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<h1 id="123">12.3 &nbsp; 构建二叉树问题<a class="headerlink" href="#123" title="Permanent link">&para;</a></h1>
<div class="admonition question">
<p class="admonition-title">Question</p>
<p>给定一棵二叉树的前序遍历 <code>preorder</code> 和中序遍历 <code>inorder</code> ，请从中构建二叉树，返回二叉树的根节点。假设二叉树中没有值重复的节点（如图 12-5 所示）。</p>
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<p><a class="glightbox" href="../build_binary_tree_problem.assets/build_tree_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="构建二叉树的示例数据" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_example.png" /></a></p>
<p align="center"> 图 12-5 &nbsp; 构建二叉树的示例数据 </p>

<h3 id="1">1. &nbsp; 判断是否为分治问题<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
<p>原问题定义为从 <code>preorder</code> 和 <code>inorder</code> 构建二叉树，是一个典型的分治问题。</p>
<ul>
<li><strong>问题可以分解</strong>：从分治的角度切入，我们可以将原问题划分为两个子问题：构建左子树、构建右子树，加上一步操作：初始化根节点。而对于每棵子树（子问题），我们仍然可以复用以上划分方法，将其划分为更小的子树（子问题），直至达到最小子问题（空子树）时终止。</li>
<li><strong>子问题是独立的</strong>：左子树和右子树是相互独立的，它们之间没有交集。在构建左子树时，我们只需关注中序遍历和前序遍历中与左子树对应的部分。右子树同理。</li>
<li><strong>子问题的解可以合并</strong>：一旦得到了左子树和右子树（子问题的解），我们就可以将它们链接到根节点上，得到原问题的解。</li>
</ul>
<h3 id="2">2. &nbsp; 如何划分子树<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
<p>根据以上分析，这道题可以使用分治来求解，<strong>但如何通过前序遍历 <code>preorder</code> 和中序遍历 <code>inorder</code> 来划分左子树和右子树呢</strong>？</p>
<p>根据定义，<code>preorder</code> 和 <code>inorder</code> 都可以划分为三个部分。</p>
<ul>
<li>前序遍历：<code>[ 根节点 | 左子树 | 右子树 ]</code> ，例如图 12-5 的树对应 <code>[ 3 | 9 | 2 1 7 ]</code> 。</li>
<li>中序遍历：<code>[ 左子树 | 根节点 ｜ 右子树 ]</code> ，例如图 12-5 的树对应 <code>[ 9 | 3 | 1 2 7 ]</code> 。</li>
</ul>
<p>以上图数据为例，我们可以通过图 12-6 所示的步骤得到划分结果。</p>
<ol>
<li>前序遍历的首元素 3 是根节点的值。</li>
<li>查找根节点 3 在 <code>inorder</code> 中的索引，利用该索引可将 <code>inorder</code> 划分为 <code>[ 9 | 3 ｜ 1 2 7 ]</code> 。</li>
<li>根据 <code>inorder</code> 的划分结果，易得左子树和右子树的节点数量分别为 1 和 3 ，从而可将 <code>preorder</code> 划分为 <code>[ 3 | 9 | 2 1 7 ]</code> 。</li>
</ol>
<p><a class="glightbox" href="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="在前序遍历和中序遍历中划分子树" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" /></a></p>
<p align="center"> 图 12-6 &nbsp; 在前序遍历和中序遍历中划分子树 </p>

<h3 id="3">3. &nbsp; 基于变量描述子树区间<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
<p>根据以上划分方法，<strong>我们已经得到根节点、左子树、右子树在 <code>preorder</code> 和 <code>inorder</code> 中的索引区间</strong>。而为了描述这些索引区间，我们需要借助几个指针变量。</p>
<ul>
<li>将当前树的根节点在 <code>preorder</code> 中的索引记为 <span class="arithmatex">\(i\)</span> 。</li>
<li>将当前树的根节点在 <code>inorder</code> 中的索引记为 <span class="arithmatex">\(m\)</span> 。</li>
<li>将当前树在 <code>inorder</code> 中的索引区间记为 <span class="arithmatex">\([l, r]\)</span> 。</li>
</ul>
<p>如表 12-1 所示，通过以上变量即可表示根节点在 <code>preorder</code> 中的索引，以及子树在 <code>inorder</code> 中的索引区间。</p>
<p align="center"> 表 12-1 &nbsp; 根节点和子树在前序遍历和中序遍历中的索引 </p>

<div class="center-table">
<table>
<thead>
<tr>
<th></th>
<th>根节点在 <code>preorder</code> 中的索引</th>
<th>子树在 <code>inorder</code> 中的索引区间</th>
</tr>
</thead>
<tbody>
<tr>
<td>当前树</td>
<td><span class="arithmatex">\(i\)</span></td>
<td><span class="arithmatex">\([l, r]\)</span></td>
</tr>
<tr>
<td>左子树</td>
<td><span class="arithmatex">\(i + 1\)</span></td>
<td><span class="arithmatex">\([l, m-1]\)</span></td>
</tr>
<tr>
<td>右子树</td>
<td><span class="arithmatex">\(i + 1 + (m - l)\)</span></td>
<td><span class="arithmatex">\([m+1, r]\)</span></td>
</tr>
</tbody>
</table>
</div>
<p>请注意，右子树根节点索引中的 <span class="arithmatex">\((m-l)\)</span> 的含义是“左子树的节点数量”，建议结合图 12-7 理解。</p>
<p><a class="glightbox" href="../build_binary_tree_problem.assets/build_tree_division_pointers.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="根节点和左右子树的索引区间表示" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_division_pointers.png" /></a></p>
<p align="center"> 图 12-7 &nbsp; 根节点和左右子树的索引区间表示 </p>

