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2026-07-09 14:06:06 +00:00 · 2023-07-19 16:10:17 +08:00
parent 63f23acdd0
commit 60b323a1c6
98 changed files with 815 additions and 479 deletions
@@ -415,7 +415,7 @@
            <a href="../../chapter_introduction/" class="md-nav__link ">
              
  
-    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m14.6 16.6 4.6-4.6-4.6-4.6L16 6l6 6-6 6-1.4-1.4m-5.2 0L4.8 12l4.6-4.6L8 6l-6 6 6 6 1.4-1.4Z"/></svg>
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
  
  <span class="md-ellipsis">
    1. &nbsp; 初识算法
@@ -691,7 +691,7 @@
            <a href="../../chapter_data_structure/" class="md-nav__link ">
              
  
-    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 3C7.58 3 4 4.79 4 7v10c0 2.21 3.59 4 8 4s8-1.79 8-4V7c0-2.21-3.58-4-8-4m6 14c0 .5-2.13 2-6 2s-6-1.5-6-2v-2.23c1.61.78 3.72 1.23 6 1.23s4.39-.45 6-1.23V17m0-4.55c-1.3.95-3.58 1.55-6 1.55s-4.7-.6-6-1.55V9.64c1.47.83 3.61 1.36 6 1.36s4.53-.53 6-1.36v2.81M12 9C8.13 9 6 7.5 6 7s2.13-2 6-2 6 1.5 6 2-2.13 2-6 2Z"/></svg>
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  <span class="md-ellipsis">
    3. &nbsp; 数据结构
@@ -858,7 +858,7 @@
            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
              
  
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  <span class="md-ellipsis">
    4. &nbsp; 数组与链表
@@ -2319,7 +2319,7 @@
            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
              
  
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  <span class="md-ellipsis">
    12. &nbsp; 分治
@@ -3196,7 +3196,7 @@
 </div>
 <div class="tabbed-block">
 <div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二叉树的数组表示 */</span>
-<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 使用 int 最大值标记空位，因此要求节点值不能为 INT_MAX</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 使用 int 最大值 INT_MAX 标记空位</span>
 <a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">};</span>
 </code></pre></div>
 </div>
@@ -3257,6 +3257,304 @@
 <p><img alt="任意类型二叉树的数组表示" src="../array_representation_of_tree.assets/array_representation_with_empty.png" /></p>
 <p align="center"> Fig. 任意类型二叉树的数组表示 </p>

+<p>以下为数组表示下二叉树的实现，包括：</p>
+<ul>
+<li>获取节点数量、节点值、左（右）子节点、父节点等基础操作；</li>
+<li>获取前序遍历、中序遍历、后序遍历、层序遍历的节点值序列；</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:11"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label><label for="__tabbed_2_9">Swift</label><label for="__tabbed_2_10">Zig</label><label for="__tabbed_2_11">Dart</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.java</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 数组表示下的二叉树类 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span> <span class="nc">ArrayBinaryTree</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">private</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</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="cm">/* 构造方法 */</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayBinaryTree</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</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="n">tree</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">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="cm">/* 节点数量 */</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">size</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="p">}</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="cm">/* 获取索引为 i 节点的值 */</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</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="c1">// 若索引越界，则返回 null ，代表空位</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</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="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="w">    </span><span class="cm">/* 获取索引为 i 节点的左子节点的索引 */</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">    </span><span class="cm">/* 获取索引为 i 节点的右子节点的索引 */</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a>
+<a id="__codelineno-11-33" name="__codelineno-11-33" href="#__codelineno-11-33"></a><span class="w">    </span><span class="cm">/* 获取索引为 i 节点的父节点的索引 */</span>
+<a id="__codelineno-11-34" name="__codelineno-11-34" href="#__codelineno-11-34"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-35" name="__codelineno-11-35" href="#__codelineno-11-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-11-36" name="__codelineno-11-36" href="#__codelineno-11-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-37" name="__codelineno-11-37" href="#__codelineno-11-37"></a>
+<a id="__codelineno-11-38" name="__codelineno-11-38" href="#__codelineno-11-38"></a><span class="w">    </span><span class="cm">/* 层序遍历 */</span>
+<a id="__codelineno-11-39" name="__codelineno-11-39" href="#__codelineno-11-39"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-40" name="__codelineno-11-40" href="#__codelineno-11-40"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-11-41" name="__codelineno-11-41" href="#__codelineno-11-41"></a><span class="w">        </span><span class="c1">// 直接遍历数组</span>
