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4. &nbsp; 数组与链表
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查找节点
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插入节点
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删除节点
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排序
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8.1. &nbsp; 堆
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7.4.1. &nbsp; 二叉搜索树的操作
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查找节点
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插入节点
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删除节点
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排序
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7.4.2. &nbsp; 二叉搜索树的效率
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7.4.3. &nbsp; 二叉搜索树常见应用
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<h1 id="74">7.4. &nbsp; 二叉搜索树<a class="headerlink" href="#74" title="Permanent link">&para;</a></h1>
<p>「二叉搜索树 Binary Search Tree」满足以下条件：</p>
<ol>
<li>对于根节点，左子树中所有节点的值 <span class="arithmatex">\(&lt;\)</span> 根节点的值 <span class="arithmatex">\(&lt;\)</span> 右子树中所有节点的值。</li>
<li>任意节点的左、右子树也是二叉搜索树，即同样满足条件 <code>1.</code> 。</li>
</ol>
<p><img alt="二叉搜索树" src="../binary_search_tree.assets/binary_search_tree.png" /></p>
<p align="center"> Fig. 二叉搜索树 </p>
<h2 id="741">7.4.1. &nbsp; 二叉搜索树的操作<a class="headerlink" href="#741" title="Permanent link">&para;</a></h2>
<h3 id="_1">查找节点<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
<p>给定目标节点值 <code>num</code> ，可以根据二叉搜索树的性质来查找。我们声明一个节点 <code>cur</code> ，从二叉树的根节点 <code>root</code> 出发，循环比较节点值 <code>cur.val</code> 和 <code>num</code> 之间的大小关系</p>
<ul>
<li>若 <code>cur.val &lt; num</code> ，说明目标节点在 <code>cur</code> 的右子树中，因此执行 <code>cur = cur.right</code> 。</li>
<li>若 <code>cur.val &gt; num</code> ，说明目标节点在 <code>cur</code> 的左子树中，因此执行 <code>cur = cur.left</code> 。</li>
<li>若 <code>cur.val = num</code> ，说明找到目标节点，跳出循环并返回该节点。</li>
</ul>
<div class="tabbed-set tabbed-alternate" data-tabs="1:4"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><img alt="二叉搜索树查找节点示例" src="../binary_search_tree.assets/bst_search_step1.png" /></p>
</div>
<div class="tabbed-block">
<p><img alt="bst_search_step2" src="../binary_search_tree.assets/bst_search_step2.png" /></p>
</div>
<div class="tabbed-block">
<p><img alt="bst_search_step3" src="../binary_search_tree.assets/bst_search_step3.png" /></p>
</div>
<div class="tabbed-block">
<p><img alt="bst_search_step4" src="../binary_search_tree.assets/bst_search_step4.png" /></p>
</div>
</div>
</div>
<p>二叉搜索树的查找操作与二分查找算法的工作原理一致，都是每轮排除一半情况。循环次数最多为二叉树的高度，当二叉树平衡时，使用 <span class="arithmatex">\(O(\log n)\)</span> 时间。</p>
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<div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 查找节点 */</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></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="p">.</span><span class="na">right</span><span class="p">;</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></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="p">.</span><span class="na">left</span><span class="p">;</span>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="w"> </span><span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w"> </span><span class="c1">// 返回目标节点</span>
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 查找节点 */</span>
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">search</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></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">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></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">-&gt;</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w"> </span><span class="c1">// 返回目标节点</span>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">search</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;查找节点&quot;&quot;&quot;</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a> <span class="n">cur</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">root</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a> <span class="c1"># 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a> <span class="k">while</span> <span class="n">cur</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a> <span class="c1"># 目标节点在 cur 的右子树中</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a> <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a> <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a> <span class="c1"># 目标节点在 cur 的左子树中</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a> <span class="k">elif</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&gt;</span> <span class="n">num</span><span class="p">:</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a> <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a> <span class="c1"># 找到目标节点，跳出循环</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a> <span class="k">break</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a> <span class="k">return</span> <span class="n">cur</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 查找节点 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">bst</span><span class="w"> </span><span class="o">*</span><span class="nx">binarySearchTree</span><span class="p">)</span><span class="w"> </span><span class="nx">search</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Right</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span><span class="p">.</span><span class="nx">Left</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w"> </span><span class="c1">// 返回目标节点</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">node</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 查找节点 */</span>
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">search</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// 返回目标节点</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 查找节点 */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">search</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="c1">// 返回目标节点</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 查找节点 */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">search</span><span class="p">(</span><span class="n">binarySearchTree</span><span class="w"> </span><span class="o">*</span><span class="n">bst</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></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">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></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">-&gt;</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="w"> </span><span class="c1">// 返回目标节点</span>
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 查找节点 */</span>
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">search</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nf">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></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="p">.</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w"> </span><span class="c1">// 返回目标节点</span>
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 查找节点 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">search</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-&gt;</span> <span class="n">TreeNode</span><span class="p">?</span> <span class="p">{</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="kd">var</span> <span class="nv">cur</span> <span class="p">=</span> <span class="n">root</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="k">while</span> <span class="n">cur</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="p">}</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="k">else</span> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="o">&gt;</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="p">}</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a> <span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a> <span class="k">break</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a> <span class="p">}</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a> <span class="p">}</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a> <span class="c1">// 返回目标节点</span>
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a> <span class="k">return</span> <span class="n">cur</span>
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.zig</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// 查找节点</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">search</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></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="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></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="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w"> </span><span class="c1">// 返回目标节点</span>
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 查找节点 */</span>
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span> <span class="nf">search</span><span class="p">(</span><span class="o">&amp;</span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Option</span><span class="o">&lt;</span><span class="n">TreeNodeRc</span><span class="o">&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的右子树中</span>
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="c1">// 目标节点在 cur 的左子树中</span>
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w"> </span><span class="c1">// 找到目标节点，跳出循环</span>
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="w"> </span><span class="c1">// 返回目标节点</span>
<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w"> </span><span class="n">cur</span>
<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
</div>
<h3 id="_2">插入节点<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h3>
<p>给定一个待插入元素 <code>num</code> ，为了保持二叉搜索树“左子树 &lt; 根节点 &lt; 右子树”的性质，插入操作分为两步：</p>
<ol>
<li><strong>查找插入位置</strong>：与查找操作相似，从根节点出发，根据当前节点值和 <code>num</code> 的大小关系循环向下搜索，直到越过叶节点（遍历至 <span class="arithmatex">\(\text{None}\)</span> ）时跳出循环。</li>
<li><strong>在该位置插入节点</strong>：初始化节点 <code>num</code> ，将该节点置于 <span class="arithmatex">\(\text{None}\)</span> 的位置。</li>
</ol>
<p>二叉搜索树不允许存在重复节点，否则将违反其定义。因此，若待插入节点在树中已存在，则不执行插入，直接返回。</p>
<p><img alt="在二叉搜索树中插入节点" src="../binary_search_tree.assets/bst_insert.png" /></p>
<p align="center"> Fig. 在二叉搜索树中插入节点 </p>