<h3 id="4">4. &nbsp; 代码实现<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
<p>为了提升查询 <span class="arithmatex">\(m\)</span> 的效率，我们借助一个哈希表 <code>hmap</code> 来存储数组 <code>inorder</code> 中元素到索引的映射：</p>
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<div class="highlight"><span class="filename">build_tree.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span> <span class="nf">dfs</span><span class="p">(</span>
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>    <span class="n">preorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span>
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">inorder_map</span><span class="p">:</span> <span class="nb">dict</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span>
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">l</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">r</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><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-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;构建二叉树：分治&quot;&quot;&quot;</span>
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 子树区间为空时终止</span>
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">if</span> <span class="n">r</span> <span class="o">-</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">return</span> <span class="kc">None</span>
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 初始化根节点</span>
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 查询 m ，从而划分左右子树</span>
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">m</span> <span class="o">=</span> <span class="n">inorder_map</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 子问题：构建左子树</span>
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">root</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</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="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 子问题：构建右子树</span>
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">root</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">m</span> <span class="o">-</span> <span class="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="c1"># 返回根节点</span>
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>    <span class="k">return</span> <span class="n">root</span>
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="k">def</span> <span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">inorder</span><span class="p">:</span> <span class="nb">list</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-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;构建二叉树&quot;&quot;&quot;</span>
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="n">inorder_map</span> <span class="o">=</span> <span class="p">{</span><span class="n">val</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">val</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">inorder</span><span class="p">)}</span>
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">inorder</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>    <span class="k">return</span> <span class="n">root</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 构建二叉树：分治 */</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">dfs</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="o">&amp;</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</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="c1">// 子树区间为空时终止</span>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</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">// 初始化根节点</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</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">preorder</span><span class="p">[</span><span class="n">i</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="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">r</span><span class="p">);</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</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="o">&amp;</span><span class="n">preorder</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">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">;</span>
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></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">inorder</span><span class="p">.</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-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</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">i</span><span class="p">;</span>
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="p">}</span>
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">size</span><span class="p">()</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-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 子树区间为空时终止</span>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></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-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</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">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">r</span><span class="p">);</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</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-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</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">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></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">inorder</span><span class="p">.</span><span class="na">length</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-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">inorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="p">}</span>
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">length</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-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</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="c1">// 子树区间为空时终止</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">null</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="c1">// 初始化根节点</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</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">// 子问题：构建左子树</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="n">root</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">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="n">root</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">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</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-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></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="m">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">inorder</span><span class="p">.</span><span class="n">Length</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-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">.</span><span class="n">TryAdd</span><span class="p">(</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="p">}</span>
<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</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-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 子树区间为空时终止</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="o">-</span><span class="nx">l</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="p">}</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></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">NewTreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">[</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="nx">root</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">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">-</span><span class="mi">1</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">// 子问题：构建右子树</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="nx">root</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">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="o">+</span><span class="nx">m</span><span class="o">-</span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="p">}</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="kd">func</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="w"> </span><span class="p">[]</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-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">))</span>
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">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="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">        </span><span class="nx">inorderMap</span><span class="p">[</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span>
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">    </span><span class="p">}</span>
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a>
<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></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">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">inorderMap</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">:</span> <span class="nb">Int</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">l</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">r</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-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>    <span class="c1">// 子树区间为空时终止</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>    <span class="k">if</span> <span class="n">r</span> <span class="o">-</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="p">{</span>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>        <span class="k">return</span> <span class="kc">nil</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="p">}</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>    <span class="c1">// 初始化根节点</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>    <span class="kd">let</span> <span class="nv">root</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">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a>    <span class="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>    <span class="kd">let</span> <span class="nv">m</span> <span class="p">=</span> <span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">!</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>    <span class="c1">// 子问题：构建左子树</span>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a>    <span class="n">root</span><span class="p">.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="n">preorder</span><span class="p">,</span> <span class="n">inorderMap</span><span class="p">:</span> <span class="n">inorderMap</span><span class="p">,</span> <span class="n">i</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="n">l</span><span class="p">:</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">:</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a>    <span class="c1">// 子问题：构建右子树</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>    <span class="n">root</span><span class="p">.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="n">preorder</span><span class="p">,</span> <span class="n">inorderMap</span><span class="p">:</span> <span class="n">inorderMap</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">m</span> <span class="o">-</span> <span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="p">:</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">:</span> <span class="n">r</span><span class="p">)</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>    <span class="c1">// 返回根节点</span>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>    <span class="k">return</span> <span class="n">root</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="p">}</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="kd">func</span> <span class="nf">buildTree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">inorder</span><span class="p">:</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-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a>    <span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a>    <span class="kd">let</span> <span class="nv">inorderMap</span> <span class="p">=</span> <span class="n">inorder</span><span class="p">.</span><span class="n">enumerated</span><span class="p">().</span><span class="bp">reduce</span><span class="p">(</span><span class="n">into</span><span class="p">:</span> <span class="p">[:])</span> <span class="p">{</span> <span class="nv">$0</span><span class="p">[</span><span class="nv">$1</span><span class="p">.</span><span class="n">element</span><span class="p">]</span> <span class="p">=</span> <span class="nv">$1</span><span class="p">.</span><span class="n">offset</span> <span class="p">}</span>
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a>    <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="n">preorder</span><span class="p">,</span> <span class="n">inorderMap</span><span class="p">:</span> <span class="n">inorderMap</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">inorder</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span> <span class="n">l</span><span class="p">:</span> <span class="n">inorder</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span> <span class="n">r</span><span class="p">:</span> <span class="n">inorder</span><span class="p">.</span><span class="n">endIndex</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</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="c1">// 子树区间为空时终止</span>
<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><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-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</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">preorder</span><span class="p">[</span><span class="nx">i</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">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</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="c1">// 子问题：构建左子树</span>
<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="nx">root</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">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="nx">root</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">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</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">// 返回根节点</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">        </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="p">}</span>
<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</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="nx">preorder</span><span class="o">:</span><span class="w"> </span><span class="kt">number</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="nx">inorderMap</span><span class="o">:</span><span class="w"> </span><span class="kt">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</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="nx">l</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="nx">r</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><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-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// 子树区间为空时终止</span>
<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><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-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</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="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</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="c1">// 子问题：构建左子树</span>
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="nx">root</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">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="nx">root</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">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">);</span>
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="p">}</span>
<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a>
<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">inorder</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-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">number</span><span class="o">&gt;</span><span class="p">();</span>
<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">        </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">    </span><span class="p">}</span>
<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span>
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="n">List</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>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">,</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="c1">// 子树区间为空时终止</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></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-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="p">}</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="c1">// 初始化根节点</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">!</span><span class="p">;</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="c1">// 子问题：构建左子树</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="c1">// 子问题：构建右子树</span>
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">  </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="c1">// 返回根节点</span>
<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="p">}</span>
<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a>
<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">List</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="n">List</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-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">  </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">  </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></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="m">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">inorder</span><span class="p">.</span><span class="n">length</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-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">    </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</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">i</span><span class="p">;</span>
<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">  </span><span class="p">}</span>
<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">dfs</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="n">preorder</span>: <span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</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="n">inorder_map</span>: <span class="kp">&amp;</span><span class="nc">HashMap</span><span class="o">&lt;</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="n">i</span>: <span class="kt">i32</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="n">l</span>: <span class="kt">i32</span><span class="p">,</span>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">r</span>: <span class="kt">i32</span><span class="p">,</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </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">// 子树区间为空时终止</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</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="p">{</span>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">None</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="p">}</span>
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">root</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">preorder</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</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="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&amp;</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]).</span><span class="n">unwrap</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">// 子问题：构建左子树</span>
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</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><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</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="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">r</span><span class="p">);</span>
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="nb">Some</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="p">}</span>
<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a>
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="k">fn</span> <span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span>: <span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">inorder</span>: <span class="kp">&amp;</span><span class="p">[</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">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></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">inorder_map</span>: <span class="nc">HashMap</span><span class="o">&lt;</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">inorder</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">        </span><span class="n">inorder_map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">);</span>
<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w">    </span><span class="p">}</span>
<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</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-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w">    </span><span class="n">root</span>
<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><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-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 子树区间为空时终止</span>
<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">));</span>
<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="n">root</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">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="n">root</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>
<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">root</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>
<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">size</span><span class="p">);</span>
<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">r</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a>
<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="cm">/* 构建二叉树 */</span>
<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">preorderSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">inorderSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">);</span>
<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></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">inorderSize</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-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</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">i</span><span class="p">;</span>
<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="p">}</span>
<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorderSize</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="n">inorderSize</span><span class="p">);</span>
<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">inorderMap</span><span class="p">);</span>
<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</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="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="p">,</span><span class="w"> </span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">,</span>
<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</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">r</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </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="c1">// 子树区间为空时终止</span>
<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</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="c1">// 查询 m ，从而划分左右子树</span>
<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="o">[</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]]!!</span>
<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</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">// 子问题：构建右子树</span>
<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</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="c1">// 返回根节点</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">root</span>
<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><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="cm">/* 构建二叉树 */</span>
<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </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="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="p">,</span><span class="w"> </span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">        </span><span class="n">inorderMap</span><span class="o">[</span><span class="n">inorder</span><span class="o">[</span><span class="n">i</span><span class="o">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><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="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</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="k">return</span><span class="w"> </span><span class="n">root</span>
<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span>
</code></pre></div>
</div>
<div class="tabbed-block">
<div class="highlight"><span class="filename">build_tree.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</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">dfs</span><span class="p">}</span>
<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</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">buildTree</span><span class="p">}</span>
</code></pre></div>
</div>
</div>
</div>
<details class="pythontutor">
<summary>可视化运行</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0Adef%20dfs%28%0A%20%20%20%20preorder%3A%20list%5Bint%5D,%0A%20%20%20%20inorder_map%3A%20dict%5Bint,%20int%5D,%0A%20%20%20%20i%3A%20int,%0A%20%20%20%20l%3A%20int,%0A%20%20%20%20r%3A%20int,%0A%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%9E%84%E5%BB%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E5%88%86%E6%B2%BB%22%22%22%0A%20%20%20%20%23%20%E5%AD%90%E6%A0%91%E5%8C%BA%E9%97%B4%E4%B8%BA%E7%A9%BA%E6%97%B6%E7%BB%88%E6%AD%A2%0A%20%20%20%20if%20r%20-%20l%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A0%B9%E8%8A%82%E7%82%B9%0A%20%20%20%20root%20%3D%20TreeNode%28preorder%5Bi%5D%29%0A%20%20%20%20%23%20%E6%9F%A5%E8%AF%A2%20m%20%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%88%92%E5%88%86%E5%B7%A6%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20m%20%3D%20inorder_map%5Bpreorder%5Bi%5D%5D%0A%20%20%20%20%23%20%E5%AD%90%E9%97%AE%E9%A2%98%EF%BC%9A%E6%9E%84%E5%BB%BA%E5%B7%A6%E5%AD%90%E6%A0%91%0A%20%20%20%20root.left%20%3D%20dfs%28preorder,%20inorder_map,%20i%20%2B%201,%20l,%20m%20-%201%29%0A%20%20%20%20%23%20%E5%AD%90%E9%97%AE%E9%A2%98%EF%BC%9A%E6%9E%84%E5%BB%BA%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20root.right%20%3D%20dfs%28preorder,%20inorder_map,%20i%20%2B%201%20%2B%20m%20-%20l,%20m%20%2B%201,%20r%29%0A%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E6%A0%B9%E8%8A%82%E7%82%B9%0A%20%20%20%20return%20root%0A%0A%0Adef%20build_tree%28preorder%3A%20list%5Bint%5D,%20inorder%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%9E%84%E5%BB%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%EF%BC%8C%E5%AD%98%E5%82%A8%20inorder%20%E5%85%83%E7%B4%A0%E5%88%B0%E7%B4%A2%E5%BC%95%E7%9A%84%E6%98%A0%E5%B0%84%0A%20%20%20%20inorder_map%20%3D%20%7Bval%3A%20i%20for%20i,%20val%20in%20enumerate%28inorder%29%7D%0A%20%20%20%20root%20%3D%20dfs%28preorder,%20inorder_map,%200,%200,%20len%28inorder%29%20-%201%29%0A%20%20%20%20return%20root%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20preorder%20%3D%20%5B3,%209,%202,%201,%207%5D%0A%20%20%20%20inorder%20%3D%20%5B9,%203,%201,%202,%207%5D%0A%20%20%20%20print%28f%22%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%20%3D%20%7Bpreorder%7D%22%29%0A%20%20%20%20print%28f%22%E4%B8%AD%E5%BA%8F%E9%81%8D%E5%8E%86%20%3D%20%7Binorder%7D%22%29%0A%20%20%20%20root%20%3D%20build_tree%28preorder,%20inorder%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=21&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
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</details>
<p>图 12-8 展示了构建二叉树的递归过程，各个节点是在向下“递”的过程中建立的，而各条边（引用）是在向上“归”的过程中建立的。</p>
<div class="tabbed-set tabbed-alternate" data-tabs="2:9"><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" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label><label for="__tabbed_2_9">&lt;9&gt;</label></div>
<div class="tabbed-content">
<div class="tabbed-block">
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="构建二叉树的递归过程" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step1.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step2" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step2.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step3" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step3.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step4" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step4.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step5" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step5.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step6" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step6.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step7" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step7.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step8" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step8.png" /></a></p>
</div>
<div class="tabbed-block">
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step9" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step9.png" /></a></p>
</div>
</div>
</div>
<p align="center"> 图 12-8 &nbsp; 构建二叉树的递归过程 </p>

