间复杂度 < / p >
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< p > 与指数阶类似，对数阶也常出现于递归函数。以下代码形成了一个高度为 < span class = "arithmatex" > \(\log_2 n\)< / span > 的递归树。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "13:10" > < input checked = "checked" id = "__tabbed_13_1" name = "__tabbed_13" type = "radio" / > < input id = "__tabbed_13_2" name = "__tabbed_13" type = "radio" / > < input id = "__tabbed_13_3" name = "__tabbed_13" type = "radio" / > < input id = "__tabbed_13_4" name = "__tabbed_13" type = "radio" / > < input id = "__tabbed_13_5" name = "__tabbed_13" type = "radio" / > < input id = "__tabbed_13_6" name = "__tabbed_13" type = "radio" / > < input id = "__tabbed_13_7" name = "__tabbed_13" type = "radio" / > < input id = "__tabbed_13_8" name = "__tabbed_13" type = "radio" / > < input id = "__tabbed_13_9" name = "__tabbed_13" type = "radio" / > < input id = "__tabbed_13_10" name = "__tabbed_13" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_13_1" > Java< / label > < label for = "__tabbed_13_2" > C++< / label > < label for = "__tabbed_13_3" > Python< / label > < label for = "__tabbed_13_4" > Go< / label > < label for = "__tabbed_13_5" > JavaScript< / label > < label for = "__tabbed_13_6" > TypeScript< / label > < label for = "__tabbed_13_7" > C< / label > < label for = "__tabbed_13_8" > C#< / label > < label for = "__tabbed_13_9" > Swift< / label > < label for = "__tabbed_13_10" > Zig< / label > < / div >
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< div class = "highlight" > < span class = "filename" > time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-120-1" name = "__codelineno-120-1" href = "#__codelineno-120-1" > < / a > < span class = "cm" > /* 对数阶（递归实现） */< / span >
< a id = "__codelineno-120-2" name = "__codelineno-120-2" href = "#__codelineno-120-2" > < / 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-120-3" name = "__codelineno-120-3" href = "#__codelineno-120-3" > < / 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-120-4" name = "__codelineno-120-4" href = "#__codelineno-120-4" > < / 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-120-5" name = "__codelineno-120-5" href = "#__codelineno-120-5" > < / a > < span class = "p" > }< / span >
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< 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" > /* 对数阶（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" > 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-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 > < 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-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 = "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-121-5" name = "__codelineno-121-5" href = "#__codelineno-121-5" > < / a > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > time_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-122-1" name = "__codelineno-122-1" href = "#__codelineno-122-1" > < / 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 >
< a id = "__codelineno-122-2" name = "__codelineno-122-2" href = "#__codelineno-122-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 对数阶（递归实现）" " " < / span >
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< a id = "__codelineno-122-3" name = "__codelineno-122-3" href = "#__codelineno-122-3" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > < =< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span > < span class = "k" > return< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-122-4" name = "__codelineno-122-4" href = "#__codelineno-122-4" > < / 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 >
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< div class = "highlight" > < span class = "filename" > time_complexity.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-123-1" name = "__codelineno-123-1" href = "#__codelineno-123-1" > < / a > < span class = "cm" > /* 对数阶（递归实现）*/< / span >
< a id = "__codelineno-123-2" name = "__codelineno-123-2" href = "#__codelineno-123-2" > < / 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-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 = "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-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 = "mi" > 0< / span >
< a id = "__codelineno-123-5" name = "__codelineno-123-5" href = "#__codelineno-123-5" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-123-6" name = "__codelineno-123-6" href = "#__codelineno-123-6" > < / 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-123-7" name = "__codelineno-123-7" href = "#__codelineno-123-7" > < / a > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > time_complexity.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-124-1" name = "__codelineno-124-1" href = "#__codelineno-124-1" > < / a > < span class = "cm" > /* 对数阶（递归实现） */< / span >
< a id = "__codelineno-124-2" name = "__codelineno-124-2" href = "#__codelineno-124-2" > < / 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-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 = "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-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 = "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-124-5" name = "__codelineno-124-5" href = "#__codelineno-124-5" > < / a > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > time_complexity.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-125-1" name = "__codelineno-125-1" href = "#__codelineno-125-1" > < / a > < span class = "cm" > /* 对数阶（递归实现） */< / span >
< a id = "__codelineno-125-2" name = "__codelineno-125-2" href = "#__codelineno-125-2" > < / 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-125-3" name = "__codelineno-125-3" href = "#__codelineno-125-3" > < / 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-125-4" name = "__codelineno-125-4" href = "#__codelineno-125-4" > < / 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-125-5" name = "__codelineno-125-5" href = "#__codelineno-125-5" > < / a > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-126-1" name = "__codelineno-126-1" href = "#__codelineno-126-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > logRecur< / span > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > time_complexity.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-127-1" name = "__codelineno-127-1" href = "#__codelineno-127-1" > < / a > < span class = "cm" > /* 对数阶（递归实现） */< / span >
< a id = "__codelineno-127-2" name = "__codelineno-127-2" href = "#__codelineno-127-2" > < / 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 >
< a id = "__codelineno-127-3" name = "__codelineno-127-3" href = "#__codelineno-127-3" > < / a > < 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" > 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-127-5" name = "__codelineno-127-5" href = "#__codelineno-127-5" > < / 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-127-6" name = "__codelineno-127-6" href = "#__codelineno-127-6" > < / 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-128-1" name = "__codelineno-128-1" href = "#__codelineno-128-1" > < / a > < span class = "cm" > /* 对数阶（递归实现） */< / span >
2023-03-03 21:53:57 +08:00
< a id = "__codelineno-128-2" name = "__codelineno-128-2" href = "#__codelineno-128-2" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-128-3" name = "__codelineno-128-3" href = "#__codelineno-128-3" > < / 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-128-4" name = "__codelineno-128-4" href = "#__codelineno-128-4" > < / a > < span class = "k" > return< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-128-5" name = "__codelineno-128-5" href = "#__codelineno-128-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-128-6" name = "__codelineno-128-6" href = "#__codelineno-128-6" > < / 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-128-7" name = "__codelineno-128-7" href = "#__codelineno-128-7" > < / 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-129-1" name = "__codelineno-129-1" href = "#__codelineno-129-1" > < / a > < span class = "c1" > // 对数阶（递归实现）< / span >
2023-02-09 22:55:35 +08:00
< a id = "__codelineno-129-2" name = "__codelineno-129-2" href = "#__codelineno-129-2" > < / 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-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 = "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-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 = "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-129-5" name = "__codelineno-129-5" href = "#__codelineno-129-5" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h3 id = "on-log-n" > 线性对数阶 < span class = "arithmatex" > \(O(n \log n)\)< / span > < a class = "headerlink" href = "#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 > 。< / p >