+<a id="__codelineno-11-42" name="__codelineno-11-42" href="#__codelineno-11-42"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-43" name="__codelineno-11-43" href="#__codelineno-11-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-11-44" name="__codelineno-11-44" href="#__codelineno-11-44"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-11-45" name="__codelineno-11-45" href="#__codelineno-11-45"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-11-46" name="__codelineno-11-46" href="#__codelineno-11-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-11-47" name="__codelineno-11-47" href="#__codelineno-11-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-48" name="__codelineno-11-48" href="#__codelineno-11-48"></a>
+<a id="__codelineno-11-49" name="__codelineno-11-49" href="#__codelineno-11-49"></a><span class="w">    </span><span class="cm">/* 深度优先遍历 */</span>
+<a id="__codelineno-11-50" name="__codelineno-11-50" href="#__codelineno-11-50"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">Integer</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-51" name="__codelineno-11-51" href="#__codelineno-11-51"></a><span class="w">        </span><span class="c1">// 若为空位，则返回</span>
+<a id="__codelineno-11-52" name="__codelineno-11-52" href="#__codelineno-11-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-11-53" name="__codelineno-11-53" href="#__codelineno-11-53"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-11-54" name="__codelineno-11-54" href="#__codelineno-11-54"></a><span class="w">        </span><span class="c1">// 前序遍历</span>
+<a id="__codelineno-11-55" name="__codelineno-11-55" href="#__codelineno-11-55"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">)</span>
+<a id="__codelineno-11-56" name="__codelineno-11-56" href="#__codelineno-11-56"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-11-57" name="__codelineno-11-57" href="#__codelineno-11-57"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-11-58" name="__codelineno-11-58" href="#__codelineno-11-58"></a><span class="w">        </span><span class="c1">// 中序遍历</span>
+<a id="__codelineno-11-59" name="__codelineno-11-59" href="#__codelineno-11-59"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">)</span>
+<a id="__codelineno-11-60" name="__codelineno-11-60" href="#__codelineno-11-60"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-11-61" name="__codelineno-11-61" href="#__codelineno-11-61"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-11-62" name="__codelineno-11-62" href="#__codelineno-11-62"></a><span class="w">        </span><span class="c1">// 后序遍历</span>
+<a id="__codelineno-11-63" name="__codelineno-11-63" href="#__codelineno-11-63"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">)</span>
+<a id="__codelineno-11-64" name="__codelineno-11-64" href="#__codelineno-11-64"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-11-65" name="__codelineno-11-65" href="#__codelineno-11-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-66" name="__codelineno-11-66" href="#__codelineno-11-66"></a>
+<a id="__codelineno-11-67" name="__codelineno-11-67" href="#__codelineno-11-67"></a><span class="w">    </span><span class="cm">/* 前序遍历 */</span>
+<a id="__codelineno-11-68" name="__codelineno-11-68" href="#__codelineno-11-68"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-69" name="__codelineno-11-69" href="#__codelineno-11-69"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-11-70" name="__codelineno-11-70" href="#__codelineno-11-70"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-11-71" name="__codelineno-11-71" href="#__codelineno-11-71"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-11-72" name="__codelineno-11-72" href="#__codelineno-11-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-73" name="__codelineno-11-73" href="#__codelineno-11-73"></a>
+<a id="__codelineno-11-74" name="__codelineno-11-74" href="#__codelineno-11-74"></a><span class="w">    </span><span class="cm">/* 中序遍历 */</span>
+<a id="__codelineno-11-75" name="__codelineno-11-75" href="#__codelineno-11-75"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-76" name="__codelineno-11-76" href="#__codelineno-11-76"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-11-77" name="__codelineno-11-77" href="#__codelineno-11-77"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-11-78" name="__codelineno-11-78" href="#__codelineno-11-78"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-11-79" name="__codelineno-11-79" href="#__codelineno-11-79"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-80" name="__codelineno-11-80" href="#__codelineno-11-80"></a>
+<a id="__codelineno-11-81" name="__codelineno-11-81" href="#__codelineno-11-81"></a><span class="w">    </span><span class="cm">/* 后序遍历 */</span>