<div class="tabbed-set tabbed-alternate" data-tabs="3:12"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Java</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Python</label><label for="__tabbed_3_4">Go</label><label for="__tabbed_3_5">JavaScript</label><label for="__tabbed_3_6">TypeScript</label><label for="__tabbed_3_7">C</label><label for="__tabbed_3_8">C#</label><label for="__tabbed_3_9">Swift</label><label for="__tabbed_3_10">Zig</label><label for="__tabbed_3_11">Dart</label><label for="__tabbed_3_12">Rust</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </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">// 若树为空，直接提前返回</span>
<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</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="kc">null</span><span class="p">;</span>
<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w"> </span><span class="c1">// 找到重复节点，直接返回</span>
<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></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><span class="p">;</span>
<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的右子树中</span>
<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></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="p">.</span><span class="na">right</span><span class="p">;</span>
<a id="__codelineno-12-16" name="__codelineno-12-16" href="#__codelineno-12-16"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的左子树中</span>
<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></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="p">.</span><span class="na">left</span><span class="p">;</span>
<a id="__codelineno-12-19" name="__codelineno-12-19" href="#__codelineno-12-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-12-20" name="__codelineno-12-20" href="#__codelineno-12-20"></a><span class="w"> </span><span class="c1">// 插入节点</span>
<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
<a id="__codelineno-12-24" name="__codelineno-12-24" href="#__codelineno-12-24"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="w"> </span><span class="c1">// 找到重复节点，直接返回</span>
<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></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><span class="p">;</span>
<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的右子树中</span>
<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的左子树中</span>
<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></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">-&gt;</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w"> </span><span class="c1">// 插入节点</span>
<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a><span class="w"> </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w"> </span><span class="n">pre</span><span class="o">-&gt;</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="p">;</span>
<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span> <span class="nf">insert</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;插入节点&quot;&quot;&quot;</span>
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a> <span class="c1"># 若树为空，直接提前返回</span>
<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a> <span class="k">return</span>
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a> <span class="c1"># 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a> <span class="n">cur</span><span class="p">,</span> <span class="n">pre</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">root</span><span class="p">,</span> <span class="kc">None</span>
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a> <span class="k">while</span> <span class="n">cur</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a> <span class="c1"># 找到重复节点，直接返回</span>
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a> <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="n">num</span><span class="p">:</span>
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a> <span class="k">return</span>
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a> <span class="n">pre</span> <span class="o">=</span> <span class="n">cur</span>
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a> <span class="c1"># 插入位置在 cur 的右子树中</span>
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a> <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a> <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a> <span class="c1"># 插入位置在 cur 的左子树中</span>
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a> <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a> <span class="c1"># 插入节点</span>
<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a> <span class="n">node</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a> <span class="k">if</span> <span class="n">pre</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a> <span class="n">pre</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">node</span>
<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a> <span class="n">pre</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">node</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">bst</span><span class="w"> </span><span class="o">*</span><span class="nx">binarySearchTree</span><span class="p">)</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span>
<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w"> </span><span class="c1">// 待插入节点之前的节点位置</span>
<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span>
<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span>
<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span>
<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w"> </span><span class="c1">// 插入节点</span>
<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span>
<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span>
<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">node</span>
<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">root</span><span class="p">,</span>
<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w"> </span><span class="c1">// 找到重复节点，直接返回</span>
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的右子树中</span>
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的左子树中</span>
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w"> </span><span class="c1">// 插入节点</span>
<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pre</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insert</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">root</span><span class="p">,</span>
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="nx">pre</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 找到重复节点，直接返回</span>
<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">;</span><span class="w"> </span><span class="c1">// 插入位置在 cur 的右子树中</span>
<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">;</span><span class="w"> </span><span class="c1">// 插入位置在 cur 的左子树中</span>
<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="w"> </span><span class="c1">// 插入节点</span>
<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">num</span><span class="p">);</span>
<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-24" name="__codelineno-17-24" href="#__codelineno-17-24"></a><span class="w"> </span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
<a id="__codelineno-17-25" name="__codelineno-17-25" href="#__codelineno-17-25"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-17-26" name="__codelineno-17-26" href="#__codelineno-17-26"></a><span class="w"> </span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
<a id="__codelineno-17-27" name="__codelineno-17-27" href="#__codelineno-17-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-17-28" name="__codelineno-17-28" href="#__codelineno-17-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">binarySearchTree</span><span class="w"> </span><span class="o">*</span><span class="n">bst</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w"> </span><span class="c1">// 找到重复节点，直接返回</span>
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的右子树中</span>
<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></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">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的左子树中</span>
<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></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">-&gt;</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="w"> </span><span class="c1">// 插入节点</span>
<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
<a id="__codelineno-18-24" name="__codelineno-18-24" href="#__codelineno-18-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-25" name="__codelineno-18-25" href="#__codelineno-18-25"></a><span class="w"> </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
<a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w"> </span><span class="n">pre</span><span class="o">-&gt;</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="p">;</span>
<a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</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="k">null</span><span class="p">;</span>
<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w"> </span><span class="c1">// 找到重复节点，直接返回</span>
<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></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><span class="p">;</span>
<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的右子树中</span>
<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的左子树中</span>
<a id="__codelineno-19-17" name="__codelineno-19-17" href="#__codelineno-19-17"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-19-18" name="__codelineno-19-18" href="#__codelineno-19-18"></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="p">.</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-19-19" name="__codelineno-19-19" href="#__codelineno-19-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-19-20" name="__codelineno-19-20" href="#__codelineno-19-20"></a>
<a id="__codelineno-19-21" name="__codelineno-19-21" href="#__codelineno-19-21"></a><span class="w"> </span><span class="c1">// 插入节点</span>
<a id="__codelineno-19-22" name="__codelineno-19-22" href="#__codelineno-19-22"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
<a id="__codelineno-19-23" name="__codelineno-19-23" href="#__codelineno-19-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-19-24" name="__codelineno-19-24" href="#__codelineno-19-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-19-25" name="__codelineno-19-25" href="#__codelineno-19-25"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
<a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</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="p">;</span>
