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@ -3468,18 +3468,27 @@
</li>
<li class="md-nav__item">
<a href="#8-dart" class="md-nav__link">
<a href="#8-typescript" class="md-nav__link">
<span class="md-ellipsis">
8. &nbsp; Dart 环境
8. &nbsp; TypeScript 环境
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#9-rust" class="md-nav__link">
<a href="#9-dart" class="md-nav__link">
<span class="md-ellipsis">
9. &nbsp; Rust 环境
9. &nbsp; Dart 环境
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#10-rust" class="md-nav__link">
<span class="md-ellipsis">
10. &nbsp; Rust 环境
</span>
</a>
@ -3779,18 +3788,27 @@
</li>
<li class="md-nav__item">
<a href="#8-dart" class="md-nav__link">
<a href="#8-typescript" class="md-nav__link">
<span class="md-ellipsis">
8. &nbsp; Dart 环境
8. &nbsp; TypeScript 环境
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#9-rust" class="md-nav__link">
<a href="#9-dart" class="md-nav__link">
<span class="md-ellipsis">
9. &nbsp; Rust 环境
9. &nbsp; Dart 环境
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#10-rust" class="md-nav__link">
<span class="md-ellipsis">
10. &nbsp; Rust 环境
</span>
</a>
@ -3884,16 +3902,21 @@
</ol>
<h3 id="7-javascript">7. &nbsp; JavaScript 环境<a class="headerlink" href="#7-javascript" title="Permanent link">&para;</a></h3>
<ol>
<li>下载并安装 <a href="https://nodejs.org/en/">node.js</a> 。</li>
<li>在 VS Code 的插件市场中搜索 <code>javascript</code> ，安装 JavaScript (ES6) code snippets 。</li>
<li>下载并安装 <a href="https://nodejs.org/en/">Node.js</a> 。</li>
<li>（可选）在 VS Code 的插件市场中搜索 <code>Prettier</code> ，安装代码格式化工具。</li>
</ol>
<h3 id="8-dart">8. &nbsp; Dart 环境<a class="headerlink" href="#8-dart" title="Permanent link">&para;</a></h3>
<h3 id="8-typescript">8. &nbsp; TypeScript 环境<a class="headerlink" href="#8-typescript" title="Permanent link">&para;</a></h3>
<ol>
<li>同 JavaScript 环境安装步骤。</li>
<li>安装 <a href="https://github.com/privatenumber/tsx?tab=readme-ov-file#global-installation">TypeScript Execute (tsx)</a> 。</li>
<li>在 VS Code 的插件市场中搜索 <code>typescript</code> ，安装 <a href="https://marketplace.visualstudio.com/items?itemName=yoavbls.pretty-ts-errors">Pretty TypeScript Errors</a> 。</li>
</ol>
<h3 id="9-dart">9. &nbsp; Dart 环境<a class="headerlink" href="#9-dart" title="Permanent link">&para;</a></h3>
<ol>
<li>下载并安装 <a href="https://dart.dev/get-dart">Dart</a> 。</li>
<li>在 VS Code 的插件市场中搜索 <code>dart</code> ，安装 <a href="https://marketplace.visualstudio.com/items?itemName=Dart-Code.dart-code">Dart</a> 。</li>
</ol>
<h3 id="9-rust">9. &nbsp; Rust 环境<a class="headerlink" href="#9-rust" title="Permanent link">&para;</a></h3>
<h3 id="10-rust">10. &nbsp; Rust 环境<a class="headerlink" href="#10-rust" title="Permanent link">&para;</a></h3>
<ol>
<li>下载并安装 <a href="https://www.rust-lang.org/tools/install">Rust</a> 。</li>
<li>在 VS Code 的插件市场中搜索 <code>rust</code> ，安装 <a href="https://marketplace.visualstudio.com/items?itemName=rust-lang.rust-analyzer">rust-analyzer</a> 。</li>

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@ -3638,17 +3638,18 @@
<ul>
<li>采用全彩印刷，能够原汁原味地发挥出本书“动画图解”的优势。</li>
<li>考究纸张材质，既保证色彩高度还原，也保留纸质书特有的质感。</li>
<li>纸质版比网页版的格式更加规范，例如图中的公式使用斜体。</li>
<li>在不提升定价的前提下，附赠思维导图折页、书签。</li>
<li>纸质书、网页版、PDF 版内容同步，随意切换阅读。</li>
</ul>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>由于纸质书和网页版的同步成本较大，因此可能会有一些细节上的不同，请您见谅！</p>
<p>由于纸质书和网页版的同步难度较大，因此可能会有一些细节上的不同，请您见谅！</p>
</div>
<p>当然，纸质书也有一些值得大家入手前考虑的地方：</p>
<ul>
<li>使用 Python 语言，可能不匹配你的主语言（也许可以趁此机会练习 Python）。</li>
<li>全彩印刷虽然大幅提升了阅读体验，但价格会比黑白印刷高一些。</li>
<li>使用 Python 语言，可能不匹配你的主语言（可以把 Python 看作伪代码，重在理解思路）。</li>
<li>全彩印刷虽然大幅提升了图解和代码的阅读体验，但价格会比黑白印刷高一些。</li>
</ul>
<div class="admonition tip">
<p class="admonition-title">Tip</p>