+<a id="__codelineno-11-82" name="__codelineno-11-82" href="#__codelineno-11-82"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-11-83" name="__codelineno-11-83" href="#__codelineno-11-83"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-11-84" name="__codelineno-11-84" href="#__codelineno-11-84"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-11-85" name="__codelineno-11-85" href="#__codelineno-11-85"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-11-86" name="__codelineno-11-86" href="#__codelineno-11-86"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-11-87" name="__codelineno-11-87" href="#__codelineno-11-87"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="cm">/* 数组表示下的二叉树类 */</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</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="k">public</span><span class="o">:</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">    </span><span class="cm">/* 构造方法 */</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="n">ArrayBinaryTree</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">)</span><span class="w"> </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">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</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="p">}</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="cm">/* 节点数量 */</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </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="w"> </span><span class="n">tree</span><span class="p">.</span><span class="n">size</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="p">}</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="cm">/* 获取索引为 i 节点的值 */</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </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">// 若索引越界，则返回 INT_MAX ，代表空位</span>
+<a id="__codelineno-12-17" name="__codelineno-12-17" href="#__codelineno-12-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-12-18" name="__codelineno-12-18" href="#__codelineno-12-18"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</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="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">[</span><span class="n">i</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="p">}</span>
+<a id="__codelineno-12-21" name="__codelineno-12-21" href="#__codelineno-12-21"></a>
+<a id="__codelineno-12-22" name="__codelineno-12-22" href="#__codelineno-12-22"></a><span class="w">    </span><span class="cm">/* 获取索引为 i 节点的左子节点的索引 */</span>
+<a id="__codelineno-12-23" name="__codelineno-12-23" href="#__codelineno-12-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </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">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-12-25" name="__codelineno-12-25" href="#__codelineno-12-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-26" name="__codelineno-12-26" href="#__codelineno-12-26"></a>
+<a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a><span class="w">    </span><span class="cm">/* 获取索引为 i 节点的右子节点的索引 */</span>
+<a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a>
+<a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a><span class="w">    </span><span class="cm">/* 获取索引为 i 节点的父节点的索引 */</span>
+<a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-34" name="__codelineno-12-34" href="#__codelineno-12-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-12-35" name="__codelineno-12-35" href="#__codelineno-12-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-36" name="__codelineno-12-36" href="#__codelineno-12-36"></a>
+<a id="__codelineno-12-37" name="__codelineno-12-37" href="#__codelineno-12-37"></a><span class="w">    </span><span class="cm">/* 层序遍历 */</span>
+<a id="__codelineno-12-38" name="__codelineno-12-38" href="#__codelineno-12-38"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-39" name="__codelineno-12-39" href="#__codelineno-12-39"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-12-40" name="__codelineno-12-40" href="#__codelineno-12-40"></a><span class="w">        </span><span class="c1">// 直接遍历数组</span>
+<a id="__codelineno-12-41" name="__codelineno-12-41" href="#__codelineno-12-41"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-42" name="__codelineno-12-42" href="#__codelineno-12-42"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">)</span>
+<a id="__codelineno-12-43" name="__codelineno-12-43" href="#__codelineno-12-43"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-12-44" name="__codelineno-12-44" href="#__codelineno-12-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-12-45" name="__codelineno-12-45" href="#__codelineno-12-45"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-12-46" name="__codelineno-12-46" href="#__codelineno-12-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-47" name="__codelineno-12-47" href="#__codelineno-12-47"></a>
+<a id="__codelineno-12-48" name="__codelineno-12-48" href="#__codelineno-12-48"></a><span class="w">    </span><span class="cm">/* 前序遍历 */</span>
+<a id="__codelineno-12-49" name="__codelineno-12-49" href="#__codelineno-12-49"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-50" name="__codelineno-12-50" href="#__codelineno-12-50"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-12-51" name="__codelineno-12-51" href="#__codelineno-12-51"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-12-52" name="__codelineno-12-52" href="#__codelineno-12-52"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-12-53" name="__codelineno-12-53" href="#__codelineno-12-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-54" name="__codelineno-12-54" href="#__codelineno-12-54"></a>
+<a id="__codelineno-12-55" name="__codelineno-12-55" href="#__codelineno-12-55"></a><span class="w">    </span><span class="cm">/* 中序遍历 */</span>
