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3.2. &nbsp; 数据结构分类
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4.1. &nbsp; 数组
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4.2. &nbsp; 链表
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4.3. &nbsp; 列表
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5.1. &nbsp; 栈
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5.2. &nbsp; 队列
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5.3. &nbsp; 双向队列
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6.1. &nbsp; 哈希表
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6.2. &nbsp; 哈希冲突处理
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7. &nbsp; &nbsp; 树
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7.1. &nbsp; 二叉树
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7.2. &nbsp; 二叉树遍历
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7.3. &nbsp; 二叉搜索树
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7.4. &nbsp; AVL 树 *
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8. &nbsp; &nbsp; 堆
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8. &nbsp; &nbsp; 堆
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8.1. &nbsp; 堆
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8.2. &nbsp; 建堆操作 *
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9. &nbsp; &nbsp; 图
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9.1. &nbsp; 图
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9.2. &nbsp; 图基础操作
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9.3. &nbsp; 图的遍历（New）
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9.4. &nbsp; 小结
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10. &nbsp; &nbsp; 查找算法
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10.1. &nbsp; 线性查找
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10.2. &nbsp; 二分查找
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10.3. &nbsp; 哈希查找
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11. &nbsp; &nbsp; 排序算法
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11.1. &nbsp; 排序简介
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11.2. &nbsp; 冒泡排序
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11.3. &nbsp; 插入排序
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11.4. &nbsp; 快速排序
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11.5. &nbsp; 归并排序
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11.6. &nbsp; 桶排序（New）
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11.7. &nbsp; 计数排序（New）
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11.8. &nbsp; 基数排序（New）
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0.2.1. &nbsp; 算法学习路线
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0.2.2. &nbsp; 行文风格约定
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0.2.4. &nbsp; 在代码实践中加深理解
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<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_preface/suggestions.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>
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<h1 id="02">0.2. &nbsp; 如何使用本书<a class="headerlink" href="#02" title="Permanent link">&para;</a></h1>
<p>建议通读本节内容，以获取最佳阅读体验。</p>
<h2 id="021">0.2.1. &nbsp; 算法学习路线<a class="headerlink" href="#021" title="Permanent link">&para;</a></h2>
<p>总体上看，我认为可将学习数据结构与算法的过程分为三个阶段。</p>
<ol>
<li><strong>算法入门</strong>。熟悉各种数据结构的特点、用法，学习各种算法的原理、流程、用途、效率等。</li>
<li><strong>刷算法题</strong>。可以先从热门题单开刷，推荐<a href="https://leetcode.cn/problem-list/xb9nqhhg/">剑指 Offer</a>、<a href="https://leetcode.cn/problem-list/2cktkvj/">LeetCode Hot 100</a>，先积累至少 100 道题量，熟悉大多数的算法问题。刚开始刷题时，“遗忘”是最大的困扰点，但这是很正常的，请不要担心。学习中有一种概念叫“周期性回顾”，同一道题隔段时间做一次，在重复 3 轮以上后，往往就能牢记于心了。</li>
<li><strong>搭建知识体系</strong>。在学习方面，可以阅读算法专栏文章、解题框架、算法教材，不断地丰富知识体系。在刷题方面，可以开始采用进阶刷题方案，例如按专题分类、一题多解、一解多题等，相关刷题心得可以在各个社区中找到。</li>
</ol>
<p>作为一本入门教程，<strong>本书内容主要对应“第一阶段”</strong>，致力于帮助你更高效地开展第二、三阶段的学习。</p>
<p><img alt="算法学习路线" src="../suggestions.assets/learning_route.png" /></p>
<p align="center"> Fig. 算法学习路线 </p>
<h2 id="022">0.2.2. &nbsp; 行文风格约定<a class="headerlink" href="#022" title="Permanent link">&para;</a></h2>
<p>标题后标注 <code>*</code> 的是选读章节，内容相对较难。如果你的时间有限，建议可以先跳过。</p>
<p>文章中的重要名词会用 <code>「括号」</code> 标注，例如 <code>「数组 Array」</code> 。建议记住这些名词，包括英文翻译，以便后续阅读文献时使用。</p>
<p>重点内容、总起句、总结句会被 <strong>加粗</strong> ，此类文字值得特别关注。</p>
<p>专有名词和有特指含义的词句会使用 <code>“双引号”</code> 标注，以避免歧义。</p>
<p>本书部分放弃了编程语言的注释规范，以换取更加紧凑的内容排版。注释主要分为三种类型：标题注释、内容注释、多行注释。</p>
<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>