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@ -4870,7 +4870,87 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayBinaryTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 数组表示下的二叉树类 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1">### 构造方法 ###</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="vi">@tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">.</span><span class="n">to_a</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="c1">### 列表容量 ###</span>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">.</span><span class="n">length</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="c1">### 获取索引为 i 节点的值 ###</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="c1"># 若索引越界，则返回 nil ，代表空位</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w"> </span><span class="c1">### 获取索引为 i 节点的左子节点的索引 ###</span>
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="mi">2</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>
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="c1">### 获取索引为 i 节点的右子节点的索引 ###</span>
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w"> </span><span class="mi">2</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">2</span>
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a>
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w"> </span><span class="c1">### 获取索引为 i 节点的父节点的索引 ###</span>
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><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="o">/</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a>
<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a><span class="w"> </span><span class="c1">### 层序遍历 ###</span>
<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span>
<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a>
<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="w"> </span><span class="c1"># 直接遍历数组</span>
<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a>
<a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-47" name="__codelineno-26-47" href="#__codelineno-26-47"></a>
<a id="__codelineno-26-48" name="__codelineno-26-48" href="#__codelineno-26-48"></a><span class="w"> </span><span class="c1">### 深度优先遍历 ###</span>
<a id="__codelineno-26-49" name="__codelineno-26-49" href="#__codelineno-26-49"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-26-50" name="__codelineno-26-50" href="#__codelineno-26-50"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-51" name="__codelineno-26-51" href="#__codelineno-26-51"></a><span class="w"> </span><span class="c1"># 前序遍历</span>
<a id="__codelineno-26-52" name="__codelineno-26-52" href="#__codelineno-26-52"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:pre</span>
<a id="__codelineno-26-53" name="__codelineno-26-53" href="#__codelineno-26-53"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-26-54" name="__codelineno-26-54" href="#__codelineno-26-54"></a><span class="w"> </span><span class="c1"># 中序遍历</span>
<a id="__codelineno-26-55" name="__codelineno-26-55" href="#__codelineno-26-55"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:in</span>
<a id="__codelineno-26-56" name="__codelineno-26-56" href="#__codelineno-26-56"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-26-57" name="__codelineno-26-57" href="#__codelineno-26-57"></a><span class="w"> </span><span class="c1"># 后序遍历</span>
<a id="__codelineno-26-58" name="__codelineno-26-58" href="#__codelineno-26-58"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:post</span>
<a id="__codelineno-26-59" name="__codelineno-26-59" href="#__codelineno-26-59"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-60" name="__codelineno-26-60" href="#__codelineno-26-60"></a>
<a id="__codelineno-26-61" name="__codelineno-26-61" href="#__codelineno-26-61"></a><span class="w"> </span><span class="c1">### 前序遍历 ###</span>
<a id="__codelineno-26-62" name="__codelineno-26-62" href="#__codelineno-26-62"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span>
<a id="__codelineno-26-63" name="__codelineno-26-63" href="#__codelineno-26-63"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-64" name="__codelineno-26-64" href="#__codelineno-26-64"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:pre</span><span class="p">)</span>
<a id="__codelineno-26-65" name="__codelineno-26-65" href="#__codelineno-26-65"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-66" name="__codelineno-26-66" href="#__codelineno-26-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-67" name="__codelineno-26-67" href="#__codelineno-26-67"></a>
<a id="__codelineno-26-68" name="__codelineno-26-68" href="#__codelineno-26-68"></a><span class="w"> </span><span class="c1">### 中序遍历 ###</span>
<a id="__codelineno-26-69" name="__codelineno-26-69" href="#__codelineno-26-69"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span>
<a id="__codelineno-26-70" name="__codelineno-26-70" href="#__codelineno-26-70"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-71" name="__codelineno-26-71" href="#__codelineno-26-71"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:in</span><span class="p">)</span>
<a id="__codelineno-26-72" name="__codelineno-26-72" href="#__codelineno-26-72"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-73" name="__codelineno-26-73" href="#__codelineno-26-73"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-74" name="__codelineno-26-74" href="#__codelineno-26-74"></a>
<a id="__codelineno-26-75" name="__codelineno-26-75" href="#__codelineno-26-75"></a><span class="w"> </span><span class="c1">### 后序遍历 ###</span>
<a id="__codelineno-26-76" name="__codelineno-26-76" href="#__codelineno-26-76"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span>
<a id="__codelineno-26-77" name="__codelineno-26-77" href="#__codelineno-26-77"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-78" name="__codelineno-26-78" href="#__codelineno-26-78"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:post</span><span class="p">)</span>
<a id="__codelineno-26-79" name="__codelineno-26-79" href="#__codelineno-26-79"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-80" name="__codelineno-26-80" href="#__codelineno-26-80"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-81" name="__codelineno-26-81" href="#__codelineno-26-81"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