< p > 主流排序算法的时间复杂度都是 < span class = "arithmatex" > \(O(n \log n )\)< / span > ，例如快速排序、归并排序、堆排序等。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "14:10" > < input checked = "checked" id = "__tabbed_14_1" name = "__tabbed_14" type = "radio" / > < input id = "__tabbed_14_2" name = "__tabbed_14" type = "radio" / > < input id = "__tabbed_14_3" name = "__tabbed_14" type = "radio" / > < input id = "__tabbed_14_4" name = "__tabbed_14" type = "radio" / > < input id = "__tabbed_14_5" name = "__tabbed_14" type = "radio" / > < input id = "__tabbed_14_6" name = "__tabbed_14" type = "radio" / > < input id = "__tabbed_14_7" name = "__tabbed_14" type = "radio" / > < input id = "__tabbed_14_8" name = "__tabbed_14" type = "radio" / > < input id = "__tabbed_14_9" name = "__tabbed_14" type = "radio" / > < input id = "__tabbed_14_10" name = "__tabbed_14" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_14_1" > Java< / label > < label for = "__tabbed_14_2" > C++< / label > < label for = "__tabbed_14_3" > Python< / label > < label for = "__tabbed_14_4" > Go< / label > < label for = "__tabbed_14_5" > JavaScript< / label > < label for = "__tabbed_14_6" > TypeScript< / label > < label for = "__tabbed_14_7" > C< / label > < label for = "__tabbed_14_8" > C#< / label > < label for = "__tabbed_14_9" > Swift< / label > < label for = "__tabbed_14_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-130-1" name = "__codelineno-130-1" href = "#__codelineno-130-1" > < / a > < span class = "cm" > /* 线性对数阶 */< / 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" > 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-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 > < 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-130-4" name = "__codelineno-130-4" href = "#__codelineno-130-4" > < / 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 = "mi" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span >
< a id = "__codelineno-130-5" name = "__codelineno-130-5" href = "#__codelineno-130-5" > < / 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-130-6" name = "__codelineno-130-6" href = "#__codelineno-130-6" > < / 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-130-7" name = "__codelineno-130-7" href = "#__codelineno-130-7" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-130-8" name = "__codelineno-130-8" href = "#__codelineno-130-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-130-9" name = "__codelineno-130-9" href = "#__codelineno-130-9" > < / 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-130-10" name = "__codelineno-130-10" href = "#__codelineno-130-10" > < / a > < span class = "p" > }< / 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-131-1" name = "__codelineno-131-1" href = "#__codelineno-131-1" > < / a > < span class = "cm" > /* 线性对数阶 */< / span >
< a id = "__codelineno-131-2" name = "__codelineno-131-2" href = "#__codelineno-131-2" > < / 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-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 = "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 >
< a id = "__codelineno-131-5" name = "__codelineno-131-5" href = "#__codelineno-131-5" > < / 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-131-6" name = "__codelineno-131-6" href = "#__codelineno-131-6" > < / 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-131-7" name = "__codelineno-131-7" href = "#__codelineno-131-7" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-131-8" name = "__codelineno-131-8" href = "#__codelineno-131-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-131-9" name = "__codelineno-131-9" href = "#__codelineno-131-9" > < / 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-131-10" name = "__codelineno-131-10" href = "#__codelineno-131-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< 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" > linear_log_recur< / span > < span class = "p" > (< / span > < span class = "n" > n< / 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" > " " " 线性对数阶 " " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-132-3" name = "__codelineno-132-3" href = "#__codelineno-132-3" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > < =< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-132-4" name = "__codelineno-132-4" href = "#__codelineno-132-4" > < / a > < span class = "n" > count< / 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 > \
< a id = "__codelineno-132-5" name = "__codelineno-132-5" href = "#__codelineno-132-5" > < / a > < 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-132-6" name = "__codelineno-132-6" href = "#__codelineno-132-6" > < / 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-132-7" name = "__codelineno-132-7" href = "#__codelineno-132-7" > < / a > < span class = "n" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-132-8" name = "__codelineno-132-8" href = "#__codelineno-132-8" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-133-1" name = "__codelineno-133-1" href = "#__codelineno-133-1" > < / a > < span class = "cm" > /* 线性对数阶 */< / span >
< a id = "__codelineno-133-2" name = "__codelineno-133-2" href = "#__codelineno-133-2" > < / 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-133-3" name = "__codelineno-133-3" href = "#__codelineno-133-3" > < / 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-133-4" name = "__codelineno-133-4" href = "#__codelineno-133-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-133-5" name = "__codelineno-133-5" href = "#__codelineno-133-5" > < / a > < span class = "w" > < / 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 = "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-133-7" name = "__codelineno-133-7" href = "#__codelineno-133-7" > < / 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-133-8" name = "__codelineno-133-8" href = "#__codelineno-133-8" > < / 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-133-9" name = "__codelineno-133-9" href = "#__codelineno-133-9" > < / a > < span class = "w" > < / span > < span class = "nx" > count< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-133-10" name = "__codelineno-133-10" href = "#__codelineno-133-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-133-11" name = "__codelineno-133-11" href = "#__codelineno-133-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > count< / span >
< a id = "__codelineno-133-12" name = "__codelineno-133-12" href = "#__codelineno-133-12" > < / 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-134-1" name = "__codelineno-134-1" href = "#__codelineno-134-1" > < / a > < span class = "cm" > /* 线性对数阶 */< / span >
< a id = "__codelineno-134-2" name = "__codelineno-134-2" href = "#__codelineno-134-2" > < / 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-134-3" name = "__codelineno-134-3" href = "#__codelineno-134-3" > < / 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-134-4" name = "__codelineno-134-4" href = "#__codelineno-134-4" > < / 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-134-5" name = "__codelineno-134-5" href = "#__codelineno-134-5" > < / 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-134-6" name = "__codelineno-134-6" href = "#__codelineno-134-6" > < / a > < span class = "w" > < / span > < span class = "nx" > 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 = "nx" > 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.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-135-1" name = "__codelineno-135-1" href = "#__codelineno-135-1" > < / a > < span class = "cm" > /* 线性对数阶 */< / span >
< a id = "__codelineno-135-2" name = "__codelineno-135-2" href = "#__codelineno-135-2" > < / 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-135-3" name = "__codelineno-135-3" href = "#__codelineno-135-3" > < / 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-135-4" name = "__codelineno-135-4" href = "#__codelineno-135-4" > < / 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-135-5" name = "__codelineno-135-5" href = "#__codelineno-135-5" > < / 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-135-6" name = "__codelineno-135-6" href = "#__codelineno-135-6" > < / a > < span class = "w" > < / span > < span class = "nx" > 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 = "nx" > 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" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-136-1" name = "__codelineno-136-1" href = "#__codelineno-136-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > linearLogRecur< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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-137-1" name = "__codelineno-137-1" href = "#__codelineno-137-1" > < / a > < span class = "cm" > /* 线性对数阶 */< / span >
< a id = "__codelineno-137-2" name = "__codelineno-137-2" href = "#__codelineno-137-2" > < / 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 >