<a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">func</span> <span class="nf">insert</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a> <span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a> <span class="k">if</span> <span class="n">root</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a> <span class="k">return</span>
<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a> <span class="p">}</span>
<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a> <span class="kd">var</span> <span class="nv">cur</span> <span class="p">=</span> <span class="n">root</span>
<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a> <span class="kd">var</span> <span class="nv">pre</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?</span>
<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a> <span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a> <span class="k">while</span> <span class="n">cur</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a> <span class="c1">// 找到重复节点，直接返回</span>
<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="p">==</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a> <span class="k">return</span>
<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a> <span class="p">}</span>
<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a> <span class="n">pre</span> <span class="p">=</span> <span class="n">cur</span>
<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a> <span class="c1">// 插入位置在 cur 的右子树中</span>
<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a> <span class="p">}</span>
<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a> <span class="c1">// 插入位置在 cur 的左子树中</span>
<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a> <span class="p">}</span>
<a id="__codelineno-20-24" name="__codelineno-20-24" href="#__codelineno-20-24"></a> <span class="p">}</span>
<a id="__codelineno-20-25" name="__codelineno-20-25" href="#__codelineno-20-25"></a> <span class="c1">// 插入节点</span>
<a id="__codelineno-20-26" name="__codelineno-20-26" href="#__codelineno-20-26"></a> <span class="kd">let</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="n">num</span><span class="p">)</span>
<a id="__codelineno-20-27" name="__codelineno-20-27" href="#__codelineno-20-27"></a> <span class="k">if</span> <span class="n">pre</span><span class="p">!.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-20-28" name="__codelineno-20-28" href="#__codelineno-20-28"></a> <span class="n">pre</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">node</span>
<a id="__codelineno-20-29" name="__codelineno-20-29" href="#__codelineno-20-29"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-20-30" name="__codelineno-20-30" href="#__codelineno-20-30"></a> <span class="n">pre</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">node</span>
<a id="__codelineno-20-31" name="__codelineno-20-31" href="#__codelineno-20-31"></a> <span class="p">}</span>
<a id="__codelineno-20-32" name="__codelineno-20-32" href="#__codelineno-20-32"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.zig</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="c1">// 插入节点</span>
<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">pre</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w"> </span><span class="c1">// 找到重复节点，直接返回</span>
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></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><span class="p">;</span>
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的右子树中</span>
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的左子树中</span>
<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-17" name="__codelineno-21-17" href="#__codelineno-21-17"></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="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-21-18" name="__codelineno-21-18" href="#__codelineno-21-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-21-19" name="__codelineno-21-19" href="#__codelineno-21-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-21-20" name="__codelineno-21-20" href="#__codelineno-21-20"></a><span class="w"> </span><span class="c1">// 插入节点</span>
<a id="__codelineno-21-21" name="__codelineno-21-21" href="#__codelineno-21-21"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">mem_allocator</span><span class="p">.</span><span class="n">create</span><span class="p">(</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">));</span>
<a id="__codelineno-21-22" name="__codelineno-21-22" href="#__codelineno-21-22"></a><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">init</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
<a id="__codelineno-21-23" name="__codelineno-21-23" href="#__codelineno-21-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-24" name="__codelineno-21-24" href="#__codelineno-21-24"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
<a id="__codelineno-21-25" name="__codelineno-21-25" href="#__codelineno-21-25"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-21-26" name="__codelineno-21-26" href="#__codelineno-21-26"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="o">?</span><span class="p">.</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="p">;</span>
<a id="__codelineno-21-27" name="__codelineno-21-27" href="#__codelineno-21-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-21-28" name="__codelineno-21-28" href="#__codelineno-21-28"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 插入节点 */</span>
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span> <span class="nf">insert</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="w"> </span><span class="c1">// 找到重复节点，直接返回</span>
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的右子树中</span>
<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></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><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></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">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a><span class="w"> </span><span class="c1">// 插入位置在 cur 的左子树中</span>
<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></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">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-24" name="__codelineno-23-24" href="#__codelineno-23-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-25" name="__codelineno-23-25" href="#__codelineno-23-25"></a><span class="w"> </span><span class="c1">// 插入节点</span>
<a id="__codelineno-23-26" name="__codelineno-23-26" href="#__codelineno-23-26"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span>::<span class="n">new</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
<a id="__codelineno-23-27" name="__codelineno-23-27" href="#__codelineno-23-27"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
<a id="__codelineno-23-28" name="__codelineno-23-28" href="#__codelineno-23-28"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-29" name="__codelineno-23-29" href="#__codelineno-23-29"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">Rc</span>::<span class="n">clone</span><span class="p">(</span><span class="o">&amp;</span><span class="n">node</span><span class="p">));</span>
<a id="__codelineno-23-30" name="__codelineno-23-30" href="#__codelineno-23-30"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-23-31" name="__codelineno-23-31" href="#__codelineno-23-31"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">Rc</span>::<span class="n">clone</span><span class="p">(</span><span class="o">&amp;</span><span class="n">node</span><span class="p">));</span>
<a id="__codelineno-23-32" name="__codelineno-23-32" href="#__codelineno-23-32"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-23-33" name="__codelineno-23-33" href="#__codelineno-23-33"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
</div>
<p>为了插入节点，我们需要利用辅助节点 <code>pre</code> 保存上一轮循环的节点，这样在遍历至 <span class="arithmatex">\(\text{None}\)</span> 时，我们可以获取到其父节点，从而完成节点插入操作。</p>
<p>与查找节点相同，插入节点使用 <span class="arithmatex">\(O(\log n)\)</span> 时间。</p>
<h3 id="_3">删除节点<a class="headerlink" href="#_3" title="Permanent link">&para;</a></h3>
<p>与插入节点类似，我们需要在删除操作后维持二叉搜索树的“左子树 &lt; 根节点 &lt; 右子树”的性质。首先，我们需要在二叉树中执行查找操作，获取待删除节点。接下来，根据待删除节点的子节点数量，删除操作需分为三种情况：</p>
<p>当待删除节点的度为 <span class="arithmatex">\(0\)</span> 时，表示待删除节点是叶节点，可以直接删除。</p>
<p><img alt="在二叉搜索树中删除节点（度为 0）" src="../binary_search_tree.assets/bst_remove_case1.png" /></p>
<p align="center"> Fig. 在二叉搜索树中删除节点（度为 0） </p>
<p>当待删除节点的度为 <span class="arithmatex">\(1\)</span> 时，将待删除节点替换为其子节点即可。</p>
<p><img alt="在二叉搜索树中删除节点（度为 1）" src="../binary_search_tree.assets/bst_remove_case2.png" /></p>
<p align="center"> Fig. 在二叉搜索树中删除节点（度为 1） </p>
<p>当待删除节点的度为 <span class="arithmatex">\(2\)</span> 时，我们无法直接删除它，而需要使用一个节点替换该节点。由于要保持二叉搜索树“左 <span class="arithmatex">\(&lt;\)</span> 根 <span class="arithmatex">\(&lt;\)</span> 右”的性质，因此这个节点可以是右子树的最小节点或左子树的最大节点。假设我们选择右子树的最小节点（或者称为中序遍历的下个节点），则删除操作为：</p>
<ol>
<li>找到待删除节点在“中序遍历序列”中的下一个节点，记为 <code>tmp</code> 。</li>
<li>将 <code>tmp</code> 的值覆盖待删除节点的值，并在树中递归删除节点 <code>tmp</code> 。</li>
</ol>
<div class="tabbed-set tabbed-alternate" data-tabs="4:4"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><img alt="二叉搜索树删除节点示例" src="../binary_search_tree.assets/bst_remove_case3_step1.png" /></p>
</div>
<div class="tabbed-block">
<p><img alt="bst_remove_case3_step2" src="../binary_search_tree.assets/bst_remove_case3_step2.png" /></p>
</div>
<div class="tabbed-block">
<p><img alt="bst_remove_case3_step3" src="../binary_search_tree.assets/bst_remove_case3_step3.png" /></p>
</div>
<div class="tabbed-block">
<p><img alt="bst_remove_case3_step4" src="../binary_search_tree.assets/bst_remove_case3_step4.png" /></p>
</div>
</div>
</div>
<p>删除节点操作同样使用 <span class="arithmatex">\(O(\log n)\)</span> 时间，其中查找待删除节点需要 <span class="arithmatex">\(O(\log n)\)</span> 时间，获取中序遍历后继节点需要 <span class="arithmatex">\(O(\log n)\)</span> 时间。</p>
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<div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</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="kc">null</span><span class="p">;</span>
<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="w"> </span><span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></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><span class="p">;</span>
<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></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="p">.</span><span class="na">right</span><span class="p">;</span>