145
chapter_tree/avl_tree/index.html
View file

@ -4308,9 +4308,19 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">height</span><span class="p">}</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">update_height</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 获取节点高度 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 空节点高度为 -1 ，叶节点高度为 0</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">height</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="k">end</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="c1">### 更新节点高度 ###</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="c1"># 节点高度等于最高子树高度 + 1</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span><span class="o">].</span><span class="n">max</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4465,7 +4475,14 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">balance_factor</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 获取平衡因子 ###</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">balance_factor</span><span class="p">(</span><span class="n">node</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="c1"># 空节点平衡因子为 0</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1"># 节点平衡因子 = 左子树高度 - 右子树高度</span>
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4712,7 +4729,19 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right_rotate</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 右旋操作 ###</span>
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">right_rotate</span><span class="p">(</span><span class="n">node</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="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1"># 以 child 为原点，将 node 向右旋转</span>
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span>
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="c1"># 更新节点高度</span>
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1"># 返回旋转后子树的根节点</span>
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4943,7 +4972,19 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left_rotate</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="c1">### 左旋操作 ###</span>
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="c1"># 以 child 为原点，将 node 向左旋转</span>
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span>
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w"> </span><span class="c1"># 更新节点高度</span>
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="w"> </span><span class="c1"># 返回旋转后子树的根节点</span>
<a id="__codelineno-68-12" name="__codelineno-68-12" href="#__codelineno-68-12"></a><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-68-13" name="__codelineno-68-13" href="#__codelineno-68-13"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -5404,7 +5445,34 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotate</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="c1">### 执行旋转操作，使该子树重新恢复平衡 ###</span>
<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w"> </span><span class="c1"># 获取节点 node 的平衡因子</span>
<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w"> </span><span class="c1"># 左遍树</span>
<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w"> </span><span class="c1"># 右旋</span>
<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w"> </span><span class="c1"># 先左旋后右旋</span>
<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-82-13" name="__codelineno-82-13" href="#__codelineno-82-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-14" name="__codelineno-82-14" href="#__codelineno-82-14"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-82-15" name="__codelineno-82-15" href="#__codelineno-82-15"></a><span class="w"> </span><span class="c1"># 右遍树</span>
<a id="__codelineno-82-16" name="__codelineno-82-16" href="#__codelineno-82-16"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-82-17" name="__codelineno-82-17" href="#__codelineno-82-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-82-18" name="__codelineno-82-18" href="#__codelineno-82-18"></a><span class="w"> </span><span class="c1"># 左旋</span>
<a id="__codelineno-82-19" name="__codelineno-82-19" href="#__codelineno-82-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-20" name="__codelineno-82-20" href="#__codelineno-82-20"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-82-21" name="__codelineno-82-21" href="#__codelineno-82-21"></a><span class="w"> </span><span class="c1"># 先右旋后左旋</span>
<a id="__codelineno-82-22" name="__codelineno-82-22" href="#__codelineno-82-22"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-82-23" name="__codelineno-82-23" href="#__codelineno-82-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-24" name="__codelineno-82-24" href="#__codelineno-82-24"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-82-25" name="__codelineno-82-25" href="#__codelineno-82-25"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-82-26" name="__codelineno-82-26" href="#__codelineno-82-26"></a><span class="w"> </span><span class="c1"># 平衡树，无须旋转，直接返回</span>
<a id="__codelineno-82-27" name="__codelineno-82-27" href="#__codelineno-82-27"></a><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-82-28" name="__codelineno-82-28" href="#__codelineno-82-28"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -5768,9 +5836,28 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a>
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert_helper</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="c1">### 插入节点 ###</span>
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="k">end</span>
<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a>
<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="c1">### 递归插入节点（辅助方法）###</span>
<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a><span class="w"> </span><span class="c1"># 1. 查找插入位置并插入节点</span>
<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-12" name="__codelineno-96-12" href="#__codelineno-96-12"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-96-13" name="__codelineno-96-13" href="#__codelineno-96-13"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-14" name="__codelineno-96-14" href="#__codelineno-96-14"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-96-15" name="__codelineno-96-15" href="#__codelineno-96-15"></a><span class="w"> </span><span class="c1"># 重复节点不插入，直接返回</span>
<a id="__codelineno-96-16" name="__codelineno-96-16" href="#__codelineno-96-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-96-17" name="__codelineno-96-17" href="#__codelineno-96-17"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-96-18" name="__codelineno-96-18" href="#__codelineno-96-18"></a><span class="w"> </span><span class="c1"># 更新节点高度</span>
<a id="__codelineno-96-19" name="__codelineno-96-19" href="#__codelineno-96-19"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-96-20" name="__codelineno-96-20" href="#__codelineno-96-20"></a><span class="w"> </span><span class="c1"># 2. 执行旋转操作，使该子树重新恢复平衡</span>
<a id="__codelineno-96-21" name="__codelineno-96-21" href="#__codelineno-96-21"></a><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-96-22" name="__codelineno-96-22" href="#__codelineno-96-22"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -6343,9 +6430,41 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a>
<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove_helper</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="c1">### 删除节点 ###</span>
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">val</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="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a><span class="k">end</span>
<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a>
<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="c1">### 递归删除节点（辅助方法）###</span>
<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="n">val</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="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-9" name="__codelineno-110-9" href="#__codelineno-110-9"></a><span class="w"> </span><span class="c1"># 1. 查找节点并删除</span>
<a id="__codelineno-110-10" name="__codelineno-110-10" href="#__codelineno-110-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-110-11" name="__codelineno-110-11" href="#__codelineno-110-11"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-12" name="__codelineno-110-12" href="#__codelineno-110-12"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-110-13" name="__codelineno-110-13" href="#__codelineno-110-13"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-14" name="__codelineno-110-14" href="#__codelineno-110-14"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-110-15" name="__codelineno-110-15" href="#__codelineno-110-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-16" name="__codelineno-110-16" href="#__codelineno-110-16"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-110-17" name="__codelineno-110-17" href="#__codelineno-110-17"></a><span class="w"> </span><span class="c1"># 子节点数量 = 0 ，直接删除 node 并返回</span>
<a id="__codelineno-110-18" name="__codelineno-110-18" href="#__codelineno-110-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-19" name="__codelineno-110-19" href="#__codelineno-110-19"></a><span class="w"> </span><span class="c1"># 子节点数量 = 1 ，直接删除 node</span>
<a id="__codelineno-110-20" name="__codelineno-110-20" href="#__codelineno-110-20"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-110-21" name="__codelineno-110-21" href="#__codelineno-110-21"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-110-22" name="__codelineno-110-22" href="#__codelineno-110-22"></a><span class="w"> </span><span class="c1"># 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
<a id="__codelineno-110-23" name="__codelineno-110-23" href="#__codelineno-110-23"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-110-24" name="__codelineno-110-24" href="#__codelineno-110-24"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">temp</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-25" name="__codelineno-110-25" href="#__codelineno-110-25"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-110-26" name="__codelineno-110-26" href="#__codelineno-110-26"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-110-27" name="__codelineno-110-27" href="#__codelineno-110-27"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-28" name="__codelineno-110-28" href="#__codelineno-110-28"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-110-29" name="__codelineno-110-29" href="#__codelineno-110-29"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-110-30" name="__codelineno-110-30" href="#__codelineno-110-30"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-110-31" name="__codelineno-110-31" href="#__codelineno-110-31"></a><span class="w"> </span><span class="c1"># 更新节点高度</span>
<a id="__codelineno-110-32" name="__codelineno-110-32" href="#__codelineno-110-32"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-110-33" name="__codelineno-110-33" href="#__codelineno-110-33"></a><span class="w"> </span><span class="c1"># 2. 执行旋转操作，使该子树重新恢复平衡</span>
<a id="__codelineno-110-34" name="__codelineno-110-34" href="#__codelineno-110-34"></a><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-110-35" name="__codelineno-110-35" href="#__codelineno-110-35"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