<p>每个递归函数内的前序遍历 <code>preorder</code> 和中序遍历 <code>inorder</code> 的划分结果如图 12-9 所示。</p>
<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_overall.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="每个递归函数中的划分结果" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_overall.png" /></a></p>
<p align="center"> 图 12-9 &nbsp; 每个递归函数中的划分结果 </p>

<p>设树的节点数量为 <span class="arithmatex">\(n\)</span> ，初始化每一个节点（执行一个递归函数 <code>dfs()</code> ）使用 <span class="arithmatex">\(O(1)\)</span> 时间。<strong>因此总体时间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
<p>哈希表存储 <code>inorder</code> 元素到索引的映射，空间复杂度为 <span class="arithmatex">\(O(n)\)</span> 。在最差情况下，即二叉树退化为链表时，递归深度达到 <span class="arithmatex">\(n\)</span> ，使用 <span class="arithmatex">\(O(n)\)</span> 的栈帧空间。<strong>因此总体空间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>

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											2023-10-06 13:31:31 +08:00
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											2024-05-01 19:57:53 +08:00
+								            <a href="/zh-hant/chapter_divide_and_conquer/build_binary_tree_problem/" hreflang="zh-Hant" class="md-select__link">
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											2023-12-22 00:01:12 +08:00
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											2023-10-06 13:31:31 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-16 04:19:01 +08:00
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-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-16 04:19:01 +08:00
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-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
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-												deploy

											
										
										
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-												deploy

											
										
										
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-												deploy

											
										
										
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											2023-08-19 22:07:40 +08:00
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											2023-12-07 20:12:31 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-08-19 22:07:40 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-08-19 22:07:40 +08:00
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											2023-07-17 17:51:12 +08:00
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											2024-04-03 04:41:32 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-08-19 22:07:40 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-12-07 20:12:31 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-12-07 20:12:31 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-12-07 20:12:31 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-17 17:51:12 +08:00
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											2024-04-03 04:41:32 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-08-28 04:36:05 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-12-07 20:12:31 +08:00
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											2024-04-03 04:41:32 +08:00
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											2023-07-17 17:51:12 +08:00
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											2024-04-03 04:41:32 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-08-28 04:36:05 +08:00
+								            第 2 章 &nbsp; 复杂度分析
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											2023-07-17 17:51:12 +08:00
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											2023-12-07 20:12:31 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-08-19 22:07:40 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-12-07 20:12:31 +08:00
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											2023-08-24 17:47:31 +08:00
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 .2 &nbsp; 迭代与递归
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											2023-12-07 20:12:31 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-08-24 17:47:31 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-12-07 20:12:31 +08:00
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											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-08-24 17:47:31 +08:00
+.4 &nbsp; 空间复杂度
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-24 17:47:31 +08:00
+.5 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_data_structure/" class="md-nav__link ">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-19 16:10:17 +08:00
+								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 3 章 &nbsp; 数据结构
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_5">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 3 章 &nbsp; 数据结构
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 数据结构分类
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 基本数据类型
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 数字编码 *
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 字符编码 *
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.5 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-11-26 02:06:45 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
-												deploy

											
										
										
											2023-07-19 16:10:17 +08:00
+								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 4 章 &nbsp; 数组与链表
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_6">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 4 章 &nbsp; 数组与链表
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 数组
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 链表
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 列表
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-11-26 02:06:45 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
 								  <span class="md-ellipsis">
 .4 &nbsp; 内存与缓存 *
 								  </span>
 								    <span class="md-status md-status--new" title="最近添加">
 								    </span>
 								      </a>
 								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-11-26 02:06:45 +08:00
+.5 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
 								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 5 章 &nbsp; 栈与队列
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_7">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 5 章 &nbsp; 栈与队列
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 栈
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 队列
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 双向队列
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_hashing/" class="md-nav__link ">
 								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-21 03:56:52 +08:00
+								    第 6 章 &nbsp; 哈希表
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_8">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-21 03:56:52 +08:00
+								            第 6 章 &nbsp; 哈希表
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 哈希表
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 哈希冲突
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 哈希算法
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_hashing/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_tree/" class="md-nav__link ">
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 								  <span class="md-ellipsis">
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											2023-08-19 22:07:40 +08:00
+								    第 7 章 &nbsp; 树
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
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											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_9">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 7 章 &nbsp; 树
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
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											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 二叉树
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
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											2023-08-19 22:07:40 +08:00
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-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 二叉树数组表示
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
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											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
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											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 二叉搜索树
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.5 &nbsp; AVL 树 *
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_tree/summary/" class="md-nav__link">
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											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
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											2023-08-19 22:07:40 +08:00
+.6 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
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											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
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											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
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											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
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											2023-07-17 17:51:12 +08:00
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											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
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											2023-08-19 22:07:40 +08:00
+								    第 8 章 &nbsp; 堆
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
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											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_10">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 8 章 &nbsp; 堆
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_heap/heap/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 堆
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 建堆操作
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_heap/top_k/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
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											2023-12-28 17:18:44 +08:00
+.3 &nbsp; Top-k 问题
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_heap/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_graph/" class="md-nav__link ">
 								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 9 章 &nbsp; 图
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_11">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 9 章 &nbsp; 图
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_graph/graph/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 图
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 图基础操作
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 图的遍历
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_graph/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-08-04 05:25:00 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_searching/" class="md-nav__link ">
 								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 10 章 &nbsp; 搜索
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_12">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 10 章 &nbsp; 搜索
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 二分查找
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-08-04 05:25:00 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 二分查找插入点
-												deploy

											
										
										
											2023-08-04 05:25:00 +08:00
+								  </span>
 								      </a>
 								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 二分查找边界
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 哈希优化策略
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.5 &nbsp; 重识搜索算法
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_searching/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.6 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_sorting/" class="md-nav__link ">
 								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 11 章 &nbsp; 排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_13">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 11 章 &nbsp; 排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 排序算法
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 选择排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 冒泡排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 插入排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.5 &nbsp; 快速排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.6 &nbsp; 归并排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.7 &nbsp; 堆排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.8 &nbsp; 桶排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.9 &nbsp; 计数排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.10 &nbsp; 基数排序
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_sorting/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.11 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-17 02:17:51 +08:00
-												deploy

											
										
										
											2023-07-17 20:19:46 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-17 04:21:02 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" checked>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../" class="md-nav__link ">
-												deploy

											
										
										
											2023-07-19 16:10:17 +08:00
+								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 12 章 &nbsp; 分治
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="true">
 								          <label class="md-nav__title" for="__nav_14">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 12 章 &nbsp; 分治
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../divide_and_conquer/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 分治算法
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 04:21:02 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 04:21:02 +08:00
+								    <li class="md-nav__item">
 								      <a href="../binary_search_recur/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 分治搜索策略
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-17 04:21:02 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-17 04:21:02 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-17 04:21:02 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item md-nav__item--active">
 								      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
+								        <label class="md-nav__link md-nav__link--active" for="__toc">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 构建树问题
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
+								  </span>
 								          <span class="md-nav__icon md-icon"></span>
 								        </label>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      <a href="./" class="md-nav__link md-nav__link--active">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 构建树问题
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
 								<nav class="md-nav md-nav--secondary" aria-label="目录">
 								    <label class="md-nav__title" for="__toc">
 								      <span class="md-nav__icon md-icon"></span>
 								      目录
 								    </label>
 								    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
 								        <li class="md-nav__item">
-												deploy

											
										
										
											2023-08-20 13:37:20 +08:00
+								  <a href="#1" class="md-nav__link">
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
+								    <span class="md-ellipsis">
 . &nbsp; 判断是否为分治问题
 								    </span>
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
+								  </a>
 								</li>
 								        <li class="md-nav__item">
-												deploy

											
										
										
											2023-08-20 13:37:20 +08:00
+								  <a href="#2" class="md-nav__link">
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
+								    <span class="md-ellipsis">
 . &nbsp; 如何划分子树
 								    </span>
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
+								  </a>
 								</li>
 								        <li class="md-nav__item">
-												deploy

											
										
										
											2023-08-20 13:37:20 +08:00
+								  <a href="#3" class="md-nav__link">
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
+								    <span class="md-ellipsis">
 . &nbsp; 基于变量描述子树区间
 								    </span>
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
+								  </a>
 								</li>
 								        <li class="md-nav__item">
-												deploy

											
										