<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></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="p">.</span><span class="na">left</span><span class="p">;</span>
<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="w"> </span><span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></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-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="w"> </span><span class="n">TreeNode</span><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="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a><span class="w"> </span><span class="c1">// 删除节点 cur</span>
<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span><span class="p">)</span>
<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></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-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-24-39" name="__codelineno-24-39" href="#__codelineno-24-39"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-40" name="__codelineno-24-40" href="#__codelineno-24-40"></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-24-41" name="__codelineno-24-41" href="#__codelineno-24-41"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
<a id="__codelineno-24-42" name="__codelineno-24-42" href="#__codelineno-24-42"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-24-43" name="__codelineno-24-43" href="#__codelineno-24-43"></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="p">.</span><span class="na">left</span><span class="p">;</span>
<a id="__codelineno-24-44" name="__codelineno-24-44" href="#__codelineno-24-44"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-24-45" name="__codelineno-24-45" href="#__codelineno-24-45"></a><span class="w"> </span><span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-24-46" name="__codelineno-24-46" href="#__codelineno-24-46"></a><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
<a id="__codelineno-24-47" name="__codelineno-24-47" href="#__codelineno-24-47"></a><span class="w"> </span><span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-24-48" name="__codelineno-24-48" href="#__codelineno-24-48"></a><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
<a id="__codelineno-24-49" name="__codelineno-24-49" href="#__codelineno-24-49"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-24-50" name="__codelineno-24-50" href="#__codelineno-24-50"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w"> </span><span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></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><span class="p">;</span>
<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></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">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></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">-&gt;</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-25-19" name="__codelineno-25-19" href="#__codelineno-25-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-20" name="__codelineno-25-20" href="#__codelineno-25-20"></a><span class="w"> </span><span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-25-21" name="__codelineno-25-21" href="#__codelineno-25-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
<a id="__codelineno-25-22" name="__codelineno-25-22" href="#__codelineno-25-22"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-25-23" name="__codelineno-25-23" href="#__codelineno-25-23"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-25-24" name="__codelineno-25-24" href="#__codelineno-25-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-25" name="__codelineno-25-25" href="#__codelineno-25-25"></a><span class="w"> </span><span class="c1">// 当子节点数量 = 0 / 1 时， child = nullptr / 该子节点</span>
<a id="__codelineno-25-26" name="__codelineno-25-26" href="#__codelineno-25-26"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</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">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-25-27" name="__codelineno-25-27" href="#__codelineno-25-27"></a><span class="w"> </span><span class="c1">// 删除节点 cur</span>
<a id="__codelineno-25-28" name="__codelineno-25-28" href="#__codelineno-25-28"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-29" name="__codelineno-25-29" href="#__codelineno-25-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">-&gt;</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="p">)</span>
<a id="__codelineno-25-30" name="__codelineno-25-30" href="#__codelineno-25-30"></a><span class="w"> </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-25-31" name="__codelineno-25-31" href="#__codelineno-25-31"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-25-32" name="__codelineno-25-32" href="#__codelineno-25-32"></a><span class="w"> </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-25-33" name="__codelineno-25-33" href="#__codelineno-25-33"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-34" name="__codelineno-25-34" href="#__codelineno-25-34"></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-25-35" name="__codelineno-25-35" href="#__codelineno-25-35"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-25-36" name="__codelineno-25-36" href="#__codelineno-25-36"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-37" name="__codelineno-25-37" href="#__codelineno-25-37"></a><span class="w"> </span><span class="c1">// 释放内存</span>
<a id="__codelineno-25-38" name="__codelineno-25-38" href="#__codelineno-25-38"></a><span class="w"> </span><span class="k">delete</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-25-39" name="__codelineno-25-39" href="#__codelineno-25-39"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-40" name="__codelineno-25-40" href="#__codelineno-25-40"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-25-41" name="__codelineno-25-41" href="#__codelineno-25-41"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-42" name="__codelineno-25-42" href="#__codelineno-25-42"></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-25-43" name="__codelineno-25-43" href="#__codelineno-25-43"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-25-44" name="__codelineno-25-44" href="#__codelineno-25-44"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-25-45" name="__codelineno-25-45" href="#__codelineno-25-45"></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">-&gt;</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-25-46" name="__codelineno-25-46" href="#__codelineno-25-46"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-47" name="__codelineno-25-47" href="#__codelineno-25-47"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmpVal</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-25-48" name="__codelineno-25-48" href="#__codelineno-25-48"></a><span class="w"> </span><span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-25-49" name="__codelineno-25-49" href="#__codelineno-25-49"></a><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-25-50" name="__codelineno-25-50" href="#__codelineno-25-50"></a><span class="w"> </span><span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-25-51" name="__codelineno-25-51" href="#__codelineno-25-51"></a><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmpVal</span><span class="p">;</span>
<a id="__codelineno-25-52" name="__codelineno-25-52" href="#__codelineno-25-52"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-25-53" name="__codelineno-25-53" href="#__codelineno-25-53"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span> <span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w"> </span><span class="sd">&quot;&quot;&quot;删除节点&quot;&quot;&quot;</span>
<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a> <span class="c1"># 若树为空，直接提前返回</span>
<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a> <span class="k">return</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="c1"># 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a> <span class="n">cur</span><span class="p">,</span> <span class="n">pre</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">root</span><span class="p">,</span> <span class="kc">None</span>
<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a> <span class="k">while</span> <span class="n">cur</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a> <span class="c1"># 找到待删除节点，跳出循环</span>
<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a> <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="n">num</span><span class="p">:</span>
<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a> <span class="k">break</span>
<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a> <span class="n">pre</span> <span class="o">=</span> <span class="n">cur</span>
<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a> <span class="c1"># 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a> <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
<a id="__codelineno-26-16" name="__codelineno-26-16" href="#__codelineno-26-16"></a> <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-26-17" name="__codelineno-26-17" href="#__codelineno-26-17"></a> <span class="c1"># 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-26-18" name="__codelineno-26-18" href="#__codelineno-26-18"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-26-19" name="__codelineno-26-19" href="#__codelineno-26-19"></a> <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-26-20" name="__codelineno-26-20" href="#__codelineno-26-20"></a> <span class="c1"># 若无待删除节点，则直接返回</span>
<a id="__codelineno-26-21" name="__codelineno-26-21" href="#__codelineno-26-21"></a> <span class="k">if</span> <span class="n">cur</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-26-22" name="__codelineno-26-22" href="#__codelineno-26-22"></a> <span class="k">return</span>
<a id="__codelineno-26-23" name="__codelineno-26-23" href="#__codelineno-26-23"></a>
<a id="__codelineno-26-24" name="__codelineno-26-24" href="#__codelineno-26-24"></a> <span class="c1"># 子节点数量 = 0 or 1</span>
<a id="__codelineno-26-25" name="__codelineno-26-25" href="#__codelineno-26-25"></a> <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-26-26" name="__codelineno-26-26" href="#__codelineno-26-26"></a> <span class="c1"># 当子节点数量 = 0 / 1 时， child = null / 该子节点</span>