106
chapter_tree/binary_search_tree/index.html
View file

@ -4053,7 +4053,26 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">search</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 查找节点 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 目标节点在 cur 的右子树中</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 目标节点在 cur 的左子树中</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1"># 找到目标节点，跳出循环</span>
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4484,7 +4503,38 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 插入节点 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 若树为空，则初始化根节点</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="c1"># 找到重复节点，直接返回</span>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="c1"># 插入位置在 cur 的右子树中</span>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="c1"># 插入位置在 cur 的左子树中</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w"> </span><span class="c1"># 插入节点</span>
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -5227,7 +5277,57 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 删除节点 ###</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">num</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="c1"># 若树为空，直接提前返回</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1"># 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span>
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="c1"># 找到待删除节点，跳出循环</span>
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a>
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="c1"># 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="c1"># 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="w"> </span><span class="c1"># 若无待删除节点，则直接返回</span>
<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-23" name="__codelineno-40-23" href="#__codelineno-40-23"></a>
<a id="__codelineno-40-24" name="__codelineno-40-24" href="#__codelineno-40-24"></a><span class="w"> </span><span class="c1"># 子节点数量 = 0 or 1</span>
<a id="__codelineno-40-25" name="__codelineno-40-25" href="#__codelineno-40-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-26" name="__codelineno-40-26" href="#__codelineno-40-26"></a><span class="w"> </span><span class="c1"># 当子节点数量 = 0 / 1 时， child = null / 该子节点</span>
<a id="__codelineno-40-27" name="__codelineno-40-27" href="#__codelineno-40-27"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-40-28" name="__codelineno-40-28" href="#__codelineno-40-28"></a><span class="w"> </span><span class="c1"># 删除节点 cur</span>
<a id="__codelineno-40-29" name="__codelineno-40-29" href="#__codelineno-40-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="vi">@root</span>
<a id="__codelineno-40-30" name="__codelineno-40-30" href="#__codelineno-40-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-40-31" name="__codelineno-40-31" href="#__codelineno-40-31"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-40-32" name="__codelineno-40-32" href="#__codelineno-40-32"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-33" name="__codelineno-40-33" href="#__codelineno-40-33"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-40-34" name="__codelineno-40-34" href="#__codelineno-40-34"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-35" name="__codelineno-40-35" href="#__codelineno-40-35"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-36" name="__codelineno-40-36" href="#__codelineno-40-36"></a><span class="w"> </span><span class="c1"># 若删除节点为根节点，则重新指定根节点</span>
<a id="__codelineno-40-37" name="__codelineno-40-37" href="#__codelineno-40-37"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-40-38" name="__codelineno-40-38" href="#__codelineno-40-38"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-39" name="__codelineno-40-39" href="#__codelineno-40-39"></a><span class="w"> </span><span class="c1"># 子节点数量 = 2</span>
<a id="__codelineno-40-40" name="__codelineno-40-40" href="#__codelineno-40-40"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-41" name="__codelineno-40-41" href="#__codelineno-40-41"></a><span class="w"> </span><span class="c1"># 获取中序遍历中 cur 的下一个节点</span>
<a id="__codelineno-40-42" name="__codelineno-40-42" href="#__codelineno-40-42"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-40-43" name="__codelineno-40-43" href="#__codelineno-40-43"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">tmp</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-44" name="__codelineno-40-44" href="#__codelineno-40-44"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-40-45" name="__codelineno-40-45" href="#__codelineno-40-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-46" name="__codelineno-40-46" href="#__codelineno-40-46"></a><span class="w"> </span><span class="c1"># 递归删除节点 tmp</span>
<a id="__codelineno-40-47" name="__codelineno-40-47" href="#__codelineno-40-47"></a><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-40-48" name="__codelineno-40-48" href="#__codelineno-40-48"></a><span class="w"> </span><span class="c1"># 用 tmp 覆盖 cur</span>
<a id="__codelineno-40-49" name="__codelineno-40-49" href="#__codelineno-40-49"></a><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-40-50" name="__codelineno-40-50" href="#__codelineno-40-50"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-51" name="__codelineno-40-51" href="#__codelineno-40-51"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

37
chapter_tree/binary_tree_traversal/index.html
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@ -4042,7 +4042,20 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">level_order</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 层序遍历 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 初始化队列，加入根节点</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">root</span><span class="o">]</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 初始化一个列表，用于保存遍历序列</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">queue</span><span class="o">.</span><span class="n">empty?</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">.</span><span class="n">shift</span><span class="w"> </span><span class="c1"># 队列出队</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="c1"># 保存节点值</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="c1"># 左子节点入队</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="c1"># 右子节点入队</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4487,9 +4500,25 @@
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_tree_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">in_order</span><span class="p">}</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">post_order</span><span class="p">}</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="c1">### 中序遍历 ###</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 访问优先级：左子树 -&gt; 根节点 -&gt; 右子树</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="k">end</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="c1">### 后序遍历 ###</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="c1"># 访问优先级：左子树 -&gt; 右子树 -&gt; 根节点</span>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