										
											2023-08-20 13:37:20 +08:00
+								  <a href="#4" class="md-nav__link">
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
+								    <span class="md-ellipsis">
 . &nbsp; 代码实现
 								    </span>
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
+								  </a>
 								</li>
 								    </ul>
 								</nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-17 02:17:51 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-17 02:17:51 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 02:17:51 +08:00
+								    <li class="md-nav__item">
 								      <a href="../hanota_problem/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 汉诺塔问题
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-17 02:17:51 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-17 02:17:51 +08:00
-												deploy

											
										
										
											2023-07-17 20:19:46 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 20:19:46 +08:00
+								    <li class="md-nav__item">
 								      <a href="../summary/" class="md-nav__link">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.5 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 20:19:46 +08:00
+								  </span>
 								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_backtracking/" class="md-nav__link ">
 								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 13 章 &nbsp; 回溯
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_15">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 13 章 &nbsp; 回溯
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 回溯算法
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 全排列问题
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 子集和问题
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; N 皇后问题
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.5 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
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-												deploy

											
										
										
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-												deploy

											
										
										
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
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											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
 								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 14 章 &nbsp; 动态规划
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
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											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_16">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 14 章 &nbsp; 动态规划
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
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											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 初探动态规划
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; DP 问题特性
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; DP 解题思路
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 0-1 背包问题
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.5 &nbsp; 完全背包问题
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.6 &nbsp; 编辑距离问题
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.7 &nbsp; 小结
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
-												deploy

											
										
										
											2023-07-21 22:50:40 +08:00
-												deploy

											
										
										
											2023-07-21 15:14:51 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
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											2023-07-17 17:51:12 +08:00
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											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
 								          <div class="md-nav__link md-nav__container">
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
+								            <a href="../../chapter_greedy/" class="md-nav__link ">
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											2023-07-17 17:51:12 +08:00
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											2023-07-20 18:24:35 +08:00
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											2023-07-17 17:51:12 +08:00
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								    第 15 章 &nbsp; 贪心
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								  </span>
 								            </a>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								                <span class="md-nav__icon md-icon"></span>
 								              </label>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_17">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+								            第 15 章 &nbsp; 贪心
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.1 &nbsp; 贪心算法
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
+								  </span>
 								      </a>
 								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.2 &nbsp; 分数背包问题
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
+								  </span>
 								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-21 15:14:51 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-21 15:14:51 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.3 &nbsp; 最大容量问题
-												deploy

											
										
										
											2023-07-21 15:14:51 +08:00
+								  </span>
 								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.4 &nbsp; 最大切分乘积问题
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-21 22:50:40 +08:00
 								      </a>
 								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-21 22:50:40 +08:00
+								    <li class="md-nav__item">
 								      <a href="../../chapter_greedy/summary/" class="md-nav__link">
 								  <span class="md-ellipsis">
-												deploy

											
										
										
											2023-08-19 22:07:40 +08:00
+.5 &nbsp; 小结
-												deploy

											
										
										
											2023-07-21 22:50:40 +08:00
+								  </span>
-												deploy

											
										
										
											2023-07-21 21:53:15 +08:00
 								      </a>
 								    </li>
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
+								          </ul>
 								        </nav>
 								    </li>
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
-												deploy

											
										
										
											2023-10-30 04:59:19 +08:00
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
 								    <li class="md-nav__item md-nav__item--nested">
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
-												deploy

											
										
										
											2023-07-20 18:24:35 +08:00
 								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_appendix/" class="md-nav__link ">
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+								    第 16 章 &nbsp; 附录
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+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
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+								            <span class="md-nav__icon md-icon"></span>
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+								            第 16 章 &nbsp; 附录
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+								    <li class="md-nav__item">
 								      <a href="../../chapter_appendix/installation/" class="md-nav__link">
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+.1 &nbsp; 编程环境安装
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+								  </span>
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+								    <li class="md-nav__item">
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+.2 &nbsp; 一起参与创作
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+								  </span>
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+								      </a>
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+								    <li class="md-nav__item">
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+								      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
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 								  <span class="md-ellipsis">
 .3 &nbsp; 术语表
 								  </span>
 								      </a>
 								    </li>
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											2023-07-17 17:51:12 +08:00
+								          </ul>
 								        </nav>
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+								    </li>
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-												deploy

											
										
										
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+								    <li class="md-nav__item md-nav__item--nested">
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-												deploy

											
										
										
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+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
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-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_reference/" class="md-nav__link ">
-												deploy

											
										
										
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+								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
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+								  <span class="md-ellipsis">
 								    参考文献
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 								            </a>
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+								          </div>
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+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_19">
-												deploy

											
										
										
											2023-07-17 17:51:12 +08:00
+								            <span class="md-nav__icon md-icon"></span>
 								            参考文献
 								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
 								          </ul>
 								        </nav>
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+								    </li>
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 								    <li class="md-nav__item md-nav__item--nested">
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+								        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_20" >
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 								          <div class="md-nav__link md-nav__container">
 								            <a href="../../chapter_paperbook/" class="md-nav__link ">
-												deploy

											
										
										
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+								    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19 2-5 4.5v11l5-4.5V2M6.5 5C4.55 5 2.45 5.4 1 6.5v14.66c0 .25.25.5.5.5.1 0 .15-.07.25-.07 1.35-.65 3.3-1.09 4.75-1.09 1.95 0 4.05.4 5.5 1.5 1.35-.85 3.8-1.5 5.5-1.5 1.65 0 3.35.31 4.75 1.06.1.05.15.03.25.03.25 0 .5-.25.5-.5V6.5c-.6-.45-1.25-.75-2-1V19c-1.1-.35-2.3-.5-3.5-.5-1.7 0-4.15.65-5.5 1.5V6.5C10.55 5.4 8.45 5 6.5 5Z"/></svg>
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+								    纸质书
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+								  </span>
 								    <span class="md-status md-status--new" title="最近添加">
 								    </span>
 								            </a>
 								          </div>
-												deploy

											
										
										
											2024-04-03 04:41:32 +08:00
+								        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_20_label" aria-expanded="false">
 								          <label class="md-nav__title" for="__nav_20">
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+								            <span class="md-nav__icon md-icon"></span>
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+								            纸质书
-												deploy

											
										
										
											2024-03-10 20:46:48 +08:00
+								          </label>
 								          <ul class="md-nav__list" data-md-scrollfix>
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 								        </nav>
 								    </li>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								  </ul>
 								</nav>
 								                  </div>
 								                </div>
 								              </div>
 								              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
 								                <div class="md-sidebar__scrollwrap">
 								                  <div class="md-sidebar__inner">
 								<nav class="md-nav md-nav--secondary" aria-label="目录">
-												deploy

											
										
										
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+								    <label class="md-nav__title" for="__toc">
 								      <span class="md-nav__icon md-icon"></span>
 								      目录
 								    </label>
 								    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
 								        <li class="md-nav__item">
-												deploy

											
										
										
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+								  <a href="#1" class="md-nav__link">
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+								    <span class="md-ellipsis">
 . &nbsp; 判断是否为分治问题
 								    </span>
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											2023-07-21 21:53:15 +08:00
+								  </a>
 								</li>
 								        <li class="md-nav__item">
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+								  <a href="#2" class="md-nav__link">
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+								    <span class="md-ellipsis">
 . &nbsp; 如何划分子树
 								    </span>
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+								  </a>
 								</li>
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+								  <a href="#3" class="md-nav__link">
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+								    <span class="md-ellipsis">
 . &nbsp; 基于变量描述子树区间
 								    </span>
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+								  </a>
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+								    <span class="md-ellipsis">
 . &nbsp; 代码实现
 								    </span>
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+								  </a>
 								</li>
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+								</nav>
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 								            <div class="md-content" data-md-component="content">
 								              <article class="md-content__inner md-typeset">
-												deploy

											
										
										
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+								                  <!-- Tags -->
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+								<!-- Actions -->
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+								<!-- Actions -->
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+								    <a
 								      href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_divide_and_conquer/build_binary_tree_problem.md"
 								      title="编辑此页"
 								      class="md-content__button md-icon"
 								    >
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+								      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+								    </a>
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+								  <!-- View button -->
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 								<!-- Page content -->
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+								<h1 id="123">12.3 &nbsp; 构建二叉树问题<a class="headerlink" href="#123" title="Permanent link">&para;</a></h1>
-												deploy

											
										
										
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+								<div class="admonition question">
 								<p class="admonition-title">Question</p>
-												deploy

											
										
										
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+								<p>给定一棵二叉树的前序遍历 <code>preorder</code> 和中序遍历 <code>inorder</code> ，请从中构建二叉树，返回二叉树的根节点。假设二叉树中没有值重复的节点（如图 12-5 所示）。</p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
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+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/build_tree_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="构建二叉树的示例数据" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_example.png" /></a></p>
-												deploy

											
										
										
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+								<p align="center"> 图 12-5 &nbsp; 构建二叉树的示例数据 </p>
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+								<h3 id="1">1. &nbsp; 判断是否为分治问题<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
-												deploy

											
										
										
											2023-12-02 06:24:11 +08:00
+								<p>原问题定义为从 <code>preorder</code> 和 <code>inorder</code> 构建二叉树，是一个典型的分治问题。</p>
-												deploy

											
										
										
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+								<ul>
-												deploy

											
										