< a id = "__codelineno-137-3" name = "__codelineno-137-3" href = "#__codelineno-137-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-137-4" name = "__codelineno-137-4" href = "#__codelineno-137-4" > < / 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-137-5" name = "__codelineno-137-5" href = "#__codelineno-137-5" > < / 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 = "m" > 2< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > +< / span >
< a id = "__codelineno-137-6" name = "__codelineno-137-6" href = "#__codelineno-137-6" > < / 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 = "m" > 2< / span > < span class = "p" > );< / span >
< a id = "__codelineno-137-7" name = "__codelineno-137-7" href = "#__codelineno-137-7" > < / 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 >
< a id = "__codelineno-137-8" name = "__codelineno-137-8" href = "#__codelineno-137-8" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-137-9" name = "__codelineno-137-9" href = "#__codelineno-137-9" > < / a > < span class = "w" > < / span > < span class = "n" > count< / span > < span class = "o" > ++< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-137-10" name = "__codelineno-137-10" href = "#__codelineno-137-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-137-11" name = "__codelineno-137-11" href = "#__codelineno-137-11" > < / 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-137-12" name = "__codelineno-137-12" href = "#__codelineno-137-12" > < / 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-138-1" name = "__codelineno-138-1" href = "#__codelineno-138-1" > < / a > < span class = "cm" > /* 线性对数阶 */< / span >
< a id = "__codelineno-138-2" name = "__codelineno-138-2" href = "#__codelineno-138-2" > < / 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-138-3" name = "__codelineno-138-3" href = "#__codelineno-138-3" > < / 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-138-4" name = "__codelineno-138-4" href = "#__codelineno-138-4" > < / a > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-138-5" name = "__codelineno-138-5" href = "#__codelineno-138-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-138-6" name = "__codelineno-138-6" href = "#__codelineno-138-6" > < / 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 >
2023-03-03 21:53:57 +08:00
< a id = "__codelineno-138-7" name = "__codelineno-138-7" href = "#__codelineno-138-7" > < / a > < span class = "k" > for< / span > < span class = "kc" > _< / span > < span class = "k" > in< / span > < span class = "n" > sequence< / span > < span class = "p" > (< / span > < span class = "bp" > first< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > ,< / span > < span class = "n" > next< / span > < span class = "p" > :< / span > < span class = "p" > {< / span > < span class = "nv" > $0< / 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 = "nv" > $0< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > :< / span > < span class = "kc" > nil< / span > < span class = "p" > })< / span > < span class = "p" > {< / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-138-8" name = "__codelineno-138-8" href = "#__codelineno-138-8" > < / a > < span class = "bp" > count< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-138-9" name = "__codelineno-138-9" href = "#__codelineno-138-9" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-138-10" name = "__codelineno-138-10" href = "#__codelineno-138-10" > < / a > < span class = "k" > return< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-138-11" name = "__codelineno-138-11" href = "#__codelineno-138-11" > < / 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-139-1" name = "__codelineno-139-1" href = "#__codelineno-139-1" > < / a > < span class = "c1" > // 线性对数阶< / span >
2023-02-09 22:55:35 +08:00
< a id = "__codelineno-139-2" name = "__codelineno-139-2" href = "#__codelineno-139-2" > < / 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-139-3" name = "__codelineno-139-3" href = "#__codelineno-139-3" > < / 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-139-4" name = "__codelineno-139-4" href = "#__codelineno-139-4" > < / 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-139-5" name = "__codelineno-139-5" href = "#__codelineno-139-5" > < / 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-139-6" name = "__codelineno-139-6" href = "#__codelineno-139-6" > < / 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-139-7" name = "__codelineno-139-7" href = "#__codelineno-139-7" > < / 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-139-8" name = "__codelineno-139-8" href = "#__codelineno-139-8" > < / 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-139-9" name = "__codelineno-139-9" href = "#__codelineno-139-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-139-10" name = "__codelineno-139-10" href = "#__codelineno-139-10" > < / 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-139-11" name = "__codelineno-139-11" href = "#__codelineno-139-11" > < / a > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-02-26 18:18:03 +08:00
< p > < img alt = "线性对数阶的时间复杂度" src = "../time_complexity.assets/time_complexity_logarithmic_linear.png" / > < / p >
2023-02-26 19:53:32 +08:00
< p align = "center" > Fig. 线性对数阶的时间复杂度 < / p >
2023-02-08 14:54:41 +08:00
< h3 id = "on_1" > 阶乘阶 < span class = "arithmatex" > \(O(n!)\)< / span > < a class = "headerlink" href = "#on_1" title = "Permanent link" > ¶ < / a > < / h3 >
< p > 阶乘阶对应数学上的「全排列」。即给定 < span class = "arithmatex" > \(n\)< / span > 个互不重复的元素，求其所有可能的排列方案，则方案数量为< / p >
< div class = "arithmatex" > \[
n! = n \times (n - 1) \times (n - 2) \times \cdots \times 2 \times 1
\]< / div >
< p > 阶乘常使用递归实现。例如以下代码，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，…… ，直至到第 < span class = "arithmatex" > \(n\)< / span > 层时终止分裂。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "15:10" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_15_1" > Java< / label > < label for = "__tabbed_15_2" > C++< / label > < label for = "__tabbed_15_3" > Python< / label > < label for = "__tabbed_15_4" > Go< / label > < label for = "__tabbed_15_5" > JavaScript< / label > < label for = "__tabbed_15_6" > TypeScript< / label > < label for = "__tabbed_15_7" > C< / label > < label for = "__tabbed_15_8" > C#< / label > < label for = "__tabbed_15_9" > Swift< / label > < label for = "__tabbed_15_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-140-1" name = "__codelineno-140-1" href = "#__codelineno-140-1" > < / a > < span class = "cm" > /* 阶乘阶（递归实现） */< / 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 = "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-140-3" name = "__codelineno-140-3" href = "#__codelineno-140-3" > < / 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-140-4" name = "__codelineno-140-4" href = "#__codelineno-140-4" > < / 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 = "mi" > 0< / 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 = "c1" > // 从 1 个分裂出 n 个< / span >
< a id = "__codelineno-140-6" name = "__codelineno-140-6" href = "#__codelineno-140-6" > < / 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-140-7" name = "__codelineno-140-7" href = "#__codelineno-140-7" > < / 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-140-8" name = "__codelineno-140-8" href = "#__codelineno-140-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-140-9" name = "__codelineno-140-9" href = "#__codelineno-140-9" > < / 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-140-10" name = "__codelineno-140-10" href = "#__codelineno-140-10" > < / a > < span class = "p" > }< / 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-141-1" name = "__codelineno-141-1" href = "#__codelineno-141-1" > < / a > < span class = "cm" > /* 阶乘阶（递归实现） */< / span >
< a id = "__codelineno-141-2" name = "__codelineno-141-2" href = "#__codelineno-141-2" > < / 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-141-3" name = "__codelineno-141-3" href = "#__codelineno-141-3" > < / 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-141-4" name = "__codelineno-141-4" href = "#__codelineno-141-4" > < / 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 = "mi" > 0< / 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 = "c1" > // 从 1 个分裂出 n 个< / span >
< a id = "__codelineno-141-6" name = "__codelineno-141-6" href = "#__codelineno-141-6" > < / 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-141-7" name = "__codelineno-141-7" href = "#__codelineno-141-7" > < / 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-141-8" name = "__codelineno-141-8" href = "#__codelineno-141-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-141-9" name = "__codelineno-141-9" href = "#__codelineno-141-9" > < / 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-141-10" name = "__codelineno-141-10" href = "#__codelineno-141-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-142-1" name = "__codelineno-142-1" href = "#__codelineno-142-1" > < / 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 >