82
en/chapter_tree/array_representation_of_tree/index.html
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@ -3340,7 +3340,87 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayBinaryTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 数组表示下的二叉树类 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1">### 构造方法 ###</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">initialize</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="vi">@tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">.</span><span class="n">to_a</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="c1">### 列表容量 ###</span>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">size</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">.</span><span class="n">length</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="c1">### 获取索引为 i 节点的值 ###</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="c1"># 若索引越界，则返回 nil ，代表空位</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</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">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="vi">@tree</span><span class="o">[</span><span class="n">i</span><span class="o">]</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w"> </span><span class="c1">### 获取索引为 i 节点的左子节点的索引 ###</span>
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="mi">2</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>
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a>
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="c1">### 获取索引为 i 节点的右子节点的索引 ###</span>
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w"> </span><span class="mi">2</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">2</span>
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a>
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w"> </span><span class="c1">### 获取索引为 i 节点的父节点的索引 ###</span>
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a><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="o">/</span><span class="w"> </span><span class="mi">2</span>
<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a>
<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a><span class="w"> </span><span class="c1">### 层序遍历 ###</span>
<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span>
<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a>
<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a><span class="w"> </span><span class="c1"># 直接遍历数组</span>
<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">...</span><span class="n">size</span>
<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a>
<a id="__codelineno-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-47" name="__codelineno-26-47" href="#__codelineno-26-47"></a>
<a id="__codelineno-26-48" name="__codelineno-26-48" href="#__codelineno-26-48"></a><span class="w"> </span><span class="c1">### 深度优先遍历 ###</span>
<a id="__codelineno-26-49" name="__codelineno-26-49" href="#__codelineno-26-49"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-26-50" name="__codelineno-26-50" href="#__codelineno-26-50"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-51" name="__codelineno-26-51" href="#__codelineno-26-51"></a><span class="w"> </span><span class="c1"># 前序遍历</span>
<a id="__codelineno-26-52" name="__codelineno-26-52" href="#__codelineno-26-52"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:pre</span>
<a id="__codelineno-26-53" name="__codelineno-26-53" href="#__codelineno-26-53"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-26-54" name="__codelineno-26-54" href="#__codelineno-26-54"></a><span class="w"> </span><span class="c1"># 中序遍历</span>
<a id="__codelineno-26-55" name="__codelineno-26-55" href="#__codelineno-26-55"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:in</span>
<a id="__codelineno-26-56" name="__codelineno-26-56" href="#__codelineno-26-56"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">)</span>
<a id="__codelineno-26-57" name="__codelineno-26-57" href="#__codelineno-26-57"></a><span class="w"> </span><span class="c1"># 后序遍历</span>
<a id="__codelineno-26-58" name="__codelineno-26-58" href="#__codelineno-26-58"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="ss">:post</span>
<a id="__codelineno-26-59" name="__codelineno-26-59" href="#__codelineno-26-59"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-60" name="__codelineno-26-60" href="#__codelineno-26-60"></a>
<a id="__codelineno-26-61" name="__codelineno-26-61" href="#__codelineno-26-61"></a><span class="w"> </span><span class="c1">### 前序遍历 ###</span>
<a id="__codelineno-26-62" name="__codelineno-26-62" href="#__codelineno-26-62"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span>
<a id="__codelineno-26-63" name="__codelineno-26-63" href="#__codelineno-26-63"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-64" name="__codelineno-26-64" href="#__codelineno-26-64"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:pre</span><span class="p">)</span>
<a id="__codelineno-26-65" name="__codelineno-26-65" href="#__codelineno-26-65"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-66" name="__codelineno-26-66" href="#__codelineno-26-66"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-67" name="__codelineno-26-67" href="#__codelineno-26-67"></a>
<a id="__codelineno-26-68" name="__codelineno-26-68" href="#__codelineno-26-68"></a><span class="w"> </span><span class="c1">### 中序遍历 ###</span>
<a id="__codelineno-26-69" name="__codelineno-26-69" href="#__codelineno-26-69"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span>
<a id="__codelineno-26-70" name="__codelineno-26-70" href="#__codelineno-26-70"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-71" name="__codelineno-26-71" href="#__codelineno-26-71"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:in</span><span class="p">)</span>
<a id="__codelineno-26-72" name="__codelineno-26-72" href="#__codelineno-26-72"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-73" name="__codelineno-26-73" href="#__codelineno-26-73"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-74" name="__codelineno-26-74" href="#__codelineno-26-74"></a>
<a id="__codelineno-26-75" name="__codelineno-26-75" href="#__codelineno-26-75"></a><span class="w"> </span><span class="c1">### 后序遍历 ###</span>
<a id="__codelineno-26-76" name="__codelineno-26-76" href="#__codelineno-26-76"></a><span class="w"> </span><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span>
<a id="__codelineno-26-77" name="__codelineno-26-77" href="#__codelineno-26-77"></a><span class="w"> </span><span class="vi">@res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-26-78" name="__codelineno-26-78" href="#__codelineno-26-78"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="ss">:post</span><span class="p">)</span>
<a id="__codelineno-26-79" name="__codelineno-26-79" href="#__codelineno-26-79"></a><span class="w"> </span><span class="vi">@res</span>
<a id="__codelineno-26-80" name="__codelineno-26-80" href="#__codelineno-26-80"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-81" name="__codelineno-26-81" href="#__codelineno-26-81"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