<a id="__codelineno-26-27" name="__codelineno-26-27" href="#__codelineno-26-27"></a> <span class="n">child</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span> <span class="ow">or</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-26-28" name="__codelineno-26-28" href="#__codelineno-26-28"></a> <span class="c1"># 删除节点 cur</span>
<a id="__codelineno-26-29" name="__codelineno-26-29" href="#__codelineno-26-29"></a> <span class="k">if</span> <span class="n">cur</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">root</span><span class="p">:</span>
<a id="__codelineno-26-30" name="__codelineno-26-30" href="#__codelineno-26-30"></a> <span class="k">if</span> <span class="n">pre</span><span class="o">.</span><span class="n">left</span> <span class="o">==</span> <span class="n">cur</span><span class="p">:</span>
<a id="__codelineno-26-31" name="__codelineno-26-31" href="#__codelineno-26-31"></a> <span class="n">pre</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">child</span>
<a id="__codelineno-26-32" name="__codelineno-26-32" href="#__codelineno-26-32"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-26-33" name="__codelineno-26-33" href="#__codelineno-26-33"></a> <span class="n">pre</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">child</span>
<a id="__codelineno-26-34" name="__codelineno-26-34" href="#__codelineno-26-34"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-26-35" name="__codelineno-26-35" href="#__codelineno-26-35"></a> <span class="c1"># 若删除节点为根节点，则重新指定根节点</span>
<a id="__codelineno-26-36" name="__codelineno-26-36" href="#__codelineno-26-36"></a> <span class="bp">self</span><span class="o">.</span><span class="n">root</span> <span class="o">=</span> <span class="n">child</span>
<a id="__codelineno-26-37" name="__codelineno-26-37" href="#__codelineno-26-37"></a> <span class="c1"># 子节点数量 = 2</span>
<a id="__codelineno-26-38" name="__codelineno-26-38" href="#__codelineno-26-38"></a> <span class="k">else</span><span class="p">:</span>
<a id="__codelineno-26-39" name="__codelineno-26-39" href="#__codelineno-26-39"></a> <span class="c1"># 获取中序遍历中 cur 的下一个节点</span>
<a id="__codelineno-26-40" name="__codelineno-26-40" href="#__codelineno-26-40"></a> <span class="n">tmp</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
<a id="__codelineno-26-41" name="__codelineno-26-41" href="#__codelineno-26-41"></a> <span class="k">while</span> <span class="n">tmp</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<a id="__codelineno-26-42" name="__codelineno-26-42" href="#__codelineno-26-42"></a> <span class="n">tmp</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">.</span><span class="n">left</span>
<a id="__codelineno-26-43" name="__codelineno-26-43" href="#__codelineno-26-43"></a> <span class="c1"># 递归删除节点 tmp</span>
<a id="__codelineno-26-44" name="__codelineno-26-44" href="#__codelineno-26-44"></a> <span class="bp">self</span><span class="o">.</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-26-45" name="__codelineno-26-45" href="#__codelineno-26-45"></a> <span class="c1"># 用 tmp 覆盖 cur</span>
<a id="__codelineno-26-46" name="__codelineno-26-46" href="#__codelineno-26-46"></a> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">.</span><span class="n">val</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">bst</span><span class="w"> </span><span class="o">*</span><span class="nx">binarySearchTree</span><span class="p">)</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">num</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span>
<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w"> </span><span class="c1">// 待删除节点之前的节点位置</span>
<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w"> </span><span class="k">break</span>
<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span>
<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w"> </span><span class="c1">// 待删除节点在右子树中</span>
<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span>
<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a><span class="w"> </span><span class="c1">// 待删除节点在左子树中</span>
<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span>
<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a><span class="w"> </span><span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a><span class="w"> </span><span class="k">return</span>
<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a><span class="w"> </span><span class="c1">// 子节点数为 0 或 1</span>
<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a><span class="w"> </span><span class="c1">// 取出待删除节点的子节点</span>
<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Left</span>
<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span>
<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a><span class="w"> </span><span class="c1">// 删除节点 cur</span>
<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">child</span>
<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">child</span>
<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></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-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">root</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">child</span>
<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a><span class="w"> </span><span class="c1">// 子节点数为 2</span>
<a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w"> </span><span class="c1">// 获取中序遍历中待删除节点 cur 的下一个节点</span>
<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Right</span>
<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">nil</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">Left</span>
<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a><span class="w"> </span><span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a><span class="w"> </span><span class="nx">bst</span><span class="p">.</span><span class="nx">remove</span><span class="p">(</span><span class="nx">tmp</span><span class="p">.</span><span class="nx">Val</span><span class="p">)</span>
<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a><span class="w"> </span><span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">Val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">Val</span>
<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">root</span><span class="p">,</span>
<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w"> </span><span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w"> </span><span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></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-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w"> </span><span class="c1">// 删除节点 cur</span>
<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pre</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">cur</span><span class="p">)</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="nx">pre</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></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-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></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-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">tmp</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w"> </span><span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">tmp</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
<a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a><span class="w"> </span><span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
<a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-28-44" name="__codelineno-28-44" href="#__codelineno-28-44"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">root</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">root</span><span class="p">,</span>
<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w"> </span><span class="nx">pre</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w"> </span><span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w"> </span><span class="nx">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">;</span>
<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">;</span><span class="w"> </span><span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w"> </span><span class="nx">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">;</span><span class="w"> </span><span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w"> </span><span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></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-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">cur.left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">cur.right</span><span class="p">;</span>
<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w"> </span><span class="c1">// 删除节点 cur</span>
<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nx">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w"> </span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w"> </span><span class="nx">pre</span><span class="o">!</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></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-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">child</span><span class="p">;</span>
<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></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-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">right</span><span class="p">;</span>
<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nx">tmp</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">!==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">left</span><span class="p">;</span>
<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a><span class="w"> </span><span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="w"> </span><span class="nx">remove</span><span class="p">(</span><span class="nx">tmp</span><span class="o">!</span><span class="p">.</span><span class="nx">val</span><span class="p">);</span>
<a id="__codelineno-29-51" name="__codelineno-29-51" href="#__codelineno-29-51"></a><span class="w"> </span><span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-29-52" name="__codelineno-29-52" href="#__codelineno-29-52"></a><span class="w"> </span><span class="nx">cur</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">.</span><span class="nx">val</span><span class="p">;</span>
<a id="__codelineno-29-53" name="__codelineno-29-53" href="#__codelineno-29-53"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-29-54" name="__codelineno-29-54" href="#__codelineno-29-54"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="c1">// 由于引入了 stdio.h ，此处无法使用 remove 关键词</span>