										
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+								<li><strong>问题可以分解</strong>：从分治的角度切入，我们可以将原问题划分为两个子问题：构建左子树、构建右子树，加上一步操作：初始化根节点。而对于每棵子树（子问题），我们仍然可以复用以上划分方法，将其划分为更小的子树（子问题），直至达到最小子问题（空子树）时终止。</li>
 								<li><strong>子问题是独立的</strong>：左子树和右子树是相互独立的，它们之间没有交集。在构建左子树时，我们只需关注中序遍历和前序遍历中与左子树对应的部分。右子树同理。</li>
-												deploy

											
										
										
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+								<li><strong>子问题的解可以合并</strong>：一旦得到了左子树和右子树（子问题的解），我们就可以将它们链接到根节点上，得到原问题的解。</li>
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											2023-07-16 04:19:01 +08:00
+								</ul>
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											2023-08-20 13:37:20 +08:00
+								<h3 id="2">2. &nbsp; 如何划分子树<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
-												deploy

											
										
										
											2023-12-02 06:24:11 +08:00
+								<p>根据以上分析，这道题可以使用分治来求解，<strong>但如何通过前序遍历 <code>preorder</code> 和中序遍历 <code>inorder</code> 来划分左子树和右子树呢</strong>？</p>
 								<p>根据定义，<code>preorder</code> 和 <code>inorder</code> 都可以划分为三个部分。</p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								<ul>
-												deploy

											
										
										
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+								<li>前序遍历：<code>[ 根节点 | 左子树 | 右子树 ]</code> ，例如图 12-5 的树对应 <code>[ 3 | 9 | 2 1 7 ]</code> 。</li>
 								<li>中序遍历：<code>[ 左子树 | 根节点 ｜ 右子树 ]</code> ，例如图 12-5 的树对应 <code>[ 9 | 3 | 1 2 7 ]</code> 。</li>
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											2023-07-16 04:19:01 +08:00
+								</ul>
-												deploy

											
										
										
											2023-08-27 23:41:10 +08:00
+								<p>以上图数据为例，我们可以通过图 12-6 所示的步骤得到划分结果。</p>
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											2023-07-16 04:19:01 +08:00
+								<ol>
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											2023-07-26 08:59:03 +08:00
+								<li>前序遍历的首元素 3 是根节点的值。</li>
 								<li>查找根节点 3 在 <code>inorder</code> 中的索引，利用该索引可将 <code>inorder</code> 划分为 <code>[ 9 | 3 ｜ 1 2 7 ]</code> 。</li>
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											2023-12-28 17:18:44 +08:00
+								<li>根据 <code>inorder</code> 的划分结果，易得左子树和右子树的节点数量分别为 1 和 3 ，从而可将 <code>preorder</code> 划分为 <code>[ 3 | 9 | 2 1 7 ]</code> 。</li>
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											2023-07-16 04:19:01 +08:00
+								</ol>
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											2023-12-02 06:24:11 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="在前序遍历和中序遍历中划分子树" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" /></a></p>
 								<p align="center"> 图 12-6 &nbsp; 在前序遍历和中序遍历中划分子树 </p>
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											2023-07-16 04:19:01 +08:00
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											2023-08-20 13:37:20 +08:00
+								<h3 id="3">3. &nbsp; 基于变量描述子树区间<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
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											2023-08-27 23:41:10 +08:00
+								<p>根据以上划分方法，<strong>我们已经得到根节点、左子树、右子树在 <code>preorder</code> 和 <code>inorder</code> 中的索引区间</strong>。而为了描述这些索引区间，我们需要借助几个指针变量。</p>
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											2023-07-16 04:19:01 +08:00
+								<ul>
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+								<li>将当前树的根节点在 <code>preorder</code> 中的索引记为 <span class="arithmatex">\(i\)</span> 。</li>
 								<li>将当前树的根节点在 <code>inorder</code> 中的索引记为 <span class="arithmatex">\(m\)</span> 。</li>
 								<li>将当前树在 <code>inorder</code> 中的索引区间记为 <span class="arithmatex">\([l, r]\)</span> 。</li>
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											2023-07-16 04:19:01 +08:00
+								</ul>
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											2023-08-22 13:50:24 +08:00
+								<p>如表 12-1 所示，通过以上变量即可表示根节点在 <code>preorder</code> 中的索引，以及子树在 <code>inorder</code> 中的索引区间。</p>
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											2023-12-02 06:24:11 +08:00
+								<p align="center"> 表 12-1 &nbsp; 根节点和子树在前序遍历和中序遍历中的索引 </p>
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											2023-08-19 19:21:30 +08:00
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											2023-07-16 04:19:01 +08:00
+								<div class="center-table">
 								<table>
 								<thead>
 								<tr>
 								<th></th>
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											2023-07-24 03:03:58 +08:00
+								<th>根节点在 <code>preorder</code> 中的索引</th>
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											2023-07-16 04:19:01 +08:00
+								<th>子树在 <code>inorder</code> 中的索引区间</th>
 								</tr>
 								</thead>
 								<tbody>
 								<tr>
 								<td>当前树</td>
 								<td><span class="arithmatex">\(i\)</span></td>
 								<td><span class="arithmatex">\([l, r]\)</span></td>
 								</tr>
 								<tr>
 								<td>左子树</td>
 								<td><span class="arithmatex">\(i + 1\)</span></td>
 								<td><span class="arithmatex">\([l, m-1]\)</span></td>
 								</tr>
 								<tr>
 								<td>右子树</td>
 								<td><span class="arithmatex">\(i + 1 + (m - l)\)</span></td>
 								<td><span class="arithmatex">\([m+1, r]\)</span></td>
 								</tr>
 								</tbody>
 								</table>
 								</div>
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											2023-12-28 17:18:44 +08:00
+								<p>请注意，右子树根节点索引中的 <span class="arithmatex">\((m-l)\)</span> 的含义是“左子树的节点数量”，建议结合图 12-7 理解。</p>
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											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/build_tree_division_pointers.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="根节点和左右子树的索引区间表示" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_division_pointers.png" /></a></p>
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											2023-08-22 13:50:24 +08:00
+								<p align="center"> 图 12-7 &nbsp; 根节点和左右子树的索引区间表示 </p>
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+								<h3 id="4">4. &nbsp; 代码实现<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
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											2023-12-02 06:24:11 +08:00
+								<p>为了提升查询 <span class="arithmatex">\(m\)</span> 的效率，我们借助一个哈希表 <code>hmap</code> 来存储数组 <code>inorder</code> 中元素到索引的映射：</p>
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											2024-03-31 03:53:09 +08:00
+								<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
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+								<div class="tabbed-content">
 								<div class="tabbed-block">
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											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span> <span class="nf">dfs</span><span class="p">(</span>
 								<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>    <span class="n">preorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span>
 								<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">inorder_map</span><span class="p">:</span> <span class="nb">dict</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span>
 								<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
 								<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">l</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
 								<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">r</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
 								<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><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-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;构建二叉树：分治&quot;&quot;&quot;</span>
 								<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 子树区间为空时终止</span>
 								<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">if</span> <span class="n">r</span> <span class="o">-</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
 								<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">return</span> <span class="kc">None</span>
 								<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 初始化根节点</span>
 								<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
 								<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">m</span> <span class="o">=</span> <span class="n">inorder_map</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
 								<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 子问题：构建左子树</span>
 								<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">root</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</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="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 								<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 子问题：构建右子树</span>
 								<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">root</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">m</span> <span class="o">-</span> <span class="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
 								<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="c1"># 返回根节点</span>
 								<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>    <span class="k">return</span> <span class="n">root</span>
 								<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>
 								<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="k">def</span> <span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">inorder</span><span class="p">:</span> <span class="nb">list</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-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;构建二叉树&quot;&quot;&quot;</span>
 								<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="n">inorder_map</span> <span class="o">=</span> <span class="p">{</span><span class="n">val</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">val</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">inorder</span><span class="p">)}</span>
 								<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">inorder</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 								<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>    <span class="k">return</span> <span class="n">root</span>
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											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
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											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 构建二叉树：分治 */</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">dfs</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="o">&amp;</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</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="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
 								<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</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">// 初始化根节点</span>
 								<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</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">preorder</span><span class="p">[</span><span class="n">i</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="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
 								<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
 								<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
 								<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">r</span><span class="p">);</span>
 								<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
 								<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
 								<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a>
 								<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</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="o">&amp;</span><span class="n">preorder</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">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">;</span>
 								<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></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">inorder</span><span class="p">.</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-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</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">i</span><span class="p">;</span>
 								<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="p">}</span>
 								<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">size</span><span class="p">()</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-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
 								<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
 								<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></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-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
 								<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</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">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
 								<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
 								<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
 								<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
 								<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">r</span><span class="p">);</span>
 								<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
 								<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
 								<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a>
 								<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</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-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</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">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
 								<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></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">inorder</span><span class="p">.</span><span class="na">length</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-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">inorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
 								<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="p">}</span>
 								<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">length</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-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
-												deploy

											
										
										
											2023-11-27 02:32:13 +08:00
+								<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span>
 								<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">null</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="c1">// 初始化根节点</span>
-												deploy

											
										
										
											2023-10-08 01:43:42 +08:00
+								<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</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">// 子问题：构建左子树</span>
-												deploy

											
										
										
											2023-10-15 21:18:34 +08:00
+								<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="n">root</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">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
-												deploy

											
										