145
en/chapter_tree/avl_tree/index.html
View file

@ -2778,9 +2778,19 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">height</span><span class="p">}</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">update_height</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 获取节点高度 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 空节点高度为 -1 ，叶节点高度为 0</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">height</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="k">end</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="c1">### 更新节点高度 ###</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="c1"># 节点高度等于最高子树高度 + 1</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span><span class="o">].</span><span class="n">max</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -2935,7 +2945,14 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">balance_factor</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 获取平衡因子 ###</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">balance_factor</span><span class="p">(</span><span class="n">node</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="c1"># 空节点平衡因子为 0</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1"># 节点平衡因子 = 左子树高度 - 右子树高度</span>
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3182,7 +3199,19 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right_rotate</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### 右旋操作 ###</span>
<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">right_rotate</span><span class="p">(</span><span class="n">node</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="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w"> </span><span class="c1"># 以 child 为原点，将 node 向右旋转</span>
<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span>
<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w"> </span><span class="c1"># 更新节点高度</span>
<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w"> </span><span class="c1"># 返回旋转后子树的根节点</span>
<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3413,7 +3442,19 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left_rotate</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="c1">### 左旋操作 ###</span>
<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w"> </span><span class="n">grand_child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w"> </span><span class="c1"># 以 child 为原点，将 node 向左旋转</span>
<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grand_child</span>
<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a><span class="w"> </span><span class="c1"># 更新节点高度</span>
<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="w"> </span><span class="c1"># 返回旋转后子树的根节点</span>
<a id="__codelineno-68-12" name="__codelineno-68-12" href="#__codelineno-68-12"></a><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-68-13" name="__codelineno-68-13" href="#__codelineno-68-13"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3874,7 +3915,34 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotate</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="c1">### 执行旋转操作，使该子树重新恢复平衡 ###</span>
<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w"> </span><span class="c1"># 获取节点 node 的平衡因子</span>
<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w"> </span><span class="c1"># 左遍树</span>
<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span>
<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w"> </span><span class="c1"># 右旋</span>
<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w"> </span><span class="c1"># 先左旋后右旋</span>
<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-82-13" name="__codelineno-82-13" href="#__codelineno-82-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-14" name="__codelineno-82-14" href="#__codelineno-82-14"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-82-15" name="__codelineno-82-15" href="#__codelineno-82-15"></a><span class="w"> </span><span class="c1"># 右遍树</span>
<a id="__codelineno-82-16" name="__codelineno-82-16" href="#__codelineno-82-16"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">balance_factor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span>
<a id="__codelineno-82-17" name="__codelineno-82-17" href="#__codelineno-82-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span>
<a id="__codelineno-82-18" name="__codelineno-82-18" href="#__codelineno-82-18"></a><span class="w"> </span><span class="c1"># 左旋</span>
<a id="__codelineno-82-19" name="__codelineno-82-19" href="#__codelineno-82-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-20" name="__codelineno-82-20" href="#__codelineno-82-20"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-82-21" name="__codelineno-82-21" href="#__codelineno-82-21"></a><span class="w"> </span><span class="c1"># 先右旋后左旋</span>
<a id="__codelineno-82-22" name="__codelineno-82-22" href="#__codelineno-82-22"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-82-23" name="__codelineno-82-23" href="#__codelineno-82-23"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-82-24" name="__codelineno-82-24" href="#__codelineno-82-24"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-82-25" name="__codelineno-82-25" href="#__codelineno-82-25"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-82-26" name="__codelineno-82-26" href="#__codelineno-82-26"></a><span class="w"> </span><span class="c1"># 平衡树，无须旋转，直接返回</span>
<a id="__codelineno-82-27" name="__codelineno-82-27" href="#__codelineno-82-27"></a><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-82-28" name="__codelineno-82-28" href="#__codelineno-82-28"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4238,9 +4306,28 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a>
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert_helper</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="c1">### 插入节点 ###</span>
<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="k">end</span>
<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a>
<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="c1">### 递归插入节点（辅助方法）###</span>
<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a><span class="w"> </span><span class="c1"># 1. 查找插入位置并插入节点</span>
<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-12" name="__codelineno-96-12" href="#__codelineno-96-12"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-96-13" name="__codelineno-96-13" href="#__codelineno-96-13"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-96-14" name="__codelineno-96-14" href="#__codelineno-96-14"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-96-15" name="__codelineno-96-15" href="#__codelineno-96-15"></a><span class="w"> </span><span class="c1"># 重复节点不插入，直接返回</span>
<a id="__codelineno-96-16" name="__codelineno-96-16" href="#__codelineno-96-16"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-96-17" name="__codelineno-96-17" href="#__codelineno-96-17"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-96-18" name="__codelineno-96-18" href="#__codelineno-96-18"></a><span class="w"> </span><span class="c1"># 更新节点高度</span>
<a id="__codelineno-96-19" name="__codelineno-96-19" href="#__codelineno-96-19"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-96-20" name="__codelineno-96-20" href="#__codelineno-96-20"></a><span class="w"> </span><span class="c1"># 2. 执行旋转操作，使该子树重新恢复平衡</span>
<a id="__codelineno-96-21" name="__codelineno-96-21" href="#__codelineno-96-21"></a><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-96-22" name="__codelineno-96-22" href="#__codelineno-96-22"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -4813,9 +4900,41 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a>
<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove_helper</span><span class="p">}</span>
<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="c1">### 删除节点 ###</span>
<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">val</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="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a><span class="k">end</span>
<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a>
<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="c1">### 递归删除节点（辅助方法）###</span>
<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="n">val</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="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-9" name="__codelineno-110-9" href="#__codelineno-110-9"></a><span class="w"> </span><span class="c1"># 1. 查找节点并删除</span>
<a id="__codelineno-110-10" name="__codelineno-110-10" href="#__codelineno-110-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-110-11" name="__codelineno-110-11" href="#__codelineno-110-11"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-12" name="__codelineno-110-12" href="#__codelineno-110-12"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-110-13" name="__codelineno-110-13" href="#__codelineno-110-13"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-14" name="__codelineno-110-14" href="#__codelineno-110-14"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-110-15" name="__codelineno-110-15" href="#__codelineno-110-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-16" name="__codelineno-110-16" href="#__codelineno-110-16"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-110-17" name="__codelineno-110-17" href="#__codelineno-110-17"></a><span class="w"> </span><span class="c1"># 子节点数量 = 0 ，直接删除 node 并返回</span>
<a id="__codelineno-110-18" name="__codelineno-110-18" href="#__codelineno-110-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">child</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-19" name="__codelineno-110-19" href="#__codelineno-110-19"></a><span class="w"> </span><span class="c1"># 子节点数量 = 1 ，直接删除 node</span>
<a id="__codelineno-110-20" name="__codelineno-110-20" href="#__codelineno-110-20"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-110-21" name="__codelineno-110-21" href="#__codelineno-110-21"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-110-22" name="__codelineno-110-22" href="#__codelineno-110-22"></a><span class="w"> </span><span class="c1"># 子节点数量 = 2 ，则将中序遍历的下个节点删除，并用该节点替换当前节点</span>
<a id="__codelineno-110-23" name="__codelineno-110-23" href="#__codelineno-110-23"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-110-24" name="__codelineno-110-24" href="#__codelineno-110-24"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">temp</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-110-25" name="__codelineno-110-25" href="#__codelineno-110-25"></a><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-110-26" name="__codelineno-110-26" href="#__codelineno-110-26"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-110-27" name="__codelineno-110-27" href="#__codelineno-110-27"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-110-28" name="__codelineno-110-28" href="#__codelineno-110-28"></a><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-110-29" name="__codelineno-110-29" href="#__codelineno-110-29"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-110-30" name="__codelineno-110-30" href="#__codelineno-110-30"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-110-31" name="__codelineno-110-31" href="#__codelineno-110-31"></a><span class="w"> </span><span class="c1"># 更新节点高度</span>
<a id="__codelineno-110-32" name="__codelineno-110-32" href="#__codelineno-110-32"></a><span class="w"> </span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-110-33" name="__codelineno-110-33" href="#__codelineno-110-33"></a><span class="w"> </span><span class="c1"># 2. 执行旋转操作，使该子树重新恢复平衡</span>
<a id="__codelineno-110-34" name="__codelineno-110-34" href="#__codelineno-110-34"></a><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<a id="__codelineno-110-35" name="__codelineno-110-35" href="#__codelineno-110-35"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