< a id = "__codelineno-142-2" name = "__codelineno-142-2" href = "#__codelineno-142-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 阶乘阶（递归实现）" " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-142-3" name = "__codelineno-142-3" href = "#__codelineno-142-3" > < / a > < span class = "k" > if< / span > < span class = "n" > n< / span > < span class = "o" > ==< / span > < span class = "mi" > 0< / span > < span class = "p" > :< / span > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-142-4" name = "__codelineno-142-4" href = "#__codelineno-142-4" > < / a > < span class = "n" > count< / span > < span class = "o" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-142-5" name = "__codelineno-142-5" href = "#__codelineno-142-5" > < / a > < span class = "c1" > # 从 1 个分裂出 n 个< / span >
< a id = "__codelineno-142-6" name = "__codelineno-142-6" href = "#__codelineno-142-6" > < / 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-142-7" name = "__codelineno-142-7" href = "#__codelineno-142-7" > < / 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-142-8" name = "__codelineno-142-8" href = "#__codelineno-142-8" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-143-1" name = "__codelineno-143-1" href = "#__codelineno-143-1" > < / a > < span class = "cm" > /* 阶乘阶（递归实现） */< / span >
< a id = "__codelineno-143-2" name = "__codelineno-143-2" href = "#__codelineno-143-2" > < / 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-143-3" name = "__codelineno-143-3" href = "#__codelineno-143-3" > < / 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-143-4" name = "__codelineno-143-4" href = "#__codelineno-143-4" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-143-5" name = "__codelineno-143-5" href = "#__codelineno-143-5" > < / a > < span class = "w" > < / 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 = "nx" > count< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-143-7" name = "__codelineno-143-7" href = "#__codelineno-143-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从 1 个分裂出 n 个< / span >
< a id = "__codelineno-143-8" name = "__codelineno-143-8" href = "#__codelineno-143-8" > < / 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-143-9" name = "__codelineno-143-9" href = "#__codelineno-143-9" > < / 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-143-10" name = "__codelineno-143-10" href = "#__codelineno-143-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-143-11" name = "__codelineno-143-11" href = "#__codelineno-143-11" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > count< / span >
< a id = "__codelineno-143-12" name = "__codelineno-143-12" href = "#__codelineno-143-12" > < / 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-144-1" name = "__codelineno-144-1" href = "#__codelineno-144-1" > < / a > < span class = "cm" > /* 阶乘阶（递归实现） */< / span >
< a id = "__codelineno-144-2" name = "__codelineno-144-2" href = "#__codelineno-144-2" > < / 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-144-3" name = "__codelineno-144-3" href = "#__codelineno-144-3" > < / 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-144-4" name = "__codelineno-144-4" href = "#__codelineno-144-4" > < / 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-144-5" name = "__codelineno-144-5" href = "#__codelineno-144-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从 1 个分裂出 n 个< / span >
< a id = "__codelineno-144-6" name = "__codelineno-144-6" href = "#__codelineno-144-6" > < / 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-144-7" name = "__codelineno-144-7" href = "#__codelineno-144-7" > < / 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-144-8" name = "__codelineno-144-8" href = "#__codelineno-144-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-144-9" name = "__codelineno-144-9" href = "#__codelineno-144-9" > < / 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-144-10" name = "__codelineno-144-10" href = "#__codelineno-144-10" > < / 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-145-1" name = "__codelineno-145-1" href = "#__codelineno-145-1" > < / a > < span class = "cm" > /* 阶乘阶（递归实现） */< / span >
< a id = "__codelineno-145-2" name = "__codelineno-145-2" href = "#__codelineno-145-2" > < / 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-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 = "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-145-4" name = "__codelineno-145-4" href = "#__codelineno-145-4" > < / 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-145-5" name = "__codelineno-145-5" href = "#__codelineno-145-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从 1 个分裂出 n 个< / span >
< a id = "__codelineno-145-6" name = "__codelineno-145-6" href = "#__codelineno-145-6" > < / 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-145-7" name = "__codelineno-145-7" href = "#__codelineno-145-7" > < / 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-145-8" name = "__codelineno-145-8" href = "#__codelineno-145-8" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-145-9" name = "__codelineno-145-9" href = "#__codelineno-145-9" > < / 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-145-10" name = "__codelineno-145-10" href = "#__codelineno-145-10" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-11 18:21:51 +08:00
< div class = "highlight" > < span class = "filename" > time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-146-1" name = "__codelineno-146-1" href = "#__codelineno-146-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > factorialRecur< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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" > /* 阶乘阶（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" > factorialRecur< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > n< / span > < span class = "p" > )< / span >
< a id = "__codelineno-147-3" name = "__codelineno-147-3" href = "#__codelineno-147-3" > < / a > < 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" > 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-147-5" name = "__codelineno-147-5" href = "#__codelineno-147-5" > < / 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 = "m" > 0< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-147-6" name = "__codelineno-147-6" href = "#__codelineno-147-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从 1 个分裂出 n 个< / span >
< a id = "__codelineno-147-7" name = "__codelineno-147-7" href = "#__codelineno-147-7" > < / 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 >
< a id = "__codelineno-147-8" name = "__codelineno-147-8" href = "#__codelineno-147-8" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-147-9" name = "__codelineno-147-9" href = "#__codelineno-147-9" > < / 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" > 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-147-10" name = "__codelineno-147-10" href = "#__codelineno-147-10" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-147-11" name = "__codelineno-147-11" href = "#__codelineno-147-11" > < / 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-147-12" name = "__codelineno-147-12" href = "#__codelineno-147-12" > < / 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-148-1" name = "__codelineno-148-1" href = "#__codelineno-148-1" > < / a > < span class = "cm" > /* 阶乘阶（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 = "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-148-3" name = "__codelineno-148-3" href = "#__codelineno-148-3" > < / 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-148-4" name = "__codelineno-148-4" href = "#__codelineno-148-4" > < / a > < span class = "k" > return< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-148-5" name = "__codelineno-148-5" href = "#__codelineno-148-5" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-148-6" name = "__codelineno-148-6" href = "#__codelineno-148-6" > < / a > < span class = "kd" > var< / span > < span class = "nv" > count< / span > < span class = "p" > =< / span > < span class = "mi" > 0< / span >
< a id = "__codelineno-148-7" name = "__codelineno-148-7" href = "#__codelineno-148-7" > < / a > < span class = "c1" > // 从 1 个分裂出 n 个< / span >
< a id = "__codelineno-148-8" name = "__codelineno-148-8" href = "#__codelineno-148-8" > < / 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-148-9" name = "__codelineno-148-9" href = "#__codelineno-148-9" > < / 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-148-10" name = "__codelineno-148-10" href = "#__codelineno-148-10" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-148-11" name = "__codelineno-148-11" href = "#__codelineno-148-11" > < / a > < span class = "k" > return< / span > < span class = "bp" > count< / span >