										
											2023-10-15 21:18:34 +08:00
+								<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="n">root</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">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
 								<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="p">}</span>
 								<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a>
 								<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="cm">/* 构建二叉树 */</span>
-												deploy

											
										
										
											2023-11-27 02:32:13 +08:00
+								<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">BuildTree</span><span class="p">(</span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
-												deploy

											
										
										
											2023-11-27 02:32:13 +08:00
+								<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="w">    </span><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></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="m">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">inorder</span><span class="p">.</span><span class="n">Length</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-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">.</span><span class="n">TryAdd</span><span class="p">(</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
 								<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="p">}</span>
-												deploy

											
										
										
											2023-11-27 02:32:13 +08:00
+								<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DFS</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">Length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
 								<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</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-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="o">-</span><span class="nx">l</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
 								<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="p">}</span>
 								<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
 								<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></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">NewTreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">])</span>
 								<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">    </span><span class="nx">m</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">[</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span>
 								<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
 								<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="nx">root</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">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">-</span><span class="mi">1</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">// 子问题：构建右子树</span>
 								<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="nx">root</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">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="o">+</span><span class="mi">1</span><span class="o">+</span><span class="nx">m</span><span class="o">-</span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">)</span>
 								<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
 								<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
 								<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="p">}</span>
 								<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a>
 								<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="kd">func</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="w"> </span><span class="p">[]</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-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">))</span>
 								<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">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="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w">        </span><span class="nx">inorderMap</span><span class="p">[</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">i</span>
 								<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w">    </span><span class="p">}</span>
 								<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a>
 								<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></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">dfsBuildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">inorder</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
 								<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span>
 								<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
 								<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span> <span class="nf">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">inorderMap</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">:</span> <span class="nb">Int</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">l</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">r</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-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>    <span class="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>    <span class="k">if</span> <span class="n">r</span> <span class="o">-</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="p">{</span>
 								<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>        <span class="k">return</span> <span class="kc">nil</span>
 								<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>    <span class="p">}</span>
 								<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>    <span class="c1">// 初始化根节点</span>
 								<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a>    <span class="kd">let</span> <span class="nv">root</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">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
 								<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a>    <span class="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>    <span class="kd">let</span> <span class="nv">m</span> <span class="p">=</span> <span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">!</span>
 								<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>    <span class="c1">// 子问题：构建左子树</span>
 								<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a>    <span class="n">root</span><span class="p">.</span><span class="kr">left</span> <span class="p">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="n">preorder</span><span class="p">,</span> <span class="n">inorderMap</span><span class="p">:</span> <span class="n">inorderMap</span><span class="p">,</span> <span class="n">i</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="n">l</span><span class="p">:</span> <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">:</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
 								<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a>    <span class="c1">// 子问题：构建右子树</span>
 								<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>    <span class="n">root</span><span class="p">.</span><span class="kr">right</span> <span class="p">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="n">preorder</span><span class="p">,</span> <span class="n">inorderMap</span><span class="p">:</span> <span class="n">inorderMap</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">m</span> <span class="o">-</span> <span class="n">l</span><span class="p">,</span> <span class="n">l</span><span class="p">:</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">:</span> <span class="n">r</span><span class="p">)</span>
 								<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>    <span class="c1">// 返回根节点</span>
 								<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>    <span class="k">return</span> <span class="n">root</span>
 								<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="p">}</span>
 								<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>
 								<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="kd">func</span> <span class="nf">buildTree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">],</span> <span class="n">inorder</span><span class="p">:</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-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a>    <span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a>    <span class="kd">let</span> <span class="nv">inorderMap</span> <span class="p">=</span> <span class="n">inorder</span><span class="p">.</span><span class="n">enumerated</span><span class="p">().</span><span class="bp">reduce</span><span class="p">(</span><span class="n">into</span><span class="p">:</span> <span class="p">[:])</span> <span class="p">{</span> <span class="nv">$0</span><span class="p">[</span><span class="nv">$1</span><span class="p">.</span><span class="n">element</span><span class="p">]</span> <span class="p">=</span> <span class="nv">$1</span><span class="p">.</span><span class="n">offset</span> <span class="p">}</span>
-												deploy

											
										
										
											2024-03-21 04:22:16 +08:00
+								<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a>    <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="n">preorder</span><span class="p">,</span> <span class="n">inorderMap</span><span class="p">:</span> <span class="n">inorderMap</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="n">inorder</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span> <span class="n">l</span><span class="p">:</span> <span class="n">inorder</span><span class="p">.</span><span class="n">startIndex</span><span class="p">,</span> <span class="n">r</span><span class="p">:</span> <span class="n">inorder</span><span class="p">.</span><span class="n">endIndex</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
 								<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</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="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><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-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
 								<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</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">preorder</span><span class="p">[</span><span class="nx">i</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">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</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="c1">// 子问题：构建左子树</span>
 								<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="nx">root</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">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
 								<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
 								<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="nx">root</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">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</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">// 返回根节点</span>
 								<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
 								<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
 								<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
 								<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
 								<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">        </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
 								<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="w">    </span><span class="p">}</span>
 								<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
 								<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
 								<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
 								<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">dfs</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="nx">preorder</span><span class="o">:</span><span class="w"> </span><span class="kt">number</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="nx">inorderMap</span><span class="o">:</span><span class="w"> </span><span class="kt">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">number</span><span class="o">&gt;</span><span class="p">,</span>
 								<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</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="nx">l</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span>
 								<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="nx">r</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span>
 								<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><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-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><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-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
 								<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</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="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</span><span class="p">]);</span>
 								<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="nx">preorder</span><span class="p">[</span><span class="nx">i</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="c1">// 子问题：构建左子树</span>
 								<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="w">    </span><span class="nx">root</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">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
 								<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
 								<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="nx">root</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">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">);</span>
 								<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
 								<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
 								<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="p">}</span>
 								<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a>
 								<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a><span class="kd">function</span><span class="w"> </span><span class="nx">buildTree</span><span class="p">(</span><span class="nx">preorder</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">inorder</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-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">number</span><span class="o">&gt;</span><span class="p">();</span>
 								<a id="__codelineno-7-27" name="__codelineno-7-27" href="#__codelineno-7-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-7-28" name="__codelineno-7-28" href="#__codelineno-7-28"></a><span class="w">        </span><span class="nx">inorderMap</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="nx">inorder</span><span class="p">[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="nx">i</span><span class="p">);</span>
 								<a id="__codelineno-7-29" name="__codelineno-7-29" href="#__codelineno-7-29"></a><span class="w">    </span><span class="p">}</span>
 								<a id="__codelineno-7-30" name="__codelineno-7-30" href="#__codelineno-7-30"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">dfs</span><span class="p">(</span><span class="nx">preorder</span><span class="p">,</span><span class="w"> </span><span class="nx">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="nx">inorder</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
 								<a id="__codelineno-7-31" name="__codelineno-7-31" href="#__codelineno-7-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">root</span><span class="p">;</span>
 								<a id="__codelineno-7-32" name="__codelineno-7-32" href="#__codelineno-7-32"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
 								<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span>
 								<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="n">List</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>
 								<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span>
 								<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span>
 								<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span>
 								<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">,</span>
 								<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></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-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="w">  </span><span class="p">}</span>
 								<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="w">  </span><span class="c1">// 初始化根节点</span>
 								<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
 								<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">!</span><span class="p">;</span>
 								<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="c1">// 子问题：构建左子树</span>
 								<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
 								<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="c1">// 子问题：构建右子树</span>
 								<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="w">  </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
 								<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="w">  </span><span class="c1">// 返回根节点</span>
 								<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="p">}</span>
 								<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a>
 								<a id="__codelineno-8-25" name="__codelineno-8-25" href="#__codelineno-8-25"></a><span class="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-8-26" name="__codelineno-8-26" href="#__codelineno-8-26"></a><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">List</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="n">List</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-8-27" name="__codelineno-8-27" href="#__codelineno-8-27"></a><span class="w">  </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-8-28" name="__codelineno-8-28" href="#__codelineno-8-28"></a><span class="w">  </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
 								<a id="__codelineno-8-29" name="__codelineno-8-29" href="#__codelineno-8-29"></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="m">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">inorder</span><span class="p">.</span><span class="n">length</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-8-30" name="__codelineno-8-30" href="#__codelineno-8-30"></a><span class="w">    </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</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">i</span><span class="p">;</span>
 								<a id="__codelineno-8-31" name="__codelineno-8-31" href="#__codelineno-8-31"></a><span class="w">  </span><span class="p">}</span>
 								<a id="__codelineno-8-32" name="__codelineno-8-32" href="#__codelineno-8-32"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
 								<a id="__codelineno-8-33" name="__codelineno-8-33" href="#__codelineno-8-33"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-8-34" name="__codelineno-8-34" href="#__codelineno-8-34"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-10-06 14:10:31 +08:00
+								<div class="highlight"><span class="filename">build_tree.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
-												deploy

											
										