106
en/chapter_tree/binary_search_tree/index.html
View file

@ -2523,7 +2523,26 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">search</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 查找节点 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1"># 目标节点在 cur 的右子树中</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="c1"># 目标节点在 cur 的左子树中</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="k">elsif</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1"># 找到目标节点，跳出循环</span>
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a>
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -2954,7 +2973,38 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1">### 插入节点 ###</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="w"> </span><span class="c1"># 若树为空，则初始化根节点</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="c1"># 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="w"> </span><span class="c1"># 找到重复节点，直接返回</span>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a><span class="w"> </span><span class="c1"># 插入位置在 cur 的右子树中</span>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="c1"># 插入位置在 cur 的左子树中</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a>
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a><span class="w"> </span><span class="c1"># 插入节点</span>
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="no">TreeNode</span><span class="o">.</span><span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span>
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -3697,7 +3747,57 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="c1">### 删除节点 ###</span>
<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">num</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="c1"># 若树为空，直接提前返回</span>
<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="vi">@root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a>
<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w"> </span><span class="c1"># 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w"> </span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="vi">@root</span><span class="p">,</span><span class="w"> </span><span class="kp">nil</span>
<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w"> </span><span class="c1"># 找到待删除节点，跳出循环</span>
<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w"> </span><span class="k">break</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a>
<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w"> </span><span class="c1"># 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span>
<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w"> </span><span class="c1"># 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="w"> </span><span class="c1"># 若无待删除节点，则直接返回</span>
<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-23" name="__codelineno-40-23" href="#__codelineno-40-23"></a>
<a id="__codelineno-40-24" name="__codelineno-40-24" href="#__codelineno-40-24"></a><span class="w"> </span><span class="c1"># 子节点数量 = 0 or 1</span>
<a id="__codelineno-40-25" name="__codelineno-40-25" href="#__codelineno-40-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-26" name="__codelineno-40-26" href="#__codelineno-40-26"></a><span class="w"> </span><span class="c1"># 当子节点数量 = 0 / 1 时， child = null / 该子节点</span>
<a id="__codelineno-40-27" name="__codelineno-40-27" href="#__codelineno-40-27"></a><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-40-28" name="__codelineno-40-28" href="#__codelineno-40-28"></a><span class="w"> </span><span class="c1"># 删除节点 cur</span>
<a id="__codelineno-40-29" name="__codelineno-40-29" href="#__codelineno-40-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="vi">@root</span>
<a id="__codelineno-40-30" name="__codelineno-40-30" href="#__codelineno-40-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-40-31" name="__codelineno-40-31" href="#__codelineno-40-31"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-40-32" name="__codelineno-40-32" href="#__codelineno-40-32"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-33" name="__codelineno-40-33" href="#__codelineno-40-33"></a><span class="w"> </span><span class="n">pre</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-40-34" name="__codelineno-40-34" href="#__codelineno-40-34"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-35" name="__codelineno-40-35" href="#__codelineno-40-35"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-36" name="__codelineno-40-36" href="#__codelineno-40-36"></a><span class="w"> </span><span class="c1"># 若删除节点为根节点，则重新指定根节点</span>
<a id="__codelineno-40-37" name="__codelineno-40-37" href="#__codelineno-40-37"></a><span class="w"> </span><span class="vi">@root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span>
<a id="__codelineno-40-38" name="__codelineno-40-38" href="#__codelineno-40-38"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-39" name="__codelineno-40-39" href="#__codelineno-40-39"></a><span class="w"> </span><span class="c1"># 子节点数量 = 2</span>
<a id="__codelineno-40-40" name="__codelineno-40-40" href="#__codelineno-40-40"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-40-41" name="__codelineno-40-41" href="#__codelineno-40-41"></a><span class="w"> </span><span class="c1"># 获取中序遍历中 cur 的下一个节点</span>
<a id="__codelineno-40-42" name="__codelineno-40-42" href="#__codelineno-40-42"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-40-43" name="__codelineno-40-43" href="#__codelineno-40-43"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">tmp</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-40-44" name="__codelineno-40-44" href="#__codelineno-40-44"></a><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-40-45" name="__codelineno-40-45" href="#__codelineno-40-45"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-46" name="__codelineno-40-46" href="#__codelineno-40-46"></a><span class="w"> </span><span class="c1"># 递归删除节点 tmp</span>
<a id="__codelineno-40-47" name="__codelineno-40-47" href="#__codelineno-40-47"></a><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-40-48" name="__codelineno-40-48" href="#__codelineno-40-48"></a><span class="w"> </span><span class="c1"># 用 tmp 覆盖 cur</span>
<a id="__codelineno-40-49" name="__codelineno-40-49" href="#__codelineno-40-49"></a><span class="w"> </span><span class="n">cur</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-40-50" name="__codelineno-40-50" href="#__codelineno-40-50"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-40-51" name="__codelineno-40-51" href="#__codelineno-40-51"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">