< a id = "__codelineno-148-12" name = "__codelineno-148-12" href = "#__codelineno-148-12" > < / 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-149-1" name = "__codelineno-149-1" href = "#__codelineno-149-1" > < / a > < span class = "c1" > // 阶乘阶（递归实现）< / span >
< a id = "__codelineno-149-2" name = "__codelineno-149-2" href = "#__codelineno-149-2" > < / 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-149-3" name = "__codelineno-149-3" href = "#__codelineno-149-3" > < / 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-149-4" name = "__codelineno-149-4" href = "#__codelineno-149-4" > < / 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-149-5" name = "__codelineno-149-5" href = "#__codelineno-149-5" > < / 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-149-6" name = "__codelineno-149-6" href = "#__codelineno-149-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从 1 个分裂出 n 个< / span >
< a id = "__codelineno-149-7" name = "__codelineno-149-7" href = "#__codelineno-149-7" > < / 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-149-8" name = "__codelineno-149-8" href = "#__codelineno-149-8" > < / 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-149-9" name = "__codelineno-149-9" href = "#__codelineno-149-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-149-10" name = "__codelineno-149-10" href = "#__codelineno-149-10" > < / 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-149-11" name = "__codelineno-149-11" href = "#__codelineno-149-11" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
2023-02-26 18:18:03 +08:00
< p > < img alt = "阶乘阶的时间复杂度" src = "../time_complexity.assets/time_complexity_factorial.png" / > < / p >
2023-02-26 19:53:32 +08:00
< p align = "center" > Fig. 阶乘阶的时间复杂度 < / p >
2023-02-24 18:46:22 +08:00
< h2 id = "226" > 2.2.6. 最差、最佳、平均时间复杂度< a class = "headerlink" href = "#226" title = "Permanent link" > ¶ < / a > < / h2 >
2023-02-08 14:54:41 +08:00
< p > < strong > 某些算法的时间复杂度不是恒定的，而是与输入数据的分布有关< / strong > 。举一个例子，输入一个长度为 < span class = "arithmatex" > \(n\)< / span > 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，但元素顺序是随机打乱的；算法的任务是返回元素 < 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，则需完整遍历数组，此时达到 < strong > 最差时间复杂度 < span class = "arithmatex" > \(O(n)\)< / span > < / strong > ； < / li >
< li > 当 < code > nums = [1, ?, ?, ...]< / code > ，即当首个数字为 < span class = "arithmatex" > \(1\)< / span > 时，无论数组多长都不需要继续遍历，此时达到 < strong > 最佳时间复杂度 < span class = "arithmatex" > \(\Omega(1)\)< / span > < / strong > ； < / li >
< / ul >
< p > 「函数渐近上界」使用大 < span class = "arithmatex" > \(O\)< / span > 记号表示，代表「最差时间复杂度」。与之对应，「函数渐近下界」用 < span class = "arithmatex" > \(\Omega\)< / span > 记号（ ） ， < / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "16:10" > < input checked = "checked" id = "__tabbed_16_1" name = "__tabbed_16" type = "radio" / > < input id = "__tabbed_16_2" name = "__tabbed_16" type = "radio" / > < input id = "__tabbed_16_3" name = "__tabbed_16" type = "radio" / > < input id = "__tabbed_16_4" name = "__tabbed_16" type = "radio" / > < input id = "__tabbed_16_5" name = "__tabbed_16" type = "radio" / > < input id = "__tabbed_16_6" name = "__tabbed_16" type = "radio" / > < input id = "__tabbed_16_7" name = "__tabbed_16" type = "radio" / > < input id = "__tabbed_16_8" name = "__tabbed_16" type = "radio" / > < input id = "__tabbed_16_9" name = "__tabbed_16" type = "radio" / > < input id = "__tabbed_16_10" name = "__tabbed_16" type = "radio" / > < div class = "tabbed-labels" > < label for = "__tabbed_16_1" > Java< / label > < label for = "__tabbed_16_2" > C++< / label > < label for = "__tabbed_16_3" > Python< / label > < label for = "__tabbed_16_4" > Go< / label > < label for = "__tabbed_16_5" > JavaScript< / label > < label for = "__tabbed_16_6" > TypeScript< / label > < label for = "__tabbed_16_7" > C< / label > < label for = "__tabbed_16_8" > C#< / label > < label for = "__tabbed_16_9" > Swift< / label > < label for = "__tabbed_16_10" > Zig< / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > worst_best_time_complexity.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-150-1" name = "__codelineno-150-1" href = "#__codelineno-150-1" > < / 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-150-2" name = "__codelineno-150-2" href = "#__codelineno-150-2" > < / 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-150-3" name = "__codelineno-150-3" href = "#__codelineno-150-3" > < / 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-150-4" name = "__codelineno-150-4" href = "#__codelineno-150-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 生成数组 nums = { 1, 2, 3, ..., n }< / span >
< a id = "__codelineno-150-5" name = "__codelineno-150-5" href = "#__codelineno-150-5" > < / 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-150-6" name = "__codelineno-150-6" href = "#__codelineno-150-6" > < / 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-150-7" name = "__codelineno-150-7" href = "#__codelineno-150-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-150-8" name = "__codelineno-150-8" href = "#__codelineno-150-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 随机打乱数组元素< / span >
< a id = "__codelineno-150-9" name = "__codelineno-150-9" href = "#__codelineno-150-9" > < / 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-150-10" name = "__codelineno-150-10" href = "#__codelineno-150-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // Integer[] -> int[]< / span >
< a id = "__codelineno-150-11" name = "__codelineno-150-11" href = "#__codelineno-150-11" > < / 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-150-12" name = "__codelineno-150-12" href = "#__codelineno-150-12" > < / 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-150-13" name = "__codelineno-150-13" href = "#__codelineno-150-13" > < / 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-150-14" name = "__codelineno-150-14" href = "#__codelineno-150-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-150-15" name = "__codelineno-150-15" href = "#__codelineno-150-15" > < / 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-150-16" name = "__codelineno-150-16" href = "#__codelineno-150-16" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-150-17" name = "__codelineno-150-17" href = "#__codelineno-150-17" > < / a >
< a id = "__codelineno-150-18" name = "__codelineno-150-18" href = "#__codelineno-150-18" > < / a > < span class = "cm" > /* 查找数组 nums 中数字 1 所在索引 */< / span >
< a id = "__codelineno-150-19" name = "__codelineno-150-19" href = "#__codelineno-150-19" > < / 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-150-20" name = "__codelineno-150-20" href = "#__codelineno-150-20" > < / 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-150-21" name = "__codelineno-150-21" href = "#__codelineno-150-21" > < / 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-150-22" name = "__codelineno-150-22" href = "#__codelineno-150-22" > < / 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-150-23" name = "__codelineno-150-23" href = "#__codelineno-150-23" > < / 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-150-24" name = "__codelineno-150-24" href = "#__codelineno-150-24" > < / 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-150-25" name = "__codelineno-150-25" href = "#__codelineno-150-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-150-26" name = "__codelineno-150-26" href = "#__codelineno-150-26" > < / 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-150-27" name = "__codelineno-150-27" href = "#__codelineno-150-27" > < / a > < span class = "p" > }< / 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-151-1" name = "__codelineno-151-1" href = "#__codelineno-151-1" > < / 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-151-2" name = "__codelineno-151-2" href = "#__codelineno-151-2" > < / 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-151-3" name = "__codelineno-151-3" href = "#__codelineno-151-3" > < / 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-151-4" name = "__codelineno-151-4" href = "#__codelineno-151-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 生成数组 nums = { 1, 2, 3, ..., n }< / span >
< a id = "__codelineno-151-5" name = "__codelineno-151-5" href = "#__codelineno-151-5" > < / 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-151-6" name = "__codelineno-151-6" href = "#__codelineno-151-6" > < / 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-151-7" name = "__codelineno-151-7" href = "#__codelineno-151-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-151-8" name = "__codelineno-151-8" href = "#__codelineno-151-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 使用系统时间生成随机种子< / span >
< a id = "__codelineno-151-9" name = "__codelineno-151-9" href = "#__codelineno-151-9" > < / 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-151-10" name = "__codelineno-151-10" href = "#__codelineno-151-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 随机打乱数组元素< / span >