										
											2024-03-18 03:11:11 +08:00
+								<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span> <span class="nf">dfs</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="n">preorder</span>: <span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</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="n">inorder_map</span>: <span class="kp">&amp;</span><span class="nc">HashMap</span><span class="o">&lt;</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="kt">i32</span><span class="o">&gt;</span><span class="p">,</span>
 								<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="n">i</span>: <span class="kt">i32</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="n">l</span>: <span class="kt">i32</span><span class="p">,</span>
 								<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">r</span>: <span class="kt">i32</span><span class="p">,</span>
 								<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">)</span><span class="w"> </span>-&gt; <span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </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">// 子树区间为空时终止</span>
 								<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</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="p">{</span>
 								<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">None</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="p">}</span>
 								<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
 								<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">root</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">preorder</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</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="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&amp;</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]).</span><span class="n">unwrap</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">// 子问题：构建左子树</span>
 								<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</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><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
 								<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorder_map</span><span class="p">,</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="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">r</span><span class="p">);</span>
 								<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
 								<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="w">    </span><span class="nb">Some</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
 								<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="p">}</span>
 								<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a>
 								<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="k">fn</span> <span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span>: <span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">],</span><span class="w"> </span><span class="n">inorder</span>: <span class="kp">&amp;</span><span class="p">[</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">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></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">inorder_map</span>: <span class="nc">HashMap</span><span class="o">&lt;</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span>::<span class="n">new</span><span class="p">();</span>
 								<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">inorder</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a><span class="w">        </span><span class="n">inorder_map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">);</span>
 								<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="w">    </span><span class="p">}</span>
 								<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">inorder_map</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</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-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a><span class="w">    </span><span class="n">root</span>
 								<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-10-18 02:17:09 +08:00
+								<div class="highlight"><span class="filename">build_tree.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
 								<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </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="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><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-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
 								<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
 								<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
 								<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">));</span>
 								<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="n">root</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">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
 								<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="n">root</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>
 								<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">root</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>
 								<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
 								<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
 								<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">size</span><span class="p">);</span>
 								<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="c1">// 子问题：构建右子树</span>
 								<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</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="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</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="n">r</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">);</span>
 								<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="c1">// 返回根节点</span>
 								<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
 								<a id="__codelineno-10-20" name="__codelineno-10-20" href="#__codelineno-10-20"></a>
 								<a id="__codelineno-10-21" name="__codelineno-10-21" href="#__codelineno-10-21"></a><span class="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-10-22" name="__codelineno-10-22" href="#__codelineno-10-22"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">preorderSize</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">inorderSize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-10-23" name="__codelineno-10-23" href="#__codelineno-10-23"></a><span class="w">    </span><span class="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
-												deploy

											
										
										
											2023-10-27 20:42:14 +08:00
+								<a id="__codelineno-10-24" name="__codelineno-10-24" href="#__codelineno-10-24"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">);</span>
-												deploy

											
										
										
											2023-10-18 02:17:09 +08:00
+								<a id="__codelineno-10-25" name="__codelineno-10-25" href="#__codelineno-10-25"></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">inorderSize</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-10-26" name="__codelineno-10-26" href="#__codelineno-10-26"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</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">i</span><span class="p">;</span>
 								<a id="__codelineno-10-27" name="__codelineno-10-27" href="#__codelineno-10-27"></a><span class="w">    </span><span class="p">}</span>
 								<a id="__codelineno-10-28" name="__codelineno-10-28" href="#__codelineno-10-28"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorderSize</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="n">inorderSize</span><span class="p">);</span>
 								<a id="__codelineno-10-29" name="__codelineno-10-29" href="#__codelineno-10-29"></a><span class="w">    </span><span class="n">free</span><span class="p">(</span><span class="n">inorderMap</span><span class="p">);</span>
 								<a id="__codelineno-10-30" name="__codelineno-10-30" href="#__codelineno-10-30"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
 								<a id="__codelineno-10-31" name="__codelineno-10-31" href="#__codelineno-10-31"></a><span class="p">}</span>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</code></pre></div>
 								</div>
-												deploy

											
										
										
											2023-07-26 10:57:52 +08:00
+								<div class="tabbed-block">
-												deploy

											
										
										
											2024-03-25 22:43:19 +08:00
+								<div class="highlight"><span class="filename">build_tree.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 构建二叉树：分治 */</span>
-												deploy

											
										
										
											2024-04-09 20:43:47 +08:00
+								<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">dfs</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="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span>
 								<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="n">inorderMap</span><span class="p">:</span><span class="w"> </span><span class="n">Map</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="p">,</span><span class="w"> </span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">,</span>
 								<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span>
 								<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w">    </span><span class="n">l</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</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">r</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span>
 								<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </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="c1">// 子树区间为空时终止</span>
 								<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">0</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span>
 								<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">    </span><span class="c1">// 初始化根节点</span>
 								<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</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="c1">// 查询 m ，从而划分左右子树</span>
 								<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="o">[</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]]!!</span>
 								<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">    </span><span class="c1">// 子问题：构建左子树</span>
 								<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</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">// 子问题：构建右子树</span>
 								<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="w">    </span><span class="n">root</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">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</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="c1">// 返回根节点</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">root</span>
 								<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><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="cm">/* 构建二叉树 */</span>
 								<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">:</span><span class="w"> </span><span class="n">IntArray</span><span class="p">):</span><span class="w"> </span><span class="n">TreeNode? </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="c1">// 初始化哈希表，存储 inorder 元素到索引的映射</span>
 								<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;</span><span class="kt">Int?</span><span class="p">,</span><span class="w"> </span><span class="kt">Int?</span><span class="o">&gt;</span><span class="p">()</span>
 								<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">indices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 								<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="w">        </span><span class="n">inorderMap</span><span class="o">[</span><span class="n">inorder</span><span class="o">[</span><span class="n">i</span><span class="o">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
 								<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><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="kd">val</span><span class="w"> </span><span class="nv">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</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="k">return</span><span class="w"> </span><span class="n">root</span>
 								<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="p">}</span>
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											2024-03-25 22:43:19 +08:00
+								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2024-03-31 03:53:09 +08:00
+								<div class="highlight"><span class="filename">build_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
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											2024-03-25 22:43:19 +08:00
+								<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
-												deploy

											
										
										
											2024-03-31 03:53:09 +08:00
+								<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span>
 								</code></pre></div>
 								</div>
 								<div class="tabbed-block">
 								<div class="highlight"><span class="filename">build_tree.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</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">dfs</span><span class="p">}</span>
 								<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
 								<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</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">buildTree</span><span class="p">}</span>
-												deploy

											
										
										
											2023-07-26 10:57:52 +08:00
+								</code></pre></div>
 								</div>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								</div>
-												deploy

											
										
										
											2024-01-07 23:43:01 +08:00
+								<details class="pythontutor">
 								<summary>可视化运行</summary>
-												deploy

											
										