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<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 标题注释，用于标注函数、类、测试样例等 */</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="cm">/**</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="cm"> * 多行</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="cm"> * 注释</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="cm"> */</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="cm">/* 标题注释，用于标注函数、类、测试样例等 */</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="cm">/**</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="cm"> * 多行</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm"> * 注释</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="cm"> */</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="sd">&quot;&quot;&quot; 标题注释，用于标注函数、类、测试样例等 &quot;&quot;&quot;</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="c1"># 内容注释，用于详解代码</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="sd">&quot;&quot;&quot;</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="sd">多行</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="sd">注释</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="sd">&quot;&quot;&quot;</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="cm">/* 标题注释，用于标注函数、类、测试样例等 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="cm">/**</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="cm"> * 多行</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm"> * 注释</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="cm"> */</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="cm">/* 标题注释，用于标注函数、类、测试样例等 */</span>
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/**</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="cm"> * 多行</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm"> * 注释</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="cm"> */</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="cm">/* 标题注释，用于标注函数、类、测试样例等 */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/**</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="cm"> * 多行</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="cm"> * 注释</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="cm"> */</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="cm">/* 标题注释，用于标注函数、类、测试样例等 */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/**</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="cm"> * 多行</span>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="cm"> * 注释</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="cm"> */</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="cm">/* 标题注释，用于标注函数、类、测试样例等 */</span>
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/**</span>
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="cm"> * 多行</span>
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="cm"> * 注释</span>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="cm"> */</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="cm">/* 标题注释，用于标注函数、类、测试样例等 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/**</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="cm"> * 多行</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="cm"> * 注释</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="cm"> */</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// 标题注释，用于标注函数、类、测试样例等</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// 多行</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="c1">// 注释</span>
</code></pre></div>
</div>
</div>
</div>
<h2 id="023">0.2.3. &nbsp; 在动画图解中高效学习<a class="headerlink" href="#023" title="Permanent link">&para;</a></h2>
<p>视频和图片相比于文字的信息密度和结构化程度更高，更容易理解。在本书中，<strong>知识重难点会主要以动画、图解的形式呈现</strong>，而文字的作用则是作为动画和图的解释与补充。</p>
<p>阅读本书时，若发现某段内容提供了动画或图解，<strong>建议你以图为主线</strong>，将文字内容（一般在图的上方）对齐到图中内容，综合来理解。</p>
<p><img alt="动画图解示例" src="../suggestions.assets/animation.gif" /></p>
<p align="center"> Fig. 动画图解示例 </p>
<h2 id="024">0.2.4. &nbsp; 在代码实践中加深理解<a class="headerlink" href="#024" title="Permanent link">&para;</a></h2>
<p>本书的配套代码托管在<a href="https://github.com/krahets/hello-algo">GitHub 仓库</a>，<strong>源代码包含详细注释，配有测试样例，可以直接运行</strong>。</p>
<ul>
<li>若学习时间紧张，<strong>建议至少将所有代码通读并运行一遍</strong>。</li>
<li>若时间允许，<strong>强烈建议对照着代码自己敲一遍</strong>。相比于读代码，写代码的过程往往能带来新的收获。</li>
</ul>
<p><img alt="运行代码示例" src="../suggestions.assets/running_code.gif" /></p>
<p align="center"> Fig. 运行代码示例 </p>
<p><strong>第一步：安装本地编程环境</strong>。参照<a href="https://www.hello-algo.com/chapter_appendix/installation/">附录教程</a>，如果已有可直接跳过。</p>
<p><strong>第二步：下载代码仓</strong>。如果已经安装 <a href="https://git-scm.com/downloads">Git</a> ，可以通过命令行来克隆代码仓。</p>
<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a>git<span class="w"> </span>clone<span class="w"> </span>https://github.com/krahets/hello-algo.git
</code></pre></div>
<p>当然，你也可以点击“Download ZIP”直接下载代码压缩包，本地解压即可。</p>
<p><img alt="克隆仓库与下载代码" src="../suggestions.assets/download_code.png" /></p>
<p align="center"> Fig. 克隆仓库与下载代码 </p>
<p><strong>第三步：运行源代码</strong>。若代码块的顶部标有文件名称，则可在仓库 <code>codes</code> 文件夹中找到对应的 <strong>源代码文件</strong>。源代码文件可以帮助你省去不必要的调试时间，将精力集中在学习内容上。</p>
<p><img alt="代码块与对应的源代码文件" src="../suggestions.assets/code_md_to_repo.png" /></p>
<p align="center"> Fig. 代码块与对应的源代码文件 </p>
<h2 id="025">0.2.5. &nbsp; 在提问讨论中共同成长<a class="headerlink" href="#025" title="Permanent link">&para;</a></h2>
<p>阅读本书时，请不要“惯着”那些弄不明白的知识点。<strong>欢迎在评论区留下你的问题</strong>，小伙伴们和我都会给予解答，您一般 2 日内会得到回复。</p>
<p>同时，也希望你可以多花时间逛逛评论区。一方面，可以看看大家遇到了什么问题，反过来查漏补缺，这往往可以引起更加深度的思考。另一方面，也希望你可以慷慨地解答小伙伴们的问题、分享自己的见解，大家互相学习与进步！</p>
<p><img alt="评论区示例" src="../suggestions.assets/comment.gif" /></p>
<p align="center"> Fig. 评论区示例 </p>
<h2 id="__comments">评论</h2>
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