< a id = "__codelineno-151-11" name = "__codelineno-151-11" href = "#__codelineno-151-11" > < / 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-151-12" name = "__codelineno-151-12" href = "#__codelineno-151-12" > < / 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-151-13" name = "__codelineno-151-13" href = "#__codelineno-151-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-151-14" name = "__codelineno-151-14" href = "#__codelineno-151-14" > < / a >
< a id = "__codelineno-151-15" name = "__codelineno-151-15" href = "#__codelineno-151-15" > < / a > < span class = "cm" > /* 查找数组 nums 中数字 1 所在索引 */< / span >
< a id = "__codelineno-151-16" name = "__codelineno-151-16" href = "#__codelineno-151-16" > < / 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 = "n" > nums< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-151-17" name = "__codelineno-151-17" href = "#__codelineno-151-17" > < / 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-151-18" name = "__codelineno-151-18" href = "#__codelineno-151-18" > < / 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-151-19" name = "__codelineno-151-19" href = "#__codelineno-151-19" > < / 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-151-20" name = "__codelineno-151-20" href = "#__codelineno-151-20" > < / 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-151-21" name = "__codelineno-151-21" href = "#__codelineno-151-21" > < / 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-151-22" name = "__codelineno-151-22" href = "#__codelineno-151-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-151-23" name = "__codelineno-151-23" href = "#__codelineno-151-23" > < / 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-151-24" name = "__codelineno-151-24" href = "#__codelineno-151-24" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-03-03 02:46:43 +08:00
< div class = "highlight" > < span class = "filename" > worst_best_time_complexity.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-152-1" name = "__codelineno-152-1" href = "#__codelineno-152-1" > < / 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 >
< a id = "__codelineno-152-2" name = "__codelineno-152-2" href = "#__codelineno-152-2" > < / 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 >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-152-3" name = "__codelineno-152-3" href = "#__codelineno-152-3" > < / a > < span class = "c1" > # 生成数组 nums =: 1, 2, 3, ..., n< / span >
< a id = "__codelineno-152-4" name = "__codelineno-152-4" href = "#__codelineno-152-4" > < / 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-152-5" name = "__codelineno-152-5" href = "#__codelineno-152-5" > < / a > < span class = "c1" > # 随机打乱数组元素< / span >
< a id = "__codelineno-152-6" name = "__codelineno-152-6" href = "#__codelineno-152-6" > < / 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-152-7" name = "__codelineno-152-7" href = "#__codelineno-152-7" > < / a > < span class = "k" > return< / span > < span class = "n" > nums< / span >
< a id = "__codelineno-152-8" name = "__codelineno-152-8" href = "#__codelineno-152-8" > < / a >
2023-03-03 02:46:43 +08:00
< a id = "__codelineno-152-9" name = "__codelineno-152-9" href = "#__codelineno-152-9" > < / 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 >
< a id = "__codelineno-152-10" name = "__codelineno-152-10" href = "#__codelineno-152-10" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 查找数组 nums 中数字 1 所在索引 " " " < / span >
2023-02-08 14:54:41 +08:00
< a id = "__codelineno-152-11" name = "__codelineno-152-11" href = "#__codelineno-152-11" > < / 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-152-12" name = "__codelineno-152-12" href = "#__codelineno-152-12" > < / 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-152-13" name = "__codelineno-152-13" href = "#__codelineno-152-13" > < / 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-152-14" name = "__codelineno-152-14" href = "#__codelineno-152-14" > < / 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-152-15" name = "__codelineno-152-15" href = "#__codelineno-152-15" > < / a > < span class = "k" > return< / span > < span class = "n" > i< / span >
< a id = "__codelineno-152-16" name = "__codelineno-152-16" href = "#__codelineno-152-16" > < / 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.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-153-1" name = "__codelineno-153-1" href = "#__codelineno-153-1" > < / 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-153-2" name = "__codelineno-153-2" href = "#__codelineno-153-2" > < / 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-153-3" name = "__codelineno-153-3" href = "#__codelineno-153-3" > < / 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-153-4" name = "__codelineno-153-4" href = "#__codelineno-153-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 生成数组 nums = { 1, 2, 3, ..., n }< / span >
< a id = "__codelineno-153-5" name = "__codelineno-153-5" href = "#__codelineno-153-5" > < / 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-153-6" name = "__codelineno-153-6" href = "#__codelineno-153-6" > < / 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-153-7" name = "__codelineno-153-7" href = "#__codelineno-153-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-153-8" name = "__codelineno-153-8" href = "#__codelineno-153-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 随机打乱数组元素< / span >
< a id = "__codelineno-153-9" name = "__codelineno-153-9" href = "#__codelineno-153-9" > < / 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-153-10" name = "__codelineno-153-10" href = "#__codelineno-153-10" > < / 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-153-11" name = "__codelineno-153-11" href = "#__codelineno-153-11" > < / a > < span class = "w" > < / span > < span class = "p" > })< / span >
< a id = "__codelineno-153-12" name = "__codelineno-153-12" href = "#__codelineno-153-12" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span >
< a id = "__codelineno-153-13" name = "__codelineno-153-13" href = "#__codelineno-153-13" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-153-14" name = "__codelineno-153-14" href = "#__codelineno-153-14" > < / a >
< a id = "__codelineno-153-15" name = "__codelineno-153-15" href = "#__codelineno-153-15" > < / a > < span class = "cm" > /* 查找数组 nums 中数字 1 所在索引 */< / span >
< a id = "__codelineno-153-16" name = "__codelineno-153-16" href = "#__codelineno-153-16" > < / 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-153-17" name = "__codelineno-153-17" href = "#__codelineno-153-17" > < / 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-153-18" name = "__codelineno-153-18" href = "#__codelineno-153-18" > < / 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-153-19" name = "__codelineno-153-19" href = "#__codelineno-153-19" > < / 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-153-20" name = "__codelineno-153-20" href = "#__codelineno-153-20" > < / 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-153-21" name = "__codelineno-153-21" href = "#__codelineno-153-21" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "nx" > i< / span >
< a id = "__codelineno-153-22" name = "__codelineno-153-22" href = "#__codelineno-153-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-153-23" name = "__codelineno-153-23" href = "#__codelineno-153-23" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-153-24" name = "__codelineno-153-24" href = "#__codelineno-153-24" > < / 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-153-25" name = "__codelineno-153-25" href = "#__codelineno-153-25" > < / 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-154-1" name = "__codelineno-154-1" href = "#__codelineno-154-1" > < / 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-154-2" name = "__codelineno-154-2" href = "#__codelineno-154-2" > < / 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-154-3" name = "__codelineno-154-3" href = "#__codelineno-154-3" > < / 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-154-4" name = "__codelineno-154-4" href = "#__codelineno-154-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 生成数组 nums = { 1, 2, 3, ..., n }< / span >
< a id = "__codelineno-154-5" name = "__codelineno-154-5" href = "#__codelineno-154-5" > < / 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-154-6" name = "__codelineno-154-6" href = "#__codelineno-154-6" > < / 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-154-7" name = "__codelineno-154-7" href = "#__codelineno-154-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-154-8" name = "__codelineno-154-8" href = "#__codelineno-154-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 随机打乱数组元素< / span >