+<a id="__codelineno-12-56" name="__codelineno-12-56" href="#__codelineno-12-56"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-57" name="__codelineno-12-57" href="#__codelineno-12-57"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-12-58" name="__codelineno-12-58" href="#__codelineno-12-58"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-12-59" name="__codelineno-12-59" href="#__codelineno-12-59"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-12-60" name="__codelineno-12-60" href="#__codelineno-12-60"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-61" name="__codelineno-12-61" href="#__codelineno-12-61"></a>
+<a id="__codelineno-12-62" name="__codelineno-12-62" href="#__codelineno-12-62"></a><span class="w">    </span><span class="cm">/* 后序遍历 */</span>
+<a id="__codelineno-12-63" name="__codelineno-12-63" href="#__codelineno-12-63"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-64" name="__codelineno-12-64" href="#__codelineno-12-64"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-12-65" name="__codelineno-12-65" href="#__codelineno-12-65"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-12-66" name="__codelineno-12-66" href="#__codelineno-12-66"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-12-67" name="__codelineno-12-67" href="#__codelineno-12-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-68" name="__codelineno-12-68" href="#__codelineno-12-68"></a>
+<a id="__codelineno-12-69" name="__codelineno-12-69" href="#__codelineno-12-69"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-12-70" name="__codelineno-12-70" href="#__codelineno-12-70"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="p">;</span>
+<a id="__codelineno-12-71" name="__codelineno-12-71" href="#__codelineno-12-71"></a>
+<a id="__codelineno-12-72" name="__codelineno-12-72" href="#__codelineno-12-72"></a><span class="w">    </span><span class="cm">/* 深度优先遍历 */</span>
+<a id="__codelineno-12-73" name="__codelineno-12-73" href="#__codelineno-12-73"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-74" name="__codelineno-12-74" href="#__codelineno-12-74"></a><span class="w">        </span><span class="c1">// 若为空位，则返回</span>
+<a id="__codelineno-12-75" name="__codelineno-12-75" href="#__codelineno-12-75"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">)</span>
+<a id="__codelineno-12-76" name="__codelineno-12-76" href="#__codelineno-12-76"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-12-77" name="__codelineno-12-77" href="#__codelineno-12-77"></a><span class="w">        </span><span class="c1">// 前序遍历</span>
+<a id="__codelineno-12-78" name="__codelineno-12-78" href="#__codelineno-12-78"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">)</span>
+<a id="__codelineno-12-79" name="__codelineno-12-79" href="#__codelineno-12-79"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-12-80" name="__codelineno-12-80" href="#__codelineno-12-80"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-12-81" name="__codelineno-12-81" href="#__codelineno-12-81"></a><span class="w">        </span><span class="c1">// 中序遍历</span>
+<a id="__codelineno-12-82" name="__codelineno-12-82" href="#__codelineno-12-82"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">)</span>
+<a id="__codelineno-12-83" name="__codelineno-12-83" href="#__codelineno-12-83"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-12-84" name="__codelineno-12-84" href="#__codelineno-12-84"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-12-85" name="__codelineno-12-85" href="#__codelineno-12-85"></a><span class="w">        </span><span class="c1">// 后序遍历</span>
+<a id="__codelineno-12-86" name="__codelineno-12-86" href="#__codelineno-12-86"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">)</span>
+<a id="__codelineno-12-87" name="__codelineno-12-87" href="#__codelineno-12-87"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-12-88" name="__codelineno-12-88" href="#__codelineno-12-88"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-89" name="__codelineno-12-89" href="#__codelineno-12-89"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">class</span> <span class="nc">ArrayBinaryTree</span><span class="p">:</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;数组表示下的二叉树类&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span> <span class="o">|</span> <span class="kc">None</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="sd">&quot;&quot;&quot;构造方法&quot;&quot;&quot;</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">__tree</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>    <span class="k">def</span> <span class="nf">size</span><span class="p">(</span><span class="bp">self</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="sd">&quot;&quot;&quot;节点数量&quot;&quot;&quot;</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">__tree</span><span class="p">)</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>    <span class="k">def</span> <span class="nf">val</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</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="sd">&quot;&quot;&quot;获取索引为 i 节点的值&quot;&quot;&quot;</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>        <span class="c1"># 若索引越界，则返回 None ，代表空位</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">():</span>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>            <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">__tree</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>
