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0.2.2. &nbsp; 在动画图解中高效学习
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0.2.3. &nbsp; 在代码实践中加深理解
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0.2.4. &nbsp; 在提问讨论中共同成长
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0.2.5. &nbsp; 算法学习路线
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5. &nbsp; 栈与队列
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6. &nbsp; 散列表
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6.1. &nbsp; 哈希表
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7. &nbsp; 树
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7. &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; 二叉树数组表示
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7.4. &nbsp; 二叉搜索树
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7.5. &nbsp; AVL 树 *
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8. &nbsp; 堆
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8. &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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8.3. &nbsp; Top-K 问题
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8.4. &nbsp; 小结
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9. &nbsp; 图
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9. &nbsp; 图
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9.1. &nbsp; 图
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11.2. &nbsp; 选择排序
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11.3. &nbsp; 冒泡排序
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11.4. &nbsp; 插入排序
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11.5. &nbsp; 快速排序
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11.6. &nbsp; 归并排序
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0.2.1. &nbsp; 行文风格约定
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0.2.2. &nbsp; 在动画图解中高效学习
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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>
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<h2 id="021">0.2.1. &nbsp; 行文风格约定<a class="headerlink" href="#021" title="Permanent link">&para;</a></h2>
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<li>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。</li>
</ul>
<div class="tabbed-set tabbed-alternate" data-tabs="1:11"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><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><label for="__tabbed_1_11">Dart</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="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 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="cm">/* 标题注释，用于标注函数、类、测试样例等 */</span>
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="c1">// 内容注释，用于详解代码</span>
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="cm">/**</span>
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="cm"> * 多行</span>
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm"> * 注释</span>
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="cm"> */</span>
</code></pre></div>
</div>
</div>
</div>
<h2 id="022">0.2.2. &nbsp; 在动画图解中高效学习<a class="headerlink" href="#022" title="Permanent link">&para;</a></h2>
<p>相较于文字，视频和图片具有更高的信息密度和结构化程度，因此更易于理解。在本书中，<strong>重点和难点知识将主要通过动画和图解形式展示</strong>，而文字则作为动画和图片的解释与补充。</p>
<p>在阅读本书时，如果发现某段内容提供了动画或图解，<strong>建议以图为主线</strong>，以文字（通常位于图像上方）为辅，综合两者来理解内容。</p>
<p><img alt="动画图解示例" src="../../index.assets/animation.gif" /></p>
<p align="center"> Fig. 动画图解示例 </p>
<h2 id="023">0.2.3. &nbsp; 在代码实践中加深理解<a class="headerlink" href="#023" 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，并附有测试样例，可直接运行</strong>。</p>
<p>如果学习时间有限，建议你至少通读并运行所有代码。如果时间充裕，<strong>建议参照代码自行敲一遍</strong>。与仅阅读代码相比，编写代码的过程往往能带来更多收获。</p>
<p><img alt="运行代码示例" src="../../index.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>。请参照<a href="https://www.hello-algo.com/chapter_appendix/installation/">附录教程</a>进行安装，如果已安装则可跳过此步骤。</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> ，可以通过以下命令克隆本仓库。</p>
<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></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，然后在本地解压即可。</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>。如果代码块顶部标有文件名称，则可以在仓库的 <code>codes</code> 文件夹中找到相应的源代码文件。源代码文件将帮助你节省不必要的调试时间，让你能够专注于学习内容。</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="024">0.2.4. &nbsp; 在提问讨论中共同成长<a class="headerlink" href="#024" title="Permanent link">&para;</a></h2>
<p>阅读本书时，请不要“惯着”那些没学明白的知识点。<strong>欢迎在评论区提出你的问题</strong>，我和其他小伙伴们将竭诚为你解答，一般情况下可在两天内得到回复。</p>
<p>同时，也希望您能在评论区多花些时间。一方面，您可以了解大家遇到的问题，从而查漏补缺，这将有助于激发更深入的思考。另一方面，希望您能慷慨地回答其他小伙伴的问题、分享您的见解，让大家共同学习和进步。</p>
<p><img alt="评论区示例" src="../../index.assets/comment.gif" /></p>
<p align="center"> Fig. 评论区示例 </p>
<h2 id="025">0.2.5. &nbsp; 算法学习路线<a class="headerlink" href="#025" title="Permanent link">&para;</a></h2>
<p>从总体上看，我们可以将学习数据结构与算法的过程划分为三个阶段：</p>
<ol>
<li><strong>算法入门</strong>。我们需要熟悉各种数据结构的特点和用法，学习不同算法的原理、流程、用途和效率等方面内容。</li>
<li><strong>刷算法题</strong>。建议从热门题目开刷，如<a href="https://leetcode.cn/problem-list/xb9nqhhg/">剑指 Offer</a>和<a href="https://leetcode.cn/problem-list/2cktkvj/">LeetCode Hot 100</a>，先积累至少 100 道题目，熟悉主流的算法问题。初次刷题时，“知识遗忘”可能是一个挑战，但请放心，这是很正常的。我们可以按照“艾宾浩斯遗忘曲线”来复习题目，通常在进行 3-5 轮的重复后，就能将其牢记在心。</li>
<li><strong>搭建知识体系</strong>。在学习方面，我们可以阅读算法专栏文章、解题框架和算法教材，以不断丰富知识体系。在刷题方面，可以尝试采用进阶刷题策略，如按专题分类、一题多解、一解多题等，相关的刷题心得可以在各个社区找到。</li>
</ol>
<p>作为一本入门教程，本书内容主要涵盖“第一阶段”，旨在帮助你更高效地展开第二和第三阶段的学习。</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="__comments">评论</h2>
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