< a id = "__codelineno-154-9" name = "__codelineno-154-9" href = "#__codelineno-154-9" > < / 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-154-10" name = "__codelineno-154-10" href = "#__codelineno-154-10" > < / 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-154-11" name = "__codelineno-154-11" href = "#__codelineno-154-11" > < / 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-154-12" name = "__codelineno-154-12" href = "#__codelineno-154-12" > < / 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-154-13" name = "__codelineno-154-13" href = "#__codelineno-154-13" > < / 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-154-14" name = "__codelineno-154-14" href = "#__codelineno-154-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-154-15" name = "__codelineno-154-15" href = "#__codelineno-154-15" > < / 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-154-16" name = "__codelineno-154-16" href = "#__codelineno-154-16" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-154-17" name = "__codelineno-154-17" href = "#__codelineno-154-17" > < / a >
< a id = "__codelineno-154-18" name = "__codelineno-154-18" href = "#__codelineno-154-18" > < / a > < span class = "cm" > /* 查找数组 nums 中数字 1 所在索引 */< / span >
< a id = "__codelineno-154-19" name = "__codelineno-154-19" href = "#__codelineno-154-19" > < / 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-154-20" name = "__codelineno-154-20" href = "#__codelineno-154-20" > < / 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-154-21" name = "__codelineno-154-21" href = "#__codelineno-154-21" > < / 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-154-22" name = "__codelineno-154-22" href = "#__codelineno-154-22" > < / 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-154-23" name = "__codelineno-154-23" href = "#__codelineno-154-23" > < / 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-154-24" name = "__codelineno-154-24" href = "#__codelineno-154-24" > < / 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-154-25" name = "__codelineno-154-25" href = "#__codelineno-154-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-154-26" name = "__codelineno-154-26" href = "#__codelineno-154-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-154-27" name = "__codelineno-154-27" href = "#__codelineno-154-27" > < / 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-154-28" name = "__codelineno-154-28" href = "#__codelineno-154-28" > < / 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-155-1" name = "__codelineno-155-1" href = "#__codelineno-155-1" > < / 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-155-2" name = "__codelineno-155-2" href = "#__codelineno-155-2" > < / 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-155-3" name = "__codelineno-155-3" href = "#__codelineno-155-3" > < / 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-155-4" name = "__codelineno-155-4" href = "#__codelineno-155-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 生成数组 nums = { 1, 2, 3, ..., n }< / span >
< a id = "__codelineno-155-5" name = "__codelineno-155-5" href = "#__codelineno-155-5" > < / 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-155-6" name = "__codelineno-155-6" href = "#__codelineno-155-6" > < / 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-155-7" name = "__codelineno-155-7" href = "#__codelineno-155-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-155-8" name = "__codelineno-155-8" href = "#__codelineno-155-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 随机打乱数组元素< / span >
< a id = "__codelineno-155-9" name = "__codelineno-155-9" href = "#__codelineno-155-9" > < / 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-155-10" name = "__codelineno-155-10" href = "#__codelineno-155-10" > < / 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-155-11" name = "__codelineno-155-11" href = "#__codelineno-155-11" > < / 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-155-12" name = "__codelineno-155-12" href = "#__codelineno-155-12" > < / 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-155-13" name = "__codelineno-155-13" href = "#__codelineno-155-13" > < / 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-155-14" name = "__codelineno-155-14" href = "#__codelineno-155-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-155-15" name = "__codelineno-155-15" href = "#__codelineno-155-15" > < / 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-155-16" name = "__codelineno-155-16" href = "#__codelineno-155-16" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-155-17" name = "__codelineno-155-17" href = "#__codelineno-155-17" > < / a >
< a id = "__codelineno-155-18" name = "__codelineno-155-18" href = "#__codelineno-155-18" > < / a > < span class = "cm" > /* 查找数组 nums 中数字 1 所在索引 */< / span >
< a id = "__codelineno-155-19" name = "__codelineno-155-19" href = "#__codelineno-155-19" > < / 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-155-20" name = "__codelineno-155-20" href = "#__codelineno-155-20" > < / 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-155-21" name = "__codelineno-155-21" href = "#__codelineno-155-21" > < / 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-155-22" name = "__codelineno-155-22" href = "#__codelineno-155-22" > < / 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-155-23" name = "__codelineno-155-23" href = "#__codelineno-155-23" > < / 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-155-24" name = "__codelineno-155-24" href = "#__codelineno-155-24" > < / 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-155-25" name = "__codelineno-155-25" href = "#__codelineno-155-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-155-26" name = "__codelineno-155-26" href = "#__codelineno-155-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-155-27" name = "__codelineno-155-27" href = "#__codelineno-155-27" > < / 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-155-28" name = "__codelineno-155-28" href = "#__codelineno-155-28" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
2023-02-28 00:16:29 +08:00
< div class = "highlight" > < span class = "filename" > worst_best_time_complexity.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-156-1" name = "__codelineno-156-1" href = "#__codelineno-156-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > randomNumbers< / span > < span class = "p" > }< / span >
< a id = "__codelineno-156-2" name = "__codelineno-156-2" href = "#__codelineno-156-2" > < / a >
< a id = "__codelineno-156-3" name = "__codelineno-156-3" href = "#__codelineno-156-3" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > findOne< / span > < span class = "p" > }< / span >
2023-02-08 14:54:41 +08:00
< / 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-157-1" name = "__codelineno-157-1" href = "#__codelineno-157-1" > < / 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-157-2" name = "__codelineno-157-2" href = "#__codelineno-157-2" > < / 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 >
< a id = "__codelineno-157-3" name = "__codelineno-157-3" href = "#__codelineno-157-3" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-157-4" name = "__codelineno-157-4" href = "#__codelineno-157-4" > < / 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-157-5" name = "__codelineno-157-5" href = "#__codelineno-157-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 生成数组 nums = { 1, 2, 3, ..., n }< / 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 = "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-157-7" name = "__codelineno-157-7" href = "#__codelineno-157-7" > < / a > < span class = "w" > < / 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 = "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-157-9" name = "__codelineno-157-9" href = "#__codelineno-157-9" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-157-10" name = "__codelineno-157-10" href = "#__codelineno-157-10" > < / a >
< a id = "__codelineno-157-11" name = "__codelineno-157-11" href = "#__codelineno-157-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // 随机打乱数组元素< / span >
< a id = "__codelineno-157-12" name = "__codelineno-157-12" href = "#__codelineno-157-12" > < / 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 = "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 >
< a id = "__codelineno-157-13" name = "__codelineno-157-13" href = "#__codelineno-157-13" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-157-14" name = "__codelineno-157-14" href = "#__codelineno-157-14" > < / 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-157-15" name = "__codelineno-157-15" href = "#__codelineno-157-15" > < / 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-157-16" name = "__codelineno-157-16" href = "#__codelineno-157-16" > < / 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-157-17" name = "__codelineno-157-17" href = "#__codelineno-157-17" > < / 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-157-18" name = "__codelineno-157-18" href = "#__codelineno-157-18" > < / 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-157-19" name = "__codelineno-157-19" href = "#__codelineno-157-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-157-20" name = "__codelineno-157-20" href = "#__codelineno-157-20" > < / 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-157-21" name = "__codelineno-157-21" href = "#__codelineno-157-21" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-157-22" name = "__codelineno-157-22" href = "#__codelineno-157-22" > < / a >