<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">removeNode</span><span class="p">(</span><span class="n">binarySearchTree</span><span class="w"> </span><span class="o">*</span><span class="n">bst</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bst</span><span class="o">-&gt;</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w"> </span><span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w"> </span><span class="c1">// 待删除节点在 root 的右子树中</span>
<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></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">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w"> </span><span class="c1">// 待删除节点在 root 的左子树中</span>
<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></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">-&gt;</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w"> </span><span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span>
<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w"> </span><span class="c1">// 判断待删除节点是否存在子节点</span>
<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w"> </span><span class="cm">/* 子节点数量 = 0 or 1 */</span>
<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="w"> </span><span class="c1">// 当子节点数量 = 0 / 1 时， child = nullptr / 该子节点</span>
<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</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">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="w"> </span><span class="c1">// 删除节点 cur</span>
<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">-&gt;</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="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="w"> </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="w"> </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a><span class="w"> </span><span class="cm">/* 子节点数量 = 2 */</span>
<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></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-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</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">-&gt;</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-30-40" name="__codelineno-30-40" href="#__codelineno-30-40"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-30-41" name="__codelineno-30-41" href="#__codelineno-30-41"></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">-&gt;</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-30-42" name="__codelineno-30-42" href="#__codelineno-30-42"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-30-43" name="__codelineno-30-43" href="#__codelineno-30-43"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">tmpVal</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-30-44" name="__codelineno-30-44" href="#__codelineno-30-44"></a><span class="w"> </span><span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-30-45" name="__codelineno-30-45" href="#__codelineno-30-45"></a><span class="w"> </span><span class="n">removeNode</span><span class="p">(</span><span class="n">bst</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-30-46" name="__codelineno-30-46" href="#__codelineno-30-46"></a><span class="w"> </span><span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-30-47" name="__codelineno-30-47" href="#__codelineno-30-47"></a><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmpVal</span><span class="p">;</span>
<a id="__codelineno-30-48" name="__codelineno-30-48" href="#__codelineno-30-48"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-30-49" name="__codelineno-30-49" href="#__codelineno-30-49"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</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="k">null</span><span class="p">;</span>
<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w"> </span><span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></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="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></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="p">.</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="w"> </span><span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-31-21" name="__codelineno-31-21" href="#__codelineno-31-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span>
<a id="__codelineno-31-22" name="__codelineno-31-22" href="#__codelineno-31-22"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-31-23" name="__codelineno-31-23" href="#__codelineno-31-23"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-31-24" name="__codelineno-31-24" href="#__codelineno-31-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-25" name="__codelineno-31-25" href="#__codelineno-31-25"></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-31-26" name="__codelineno-31-26" href="#__codelineno-31-26"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><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="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-31-27" name="__codelineno-31-27" href="#__codelineno-31-27"></a><span class="w"> </span><span class="c1">// 删除节点 cur</span>
<a id="__codelineno-31-28" name="__codelineno-31-28" href="#__codelineno-31-28"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-29" name="__codelineno-31-29" href="#__codelineno-31-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</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="p">)</span>
<a id="__codelineno-31-30" name="__codelineno-31-30" href="#__codelineno-31-30"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-31-31" name="__codelineno-31-31" href="#__codelineno-31-31"></a><span class="w"> </span><span class="k">else</span>
<a id="__codelineno-31-32" name="__codelineno-31-32" href="#__codelineno-31-32"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-31-33" name="__codelineno-31-33" href="#__codelineno-31-33"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-34" name="__codelineno-31-34" href="#__codelineno-31-34"></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-31-35" name="__codelineno-31-35" href="#__codelineno-31-35"></a><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-31-36" name="__codelineno-31-36" href="#__codelineno-31-36"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-31-37" name="__codelineno-31-37" href="#__codelineno-31-37"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-31-38" name="__codelineno-31-38" href="#__codelineno-31-38"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-31-39" name="__codelineno-31-39" href="#__codelineno-31-39"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-40" name="__codelineno-31-40" href="#__codelineno-31-40"></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-31-41" name="__codelineno-31-41" href="#__codelineno-31-41"></a><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-31-42" name="__codelineno-31-42" href="#__codelineno-31-42"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-31-43" name="__codelineno-31-43" href="#__codelineno-31-43"></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="p">.</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-31-44" name="__codelineno-31-44" href="#__codelineno-31-44"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-31-45" name="__codelineno-31-45" href="#__codelineno-31-45"></a><span class="w"> </span><span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-31-46" name="__codelineno-31-46" href="#__codelineno-31-46"></a><span class="w"> </span><span class="k">remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-31-47" name="__codelineno-31-47" href="#__codelineno-31-47"></a><span class="w"> </span><span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-31-48" name="__codelineno-31-48" href="#__codelineno-31-48"></a><span class="w"> </span><span class="n">cur</span><span class="p">.</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="p">.</span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-31-49" name="__codelineno-31-49" href="#__codelineno-31-49"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-31-50" name="__codelineno-31-50" href="#__codelineno-31-50"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">func</span> <span class="nf">remove</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a> <span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a> <span class="k">if</span> <span class="n">root</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a> <span class="k">return</span>
<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a> <span class="p">}</span>
<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a> <span class="kd">var</span> <span class="nv">cur</span> <span class="p">=</span> <span class="n">root</span>
<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a> <span class="kd">var</span> <span class="nv">pre</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">?</span>
<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a> <span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a> <span class="k">while</span> <span class="n">cur</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a> <span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="p">==</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a> <span class="k">break</span>
<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a> <span class="p">}</span>
<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a> <span class="n">pre</span> <span class="p">=</span> <span class="n">cur</span>
<a id="__codelineno-32-16" name="__codelineno-32-16" href="#__codelineno-32-16"></a> <span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-32-17" name="__codelineno-32-17" href="#__codelineno-32-17"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">!.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span> <span class="p">{</span>
<a id="__codelineno-32-18" name="__codelineno-32-18" href="#__codelineno-32-18"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-32-19" name="__codelineno-32-19" href="#__codelineno-32-19"></a> <span class="p">}</span>
<a id="__codelineno-32-20" name="__codelineno-32-20" href="#__codelineno-32-20"></a> <span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-32-21" name="__codelineno-32-21" href="#__codelineno-32-21"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-32-22" name="__codelineno-32-22" href="#__codelineno-32-22"></a> <span class="n">cur</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-32-23" name="__codelineno-32-23" href="#__codelineno-32-23"></a> <span class="p">}</span>