+<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>    <span class="k">def</span> <span class="nf">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</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="sd">&quot;&quot;&quot;获取索引为 i 节点的左子节点的索引&quot;&quot;&quot;</span>
+<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>    <span class="k">def</span> <span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</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="sd">&quot;&quot;&quot;获取索引为 i 节点的右子节点的索引&quot;&quot;&quot;</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>        <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
+<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>    <span class="k">def</span> <span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;获取索引为 i 节点的父节点的索引&quot;&quot;&quot;</span>
+<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>        <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
+<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>
+<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>    <span class="k">def</span> <span class="nf">level_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;层序遍历&quot;&quot;&quot;</span>
+<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>        <span class="c1"># 直接遍历数组</span>
+<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
+<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
+<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>
+<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>    <span class="k">def</span> <span class="nf">__dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">order</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
+<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;深度优先遍历&quot;&quot;&quot;</span>
+<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>            <span class="k">return</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>        <span class="c1"># 前序遍历</span>
+<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">&quot;pre&quot;</span><span class="p">:</span>
+<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">__dfs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a>        <span class="c1"># 中序遍历</span>
+<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a>        <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">&quot;in&quot;</span><span class="p">:</span>
+<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">__dfs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a>        <span class="c1"># 后序遍历</span>
+<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a>        <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">&quot;post&quot;</span><span class="p">:</span>
+<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a>
+<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a>    <span class="k">def</span> <span class="nf">pre_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前序遍历&quot;&quot;&quot;</span>
+<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">__dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">&quot;pre&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
+<a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a>
+<a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a>    <span class="k">def</span> <span class="nf">in_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;中序遍历&quot;&quot;&quot;</span>
+<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-13-65" name="__codelineno-13-65" href="#__codelineno-13-65"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">__dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">&quot;in&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-66" name="__codelineno-13-66" href="#__codelineno-13-66"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
+<a id="__codelineno-13-67" name="__codelineno-13-67" href="#__codelineno-13-67"></a>
+<a id="__codelineno-13-68" name="__codelineno-13-68" href="#__codelineno-13-68"></a>    <span class="k">def</span> <span class="nf">post_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-69" name="__codelineno-13-69" href="#__codelineno-13-69"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;后序遍历&quot;&quot;&quot;</span>
+<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-13-71" name="__codelineno-13-71" href="#__codelineno-13-71"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">__dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">&quot;post&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.go</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.js</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.ts</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.c</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">arrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.cs</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.zig</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
 <h2 id="733">7.3.3. &nbsp; 优势与局限性<a class="headerlink" href="#733" title="Permanent link">&para;</a></h2>
 <p>二叉树的数组表示存在以下优点：</p>
 <ul>