< a id = "__codelineno-157-23" name = "__codelineno-157-23" href = "#__codelineno-157-23" > < / a > < span class = "cm" > /* 查找数组 nums 中数字 1 所在索引 */< / span >
< a id = "__codelineno-157-24" name = "__codelineno-157-24" href = "#__codelineno-157-24" > < / 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 >
< a id = "__codelineno-157-25" name = "__codelineno-157-25" href = "#__codelineno-157-25" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-157-26" name = "__codelineno-157-26" href = "#__codelineno-157-26" > < / 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 >
< a id = "__codelineno-157-27" name = "__codelineno-157-27" href = "#__codelineno-157-27" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-157-28" name = "__codelineno-157-28" href = "#__codelineno-157-28" > < / 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-157-29" name = "__codelineno-157-29" href = "#__codelineno-157-29" > < / 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-157-30" name = "__codelineno-157-30" href = "#__codelineno-157-30" > < / 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-157-31" name = "__codelineno-157-31" href = "#__codelineno-157-31" > < / 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-157-32" name = "__codelineno-157-32" href = "#__codelineno-157-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-157-33" name = "__codelineno-157-33" href = "#__codelineno-157-33" > < / 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-157-34" name = "__codelineno-157-34" href = "#__codelineno-157-34" > < / 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-158-1" name = "__codelineno-158-1" href = "#__codelineno-158-1" > < / 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-158-2" name = "__codelineno-158-2" href = "#__codelineno-158-2" > < / 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-158-3" name = "__codelineno-158-3" href = "#__codelineno-158-3" > < / a > < span class = "c1" > // 生成数组 nums = { 1, 2, 3, ..., n }< / span >
< a id = "__codelineno-158-4" name = "__codelineno-158-4" href = "#__codelineno-158-4" > < / 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-158-5" name = "__codelineno-158-5" href = "#__codelineno-158-5" > < / a > < span class = "c1" > // 随机打乱数组元素< / span >
< a id = "__codelineno-158-6" name = "__codelineno-158-6" href = "#__codelineno-158-6" > < / a > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > shuffle< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-158-7" name = "__codelineno-158-7" href = "#__codelineno-158-7" > < / a > < span class = "k" > return< / span > < span class = "n" > nums< / span >
< a id = "__codelineno-158-8" name = "__codelineno-158-8" href = "#__codelineno-158-8" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-158-9" name = "__codelineno-158-9" href = "#__codelineno-158-9" > < / a >
< a id = "__codelineno-158-10" name = "__codelineno-158-10" href = "#__codelineno-158-10" > < / a > < span class = "cm" > /* 查找数组 nums 中数字 1 所在索引 */< / span >
< a id = "__codelineno-158-11" name = "__codelineno-158-11" href = "#__codelineno-158-11" > < / 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-158-12" name = "__codelineno-158-12" href = "#__codelineno-158-12" > < / 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-158-13" name = "__codelineno-158-13" href = "#__codelineno-158-13" > < / 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-158-14" name = "__codelineno-158-14" href = "#__codelineno-158-14" > < / 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-158-15" name = "__codelineno-158-15" href = "#__codelineno-158-15" > < / 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-158-16" name = "__codelineno-158-16" href = "#__codelineno-158-16" > < / a > < span class = "k" > return< / span > < span class = "n" > i< / span >
< a id = "__codelineno-158-17" name = "__codelineno-158-17" href = "#__codelineno-158-17" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-158-18" name = "__codelineno-158-18" href = "#__codelineno-158-18" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-158-19" name = "__codelineno-158-19" href = "#__codelineno-158-19" > < / a > < span class = "k" > return< / span > < span class = "o" > -< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-158-20" name = "__codelineno-158-20" href = "#__codelineno-158-20" > < / 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-159-1" name = "__codelineno-159-1" href = "#__codelineno-159-1" > < / 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-159-2" name = "__codelineno-159-2" href = "#__codelineno-159-2" > < / 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-159-3" name = "__codelineno-159-3" href = "#__codelineno-159-3" > < / 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-159-4" name = "__codelineno-159-4" href = "#__codelineno-159-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 生成数组 nums = { 1, 2, 3, ..., n }< / span >
< a id = "__codelineno-159-5" name = "__codelineno-159-5" href = "#__codelineno-159-5" > < / 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-159-6" name = "__codelineno-159-6" href = "#__codelineno-159-6" > < / 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-159-7" name = "__codelineno-159-7" href = "#__codelineno-159-7" > < / a > < span class = "w" > < / 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 = "c1" > // 随机打乱数组元素< / span >
< a id = "__codelineno-159-9" name = "__codelineno-159-9" href = "#__codelineno-159-9" > < / 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-159-10" name = "__codelineno-159-10" href = "#__codelineno-159-10" > < / 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-159-11" name = "__codelineno-159-11" href = "#__codelineno-159-11" > < / 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-159-12" name = "__codelineno-159-12" href = "#__codelineno-159-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-159-13" name = "__codelineno-159-13" href = "#__codelineno-159-13" > < / a >
< a id = "__codelineno-159-14" name = "__codelineno-159-14" href = "#__codelineno-159-14" > < / a > < span class = "c1" > // 查找数组 nums 中数字 1 所在索引< / span >
< a id = "__codelineno-159-15" name = "__codelineno-159-15" href = "#__codelineno-159-15" > < / 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-159-16" name = "__codelineno-159-16" href = "#__codelineno-159-16" > < / 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-159-17" name = "__codelineno-159-17" href = "#__codelineno-159-17" > < / 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-159-18" name = "__codelineno-159-18" href = "#__codelineno-159-18" > < / 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-159-19" name = "__codelineno-159-19" href = "#__codelineno-159-19" > < / 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-159-20" name = "__codelineno-159-20" href = "#__codelineno-159-20" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-159-21" name = "__codelineno-159-21" href = "#__codelineno-159-21" > < / 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-159-22" name = "__codelineno-159-22" href = "#__codelineno-159-22" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< div class = "admonition tip" >
< p class = "admonition-title" > Tip< / p >
< p > 我们在实际应用中很少使用「最佳时间复杂度」，因为往往只有很小概率下才能达到，会带来一定的误导性。反之，「最差时间复杂度」最为实用，因为它给出了一个“效率安全值”，让我们可以放心地使用算法。< / p >
< / div >
< p > 从上述示例可以看出，最差或最佳时间复杂度只出现在“特殊分布的数据”中，这些情况的出现概率往往很小，因此并不能最真实地反映算法运行效率。< strong > 相对地，「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，用 < span class = "arithmatex" > \(\Theta\)< / span > 记号（ ） < / strong > 。< / 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则是数组长度的一半 < span class = "arithmatex" > \(\frac{n}{2}\)< / span > ，平均时间复杂度为 < span class = "arithmatex" > \(\Theta(\frac{n}{2}) = \Theta(n)\)< / span > 。< / p >
< p > 但在实际应用中，尤其是较为复杂的算法，计算平均时间复杂度比较困难，因为很难简便地分析出在数据分布下的整体数学期望。这种情况下，我们一般使用最差时间复杂度来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 > 实际中我们经常使用「大 < span class = "arithmatex" > \(O\)< / span > 符号」来表示「平均复杂度」，这样严格意义上来说是不规范的。这可能是因为 < span class = "arithmatex" > \(O\)< / span > 符号实在是太朗朗上口了。< / br > 如果在本书和其他资料中看到类似 < strong > 平均时间复杂度 < span class = "arithmatex" > \(O(n)\)< / span > < / strong > 的表述，请你直接理解为 < span class = "arithmatex" > \(\Theta(n)\)< / span > 即可。< / p >
< / div >
< h2 id = "__comments" > 评论< / h2 >
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