<a id="__codelineno-32-24" name="__codelineno-32-24" href="#__codelineno-32-24"></a> <span class="p">}</span>
<a id="__codelineno-32-25" name="__codelineno-32-25" href="#__codelineno-32-25"></a> <span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-32-26" name="__codelineno-32-26" href="#__codelineno-32-26"></a> <span class="k">if</span> <span class="n">cur</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-32-27" name="__codelineno-32-27" href="#__codelineno-32-27"></a> <span class="k">return</span>
<a id="__codelineno-32-28" name="__codelineno-32-28" href="#__codelineno-32-28"></a> <span class="p">}</span>
<a id="__codelineno-32-29" name="__codelineno-32-29" href="#__codelineno-32-29"></a> <span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-32-30" name="__codelineno-32-30" href="#__codelineno-32-30"></a> <span class="k">if</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span> <span class="p">==</span> <span class="kc">nil</span> <span class="o">||</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span> <span class="p">==</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-32-31" name="__codelineno-32-31" href="#__codelineno-32-31"></a> <span class="c1">// 当子节点数量 = 0 / 1 时， child = null / 该子节点</span>
<a id="__codelineno-32-32" name="__codelineno-32-32" href="#__codelineno-32-32"></a> <span class="kd">let</span> <span class="nv">child</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">?</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">left</span> <span class="p">:</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-32-33" name="__codelineno-32-33" href="#__codelineno-32-33"></a> <span class="c1">// 删除节点 cur</span>
<a id="__codelineno-32-34" name="__codelineno-32-34" href="#__codelineno-32-34"></a> <span class="k">if</span> <span class="n">cur</span> <span class="o">!==</span> <span class="n">root</span> <span class="p">{</span>
<a id="__codelineno-32-35" name="__codelineno-32-35" href="#__codelineno-32-35"></a> <span class="k">if</span> <span class="n">pre</span><span class="p">?.</span><span class="kr">left</span> <span class="p">===</span> <span class="n">cur</span> <span class="p">{</span>
<a id="__codelineno-32-36" name="__codelineno-32-36" href="#__codelineno-32-36"></a> <span class="n">pre</span><span class="p">?.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-32-37" name="__codelineno-32-37" href="#__codelineno-32-37"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-32-38" name="__codelineno-32-38" href="#__codelineno-32-38"></a> <span class="n">pre</span><span class="p">?.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-32-39" name="__codelineno-32-39" href="#__codelineno-32-39"></a> <span class="p">}</span>
<a id="__codelineno-32-40" name="__codelineno-32-40" href="#__codelineno-32-40"></a> <span class="p">}</span> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-32-41" name="__codelineno-32-41" href="#__codelineno-32-41"></a> <span class="c1">// 若删除节点为根节点，则重新指定根节点</span>
<a id="__codelineno-32-42" name="__codelineno-32-42" href="#__codelineno-32-42"></a> <span class="n">root</span> <span class="p">=</span> <span class="n">child</span>
<a id="__codelineno-32-43" name="__codelineno-32-43" href="#__codelineno-32-43"></a> <span class="p">}</span>
<a id="__codelineno-32-44" name="__codelineno-32-44" href="#__codelineno-32-44"></a> <span class="p">}</span>
<a id="__codelineno-32-45" name="__codelineno-32-45" href="#__codelineno-32-45"></a> <span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-32-46" name="__codelineno-32-46" href="#__codelineno-32-46"></a> <span class="k">else</span> <span class="p">{</span>
<a id="__codelineno-32-47" name="__codelineno-32-47" href="#__codelineno-32-47"></a> <span class="c1">// 获取中序遍历中 cur 的下一个节点</span>
<a id="__codelineno-32-48" name="__codelineno-32-48" href="#__codelineno-32-48"></a> <span class="kd">var</span> <span class="nv">tmp</span> <span class="p">=</span> <span class="n">cur</span><span class="p">?.</span><span class="kr">right</span>
<a id="__codelineno-32-49" name="__codelineno-32-49" href="#__codelineno-32-49"></a> <span class="k">while</span> <span class="n">tmp</span><span class="p">?.</span><span class="kr">left</span> <span class="o">!=</span> <span class="kc">nil</span> <span class="p">{</span>
<a id="__codelineno-32-50" name="__codelineno-32-50" href="#__codelineno-32-50"></a> <span class="n">tmp</span> <span class="p">=</span> <span class="n">tmp</span><span class="p">?.</span><span class="kr">left</span>
<a id="__codelineno-32-51" name="__codelineno-32-51" href="#__codelineno-32-51"></a> <span class="p">}</span>
<a id="__codelineno-32-52" name="__codelineno-32-52" href="#__codelineno-32-52"></a> <span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-32-53" name="__codelineno-32-53" href="#__codelineno-32-53"></a> <span class="n">remove</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="n">tmp</span><span class="p">!.</span><span class="n">val</span><span class="p">)</span>
<a id="__codelineno-32-54" name="__codelineno-32-54" href="#__codelineno-32-54"></a> <span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-32-55" name="__codelineno-32-55" href="#__codelineno-32-55"></a> <span class="n">cur</span><span class="p">?.</span><span class="n">val</span> <span class="p">=</span> <span class="n">tmp</span><span class="p">!.</span><span class="n">val</span>
<a id="__codelineno-32-56" name="__codelineno-32-56" href="#__codelineno-32-56"></a> <span class="p">}</span>
<a id="__codelineno-32-57" name="__codelineno-32-57" href="#__codelineno-32-57"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.zig</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="c1">// 删除节点</span>
<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">pre</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">inc</span><span class="p">.</span><span class="n">TreeNode</span><span class="p">(</span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w"> </span><span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></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="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-33-16" name="__codelineno-33-16" href="#__codelineno-33-16"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-17" name="__codelineno-33-17" href="#__codelineno-33-17"></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="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-33-18" name="__codelineno-33-18" href="#__codelineno-33-18"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-33-19" name="__codelineno-33-19" href="#__codelineno-33-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-33-20" name="__codelineno-33-20" href="#__codelineno-33-20"></a><span class="w"> </span><span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-33-21" name="__codelineno-33-21" href="#__codelineno-33-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-33-22" name="__codelineno-33-22" href="#__codelineno-33-22"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-33-23" name="__codelineno-33-23" href="#__codelineno-33-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="k">or</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-24" name="__codelineno-33-24" href="#__codelineno-33-24"></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-33-25" name="__codelineno-33-25" href="#__codelineno-33-25"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-33-26" name="__codelineno-33-26" href="#__codelineno-33-26"></a><span class="w"> </span><span class="c1">// 删除节点 cur</span>
<a id="__codelineno-33-27" name="__codelineno-33-27" href="#__codelineno-33-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</span><span class="o">?</span><span class="p">.</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="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-28" name="__codelineno-33-28" href="#__codelineno-33-28"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-33-29" name="__codelineno-33-29" href="#__codelineno-33-29"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-30" name="__codelineno-33-30" href="#__codelineno-33-30"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-33-31" name="__codelineno-33-31" href="#__codelineno-33-31"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-33-32" name="__codelineno-33-32" href="#__codelineno-33-32"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-33-33" name="__codelineno-33-33" href="#__codelineno-33-33"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-34" name="__codelineno-33-34" href="#__codelineno-33-34"></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-33-35" name="__codelineno-33-35" href="#__codelineno-33-35"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">right</span><span class="p">;</span>
<a id="__codelineno-33-36" name="__codelineno-33-36" href="#__codelineno-33-36"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-33-37" name="__codelineno-33-37" href="#__codelineno-33-37"></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="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">left</span><span class="p">;</span>
<a id="__codelineno-33-38" name="__codelineno-33-38" href="#__codelineno-33-38"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-33-39" name="__codelineno-33-39" href="#__codelineno-33-39"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">tmp_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-33-40" name="__codelineno-33-40" href="#__codelineno-33-40"></a><span class="w"> </span><span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-33-41" name="__codelineno-33-41" href="#__codelineno-33-41"></a><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="p">);</span>
<a id="__codelineno-33-42" name="__codelineno-33-42" href="#__codelineno-33-42"></a><span class="w"> </span><span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-33-43" name="__codelineno-33-43" href="#__codelineno-33-43"></a><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp_val</span><span class="p">;</span>
<a id="__codelineno-33-44" name="__codelineno-33-44" href="#__codelineno-33-44"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-33-45" name="__codelineno-33-45" href="#__codelineno-33-45"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 删除节点 */</span>