37
en/chapter_tree/binary_tree_traversal/index.html
View file

@ -2512,7 +2512,20 @@
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">level_order</span><span class="p">}</span>
<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">### 层序遍历 ###</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w"> </span><span class="c1"># 初始化队列，加入根节点</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[</span><span class="n">root</span><span class="o">]</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="c1"># 初始化一个列表，用于保存遍历序列</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">[]</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="o">!</span><span class="n">queue</span><span class="o">.</span><span class="n">empty?</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">.</span><span class="n">shift</span><span class="w"> </span><span class="c1"># 队列出队</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="w"> </span><span class="c1"># 保存节点值</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="c1"># 左子节点入队</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="w"> </span><span class="k">unless</span><span class="w"> </span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="o">.</span><span class="n">nil?</span><span class="w"> </span><span class="c1"># 右子节点入队</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w"> </span><span class="k">end</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="n">res</span>
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="k">end</span>
</code></pre></div>
</div>
<div class="tabbed-block">
@ -2957,9 +2970,25 @@
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_tree_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">in_order</span><span class="p">}</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">post_order</span><span class="p">}</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="c1">### 中序遍历 ###</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>
<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="w"> </span><span class="c1"># 访问优先级：左子树 -&gt; 根节点 -&gt; 右子树</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="w"> </span><span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="w"> </span><span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="k">end</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a><span class="c1">### 后序遍历 ###</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">nil?</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a><span class="w"> </span><span class="c1"># 访问优先级：左子树 -&gt; 右子树 -&gt; 根节点</span>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a><span class="w"> </span><span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a><span class="w"> </span><span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a><span class="w"> </span><span class="vg">$res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">root</span><span class="o">.</span><span class="n">val</span>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a><span class="k">end</span>
</code></pre></div>
</div>
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</li>
<li class="md-nav__item">
<a href="#8-dart" class="md-nav__link">
<a href="#8-typescript" class="md-nav__link">
<span class="md-ellipsis">
8. &nbsp; Dart 環境
8. &nbsp; TypeScript 環境
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#9-rust" class="md-nav__link">
<a href="#9-dart" class="md-nav__link">
<span class="md-ellipsis">
9. &nbsp; Rust 環境
9. &nbsp; Dart 環境
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#10-rust" class="md-nav__link">
<span class="md-ellipsis">
10. &nbsp; Rust 環境
</span>
</a>
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<li class="md-nav__item">
<a href="#8-dart" class="md-nav__link">
<a href="#8-typescript" class="md-nav__link">
<span class="md-ellipsis">
8. &nbsp; Dart 環境
8. &nbsp; TypeScript 環境
</span>
</a>
</li>
<li class="md-nav__item">
<a href="#9-rust" class="md-nav__link">
<a href="#9-dart" class="md-nav__link">
<span class="md-ellipsis">
9. &nbsp; Rust 環境
9. &nbsp; Dart 環境
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<span class="md-ellipsis">
10. &nbsp; Rust 環境
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</ol>
<h3 id="7-javascript">7. &nbsp; JavaScript 環境<a class="headerlink" href="#7-javascript" title="Permanent link">&para;</a></h3>
<ol>
<li>下載並安裝 <a href="https://nodejs.org/en/">node.js</a> 。</li>
<li>在 VS Code 的擴充功能市場中搜索 <code>javascript</code> ，安裝 JavaScript (ES6) code snippets 。</li>
<li>下載並安裝 <a href="https://nodejs.org/en/">Node.js</a> 。</li>
<li>（可選）在 VS Code 的擴充功能市場中搜索 <code>Prettier</code> ，安裝程式碼格式化工具。</li>
</ol>
<h3 id="8-dart">8. &nbsp; Dart 環境<a class="headerlink" href="#8-dart" title="Permanent link">&para;</a></h3>
<h3 id="8-typescript">8. &nbsp; TypeScript 環境<a class="headerlink" href="#8-typescript" title="Permanent link">&para;</a></h3>
<ol>
<li>同 JavaScript 環境安裝步驟。</li>
<li>安裝 <a href="https://github.com/privatenumber/tsx?tab=readme-ov-file#global-installation">TypeScript Execute (tsx)</a> 。</li>
<li>在 VS Code 的擴充功能市場中搜索 <code>typescript</code> ，安裝 <a href="https://marketplace.visualstudio.com/items?itemName=yoavbls.pretty-ts-errors">Pretty TypeScript Errors</a> 。</li>
</ol>
<h3 id="9-dart">9. &nbsp; Dart 環境<a class="headerlink" href="#9-dart" title="Permanent link">&para;</a></h3>
<ol>
<li>下載並安裝 <a href="https://dart.dev/get-dart">Dart</a> 。</li>
<li>在 VS Code 的擴充功能市場中搜索 <code>dart</code> ，安裝 <a href="https://marketplace.visualstudio.com/items?itemName=Dart-Code.dart-code">Dart</a> 。</li>
</ol>
<h3 id="9-rust">9. &nbsp; Rust 環境<a class="headerlink" href="#9-rust" title="Permanent link">&para;</a></h3>
<h3 id="10-rust">10. &nbsp; Rust 環境<a class="headerlink" href="#10-rust" title="Permanent link">&para;</a></h3>
<ol>
<li>下載並安裝 <a href="https://www.rust-lang.org/tools/install">Rust</a> 。</li>
<li>在 VS Code 的擴充功能市場中搜索 <code>rust</code> ，安裝 <a href="https://marketplace.visualstudio.com/items?itemName=rust-lang.rust-analyzer">rust-analyzer</a> 。</li>

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