<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="k">pub</span><span class="w"> </span><span class="k">fn</span> <span class="nf">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="c1">// 若树为空，直接提前返回</span>
<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span>
<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span>
<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">None</span><span class="p">;</span>
<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w"> </span><span class="c1">// 循环查找，越过叶节点后跳出</span>
<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="w"> </span><span class="c1">// 找到待删除节点，跳出循环</span>
<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的右子树中</span>
<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></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><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-18" name="__codelineno-35-18" href="#__codelineno-35-18"></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">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-35-19" name="__codelineno-35-19" href="#__codelineno-35-19"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-20" name="__codelineno-35-20" href="#__codelineno-35-20"></a><span class="w"> </span><span class="c1">// 待删除节点在 cur 的左子树中</span>
<a id="__codelineno-35-21" name="__codelineno-35-21" href="#__codelineno-35-21"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-22" name="__codelineno-35-22" href="#__codelineno-35-22"></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">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-35-23" name="__codelineno-35-23" href="#__codelineno-35-23"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-24" name="__codelineno-35-24" href="#__codelineno-35-24"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-25" name="__codelineno-35-25" href="#__codelineno-35-25"></a><span class="w"> </span><span class="c1">// 若无待删除节点，则直接返回</span>
<a id="__codelineno-35-26" name="__codelineno-35-26" href="#__codelineno-35-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-27" name="__codelineno-35-27" href="#__codelineno-35-27"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
<a id="__codelineno-35-28" name="__codelineno-35-28" href="#__codelineno-35-28"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-29" name="__codelineno-35-29" href="#__codelineno-35-29"></a><span class="w"> </span><span class="kd">let</span><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="p">.</span><span class="n">unwrap</span><span class="p">();</span>
<a id="__codelineno-35-30" name="__codelineno-35-30" href="#__codelineno-35-30"></a><span class="w"> </span><span class="c1">// 子节点数量 = 0 or 1</span>
<a id="__codelineno-35-31" name="__codelineno-35-31" href="#__codelineno-35-31"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">is_none</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-32" name="__codelineno-35-32" href="#__codelineno-35-32"></a><span class="w"> </span><span class="c1">// 当子节点数量 = 0 / 1 时， child = nullptr / 该子节点</span>
<a id="__codelineno-35-33" name="__codelineno-35-33" href="#__codelineno-35-33"></a><span class="w"> </span><span class="kd">let</span><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="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">or_else</span><span class="p">(</span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
<a id="__codelineno-35-34" name="__codelineno-35-34" href="#__codelineno-35-34"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">unwrap</span><span class="p">();</span>
<a id="__codelineno-35-35" name="__codelineno-35-35" href="#__codelineno-35-35"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
<a id="__codelineno-35-36" name="__codelineno-35-36" href="#__codelineno-35-36"></a><span class="w"> </span><span class="c1">// 删除节点 cur</span>
<a id="__codelineno-35-37" name="__codelineno-35-37" href="#__codelineno-35-37"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="o">!</span><span class="n">Rc</span>::<span class="n">ptr_eq</span><span class="p">(</span><span class="o">&amp;</span><span class="n">cur</span><span class="p">,</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="p">.</span><span class="n">as_ref</span><span class="p">().</span><span class="n">unwrap</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-38" name="__codelineno-35-38" href="#__codelineno-35-38"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">Rc</span>::<span class="n">ptr_eq</span><span class="p">(</span><span class="o">&amp;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cur</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-39" name="__codelineno-35-39" href="#__codelineno-35-39"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-35-40" name="__codelineno-35-40" href="#__codelineno-35-40"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-41" name="__codelineno-35-41" href="#__codelineno-35-41"></a><span class="w"> </span><span class="n">pre</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-35-42" name="__codelineno-35-42" href="#__codelineno-35-42"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-43" name="__codelineno-35-43" href="#__codelineno-35-43"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-44" name="__codelineno-35-44" href="#__codelineno-35-44"></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-35-45" name="__codelineno-35-45" href="#__codelineno-35-45"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
<a id="__codelineno-35-46" name="__codelineno-35-46" href="#__codelineno-35-46"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-47" name="__codelineno-35-47" href="#__codelineno-35-47"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-48" name="__codelineno-35-48" href="#__codelineno-35-48"></a><span class="w"> </span><span class="c1">// 子节点数量 = 2</span>
<a id="__codelineno-35-49" name="__codelineno-35-49" href="#__codelineno-35-49"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-50" name="__codelineno-35-50" href="#__codelineno-35-50"></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-35-51" name="__codelineno-35-51" href="#__codelineno-35-51"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">right</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-35-52" name="__codelineno-35-52" href="#__codelineno-35-52"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">clone</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-53" name="__codelineno-35-53" href="#__codelineno-35-53"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">is_some</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-54" name="__codelineno-35-54" href="#__codelineno-35-54"></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">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">left</span><span class="p">.</span><span class="n">clone</span><span class="p">();</span>
<a id="__codelineno-35-55" name="__codelineno-35-55" href="#__codelineno-35-55"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-35-56" name="__codelineno-35-56" href="#__codelineno-35-56"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
<a id="__codelineno-35-57" name="__codelineno-35-57" href="#__codelineno-35-57"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-58" name="__codelineno-35-58" href="#__codelineno-35-58"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-59" name="__codelineno-35-59" href="#__codelineno-35-59"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">tmpval</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">unwrap</span><span class="p">().</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-35-60" name="__codelineno-35-60" href="#__codelineno-35-60"></a><span class="w"> </span><span class="c1">// 递归删除节点 tmp</span>
<a id="__codelineno-35-61" name="__codelineno-35-61" href="#__codelineno-35-61"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">tmpval</span><span class="p">);</span>
<a id="__codelineno-35-62" name="__codelineno-35-62" href="#__codelineno-35-62"></a><span class="w"> </span><span class="c1">// 用 tmp 覆盖 cur</span>
<a id="__codelineno-35-63" name="__codelineno-35-63" href="#__codelineno-35-63"></a><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmpval</span><span class="p">;</span>
<a id="__codelineno-35-64" name="__codelineno-35-64" href="#__codelineno-35-64"></a><span class="w"> </span><span class="p">}</span>
<a id="__codelineno-35-65" name="__codelineno-35-65" href="#__codelineno-35-65"></a><span class="p">}</span>
</code></pre></div>
</div>
</div>
</div>
<h3 id="_4">排序<a class="headerlink" href="#_4" title="Permanent link">&para;</a></h3>
<p>我们知道，二叉树的中序遍历遵循“左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右”的遍历顺序，而二叉搜索树满足“左子节点 <span class="arithmatex">\(&lt;\)</span> 根节点 <span class="arithmatex">\(&lt;\)</span> 右子节点”的大小关系。因此，在二叉搜索树中进行中序遍历时，总是会优先遍历下一个最小节点，从而得出一个重要性质：<strong>二叉搜索树的中序遍历序列是升序的</strong>。</p>
<p>利用中序遍历升序的性质，我们在二叉搜索树中获取有序数据仅需 <span class="arithmatex">\(O(n)\)</span> 时间，无需额外排序，非常高效。</p>
<p><img alt="二叉搜索树的中序遍历序列" src="../binary_search_tree.assets/bst_inorder_traversal.png" /></p>
<p align="center"> Fig. 二叉搜索树的中序遍历序列 </p>
<h2 id="742">7.4.2. &nbsp; 二叉搜索树的效率<a class="headerlink" href="#742" title="Permanent link">&para;</a></h2>
<p>给定一组数据，我们考虑使用数组或二叉搜索树存储。</p>
<p>观察可知，二叉搜索树的各项操作的时间复杂度都是对数阶，具有稳定且高效的性能表现。只有在高频添加、低频查找删除的数据适用场景下，数组比二叉搜索树的效率更高。</p>
<div class="center-table">
<table>
<thead>
<tr>
<th></th>
<th>无序数组</th>
<th>二叉搜索树</th>
</tr>
</thead>
<tbody>
<tr>
<td>查找元素</td>
<td><span class="arithmatex">\(O(n)\)</span></td>
<td><span class="arithmatex">\(O(\log n)\)</span></td>
</tr>
<tr>
<td>插入元素</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
<td><span class="arithmatex">\(O(\log n)\)</span></td>
</tr>
<tr>
<td>删除元素</td>
<td><span class="arithmatex">\(O(n)\)</span></td>
<td><span class="arithmatex">\(O(\log n)\)</span></td>
</tr>
</tbody>
</table>
</div>
<p>在理想情况下，二叉搜索树是“平衡”的，这样就可以在 <span class="arithmatex">\(\log n\)</span> 轮循环内查找任意节点。</p>
<p>然而，如果我们在二叉搜索树中不断地插入和删除节点，可能导致二叉树退化为链表，这时各种操作的时间复杂度也会退化为 <span class="arithmatex">\(O(n)\)</span> 。</p>
<p><img alt="二叉搜索树的平衡与退化" src="../binary_search_tree.assets/bst_degradation.png" /></p>
<p align="center"> Fig. 二叉搜索树的平衡与退化 </p>
<h2 id="743">7.4.3. &nbsp; 二叉搜索树常见应用<a class="headerlink" href="#743" title="Permanent link">&para;</a></h2>
<ul>
<li>用作系统中的多级索引，实现高效的查找、插入、删除操作。</li>
<li>作为某些搜索算法的底层数据结构。</li>
<li>用于存储数据流，以保持其有序状态。</li>
</ul>
<h2 id="__comments">评论</h2>
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