										
											2024-01-09 16:00:33 +08:00
+								<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0Adef%20dfs%28%0A%20%20%20%20preorder%3A%20list%5Bint%5D,%0A%20%20%20%20inorder_map%3A%20dict%5Bint,%20int%5D,%0A%20%20%20%20i%3A%20int,%0A%20%20%20%20l%3A%20int,%0A%20%20%20%20r%3A%20int,%0A%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%9E%84%E5%BB%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E5%88%86%E6%B2%BB%22%22%22%0A%20%20%20%20%23%20%E5%AD%90%E6%A0%91%E5%8C%BA%E9%97%B4%E4%B8%BA%E7%A9%BA%E6%97%B6%E7%BB%88%E6%AD%A2%0A%20%20%20%20if%20r%20-%20l%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A0%B9%E8%8A%82%E7%82%B9%0A%20%20%20%20root%20%3D%20TreeNode%28preorder%5Bi%5D%29%0A%20%20%20%20%23%20%E6%9F%A5%E8%AF%A2%20m%20%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%88%92%E5%88%86%E5%B7%A6%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20m%20%3D%20inorder_map%5Bpreorder%5Bi%5D%5D%0A%20%20%20%20%23%20%E5%AD%90%E9%97%AE%E9%A2%98%EF%BC%9A%E6%9E%84%E5%BB%BA%E5%B7%A6%E5%AD%90%E6%A0%91%0A%20%20%20%20root.left%20%3D%20dfs%28preorder,%20inorder_map,%20i%20%2B%201,%20l,%20m%20-%201%29%0A%20%20%20%20%23%20%E5%AD%90%E9%97%AE%E9%A2%98%EF%BC%9A%E6%9E%84%E5%BB%BA%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20root.right%20%3D%20dfs%28preorder,%20inorder_map,%20i%20%2B%201%20%2B%20m%20-%20l,%20m%20%2B%201,%20r%29%0A%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E6%A0%B9%E8%8A%82%E7%82%B9%0A%20%20%20%20return%20root%0A%0A%0Adef%20build_tree%28preorder%3A%20list%5Bint%5D,%20inorder%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%9E%84%E5%BB%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%EF%BC%8C%E5%AD%98%E5%82%A8%20inorder%20%E5%85%83%E7%B4%A0%E5%88%B0%E7%B4%A2%E5%BC%95%E7%9A%84%E6%98%A0%E5%B0%84%0A%20%20%20%20inorder_map%20%3D%20%7Bval%3A%20i%20for%20i,%20val%20in%20enumerate%28inorder%29%7D%0A%20%20%20%20root%20%3D%20dfs%28preorder,%20inorder_map,%200,%200,%20len%28inorder%29%20-%201%29%0A%20%20%20%20return%20root%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20preorder%20%3D%20%5B3,%209,%202,%201,%207%5D%0A%20%20%20%20inorder%20%3D%20%5B9,%203,%201,%202,%207%5D%0A%20%20%20%20print%28f%22%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%20%3D%20%7Bpreorder%7D%22%29%0A%20%20%20%20print%28f%22%E4%B8%AD%E5%BA%8F%E9%81%8D%E5%8E%86%20%3D%20%7Binorder%7D%22%29%0A%20%20%20%20root%20%3D%20build_tree%28preorder,%20inorder%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=21&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
 								<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20TreeNode%3A%0A%20%20%20%20%22%22%22%E4%BA%8C%E5%8F%89%E6%A0%91%E8%8A%82%E7%82%B9%E7%B1%BB%22%22%22%0A%20%20%20%20def%20__init__%28self,%20val%3A%20int%20%3D%200%29%3A%0A%20%20%20%20%20%20%20%20self.val%3A%20int%20%3D%20val%20%20%23%20%E8%8A%82%E7%82%B9%E5%80%BC%0A%20%20%20%20%20%20%20%20self.left%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%20%20%20%20%20%20%20%20self.right%3A%20TreeNode%20%7C%20None%20%3D%20None%20%20%23%20%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E5%BC%95%E7%94%A8%0A%0Adef%20dfs%28%0A%20%20%20%20preorder%3A%20list%5Bint%5D,%0A%20%20%20%20inorder_map%3A%20dict%5Bint,%20int%5D,%0A%20%20%20%20i%3A%20int,%0A%20%20%20%20l%3A%20int,%0A%20%20%20%20r%3A%20int,%0A%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%9E%84%E5%BB%BA%E4%BA%8C%E5%8F%89%E6%A0%91%EF%BC%9A%E5%88%86%E6%B2%BB%22%22%22%0A%20%20%20%20%23%20%E5%AD%90%E6%A0%91%E5%8C%BA%E9%97%B4%E4%B8%BA%E7%A9%BA%E6%97%B6%E7%BB%88%E6%AD%A2%0A%20%20%20%20if%20r%20-%20l%20%3C%200%3A%0A%20%20%20%20%20%20%20%20return%20None%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E6%A0%B9%E8%8A%82%E7%82%B9%0A%20%20%20%20root%20%3D%20TreeNode%28preorder%5Bi%5D%29%0A%20%20%20%20%23%20%E6%9F%A5%E8%AF%A2%20m%20%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%88%92%E5%88%86%E5%B7%A6%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20m%20%3D%20inorder_map%5Bpreorder%5Bi%5D%5D%0A%20%20%20%20%23%20%E5%AD%90%E9%97%AE%E9%A2%98%EF%BC%9A%E6%9E%84%E5%BB%BA%E5%B7%A6%E5%AD%90%E6%A0%91%0A%20%20%20%20root.left%20%3D%20dfs%28preorder,%20inorder_map,%20i%20%2B%201,%20l,%20m%20-%201%29%0A%20%20%20%20%23%20%E5%AD%90%E9%97%AE%E9%A2%98%EF%BC%9A%E6%9E%84%E5%BB%BA%E5%8F%B3%E5%AD%90%E6%A0%91%0A%20%20%20%20root.right%20%3D%20dfs%28preorder,%20inorder_map,%20i%20%2B%201%20%2B%20m%20-%20l,%20m%20%2B%201,%20r%29%0A%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E6%A0%B9%E8%8A%82%E7%82%B9%0A%20%20%20%20return%20root%0A%0A%0Adef%20build_tree%28preorder%3A%20list%5Bint%5D,%20inorder%3A%20list%5Bint%5D%29%20-%3E%20TreeNode%20%7C%20None%3A%0A%20%20%20%20%22%22%22%E6%9E%84%E5%BB%BA%E4%BA%8C%E5%8F%89%E6%A0%91%22%22%22%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%93%88%E5%B8%8C%E8%A1%A8%EF%BC%8C%E5%AD%98%E5%82%A8%20inorder%20%E5%85%83%E7%B4%A0%E5%88%B0%E7%B4%A2%E5%BC%95%E7%9A%84%E6%98%A0%E5%B0%84%0A%20%20%20%20inorder_map%20%3D%20%7Bval%3A%20i%20for%20i,%20val%20in%20enumerate%28inorder%29%7D%0A%20%20%20%20root%20%3D%20dfs%28preorder,%20inorder_map,%200,%200,%20len%28inorder%29%20-%201%29%0A%20%20%20%20return%20root%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20preorder%20%3D%20%5B3,%209,%202,%201,%207%5D%0A%20%20%20%20inorder%20%3D%20%5B9,%203,%201,%202,%207%5D%0A%20%20%20%20print%28f%22%E5%89%8D%E5%BA%8F%E9%81%8D%E5%8E%86%20%3D%20%7Bpreorder%7D%22%29%0A%20%20%20%20print%28f%22%E4%B8%AD%E5%BA%8F%E9%81%8D%E5%8E%86%20%3D%20%7Binorder%7D%22%29%0A%20%20%20%20root%20%3D%20build_tree%28preorder,%20inorder%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=21&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">全屏观看 &gt;</a></div></p>
-												deploy

											
										
										
											2024-01-07 23:43:01 +08:00
+								</details>
-												deploy

											
										
										
											2023-12-02 06:24:11 +08:00
+								<p>图 12-8 展示了构建二叉树的递归过程，各个节点是在向下“递”的过程中建立的，而各条边（引用）是在向上“归”的过程中建立的。</p>
-												deploy

											
										
										
											2023-08-30 02:52:40 +08:00
+								<div class="tabbed-set tabbed-alternate" data-tabs="2:9"><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" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label><label for="__tabbed_2_9">&lt;9&gt;</label></div>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								<div class="tabbed-content">
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="构建二叉树的递归过程" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step1.png" /></a></p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step2" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step2.png" /></a></p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step3" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step3.png" /></a></p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step4" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step4.png" /></a></p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step5" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step5.png" /></a></p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step6" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step6.png" /></a></p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step7" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step7.png" /></a></p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step8" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step8.png" /></a></p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								<div class="tabbed-block">
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step9" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step9.png" /></a></p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</div>
 								</div>
 								</div>
-												deploy

											
										
										
											2023-08-22 13:50:24 +08:00
+								<p align="center"> 图 12-8 &nbsp; 构建二叉树的递归过程 </p>
-												deploy

											
										
										
											2023-08-17 05:12:16 +08:00
-												deploy

											
										
										
											2023-08-30 02:52:40 +08:00
+								<p>每个递归函数内的前序遍历 <code>preorder</code> 和中序遍历 <code>inorder</code> 的划分结果如图 12-9 所示。</p>
-												deploy

											
										
										
											2023-11-09 05:13:54 +08:00
+								<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_overall.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="每个递归函数中的划分结果" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_overall.png" /></a></p>
-												deploy

											
										
										
											2023-08-30 05:22:54 +08:00
+								<p align="center"> 图 12-9 &nbsp; 每个递归函数中的划分结果 </p>
-												deploy

											
										
										
											2023-08-30 02:52:40 +08:00
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								<p>设树的节点数量为 <span class="arithmatex">\(n\)</span> ，初始化每一个节点（执行一个递归函数 <code>dfs()</code> ）使用 <span class="arithmatex">\(O(1)\)</span> 时间。<strong>因此总体时间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
-												deploy

											
										
										
											2023-12-02 06:24:11 +08:00
+								<p>哈希表存储 <code>inorder</code> 元素到索引的映射，空间复杂度为 <span class="arithmatex">\(O(n)\)</span> 。在最差情况下，即二叉树退化为链表时，递归深度达到 <span class="arithmatex">\(n\)</span> ，使用 <span class="arithmatex">\(O(n)\)</span> 的栈帧空间。<strong>因此总体空间复杂度为 <span class="arithmatex">\(O(n)\)</span></strong> 。</p>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-09-21 20:44:52 +08:00
+								<!-- Source file information -->
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-09-21 20:44:52 +08:00
+								<!-- Was this page helpful? -->
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-09-21 20:44:52 +08:00
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 								</nav>
 								<!-- Comment system -->
-												deploy

											
										
										
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-												deploy

											
										
										
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-												deploy

											
										
										
											2024-01-04 15:23:24 +08:00
+								  <h5 align="center" id="__comments">欢迎在评论区留下你的见解、问题或建议</h5>
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								  <!-- Insert generated snippet here -->
 								  <script
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-												deploy

											
										
										
											2024-02-08 08:40:29 +08:00
+								    data-theme="light"
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    data-lang="zh-CN"
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											2023-09-12 03:15:25 +08:00
+								      var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								      giscus.setAttribute("data-theme", theme)
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											2023-09-12 03:15:25 +08:00
+								          var theme = palette.color.scheme === "slate" ? "dark_dimmed" : "light"
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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											2023-12-07 20:12:31 +08:00
+								<script>var target=document.getElementById(location.hash.slice(1));target&&target.name&&(target.checked=target.name.startsWith("__tabbed_"))</script>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								        </div>
 								          <button type="button" class="md-top md-icon" data-md-component="top" hidden>
-												deploy

											
										
										
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 								  <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 20h-2V8l-5.5 5.5-1.42-1.42L12 4.16l7.92 7.92-1.42 1.42L13 8v12Z"/></svg>
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											2023-10-06 13:31:31 +08:00
+								        <footer class="md-footer">
 								      <nav class="md-footer__inner md-grid" aria-label="页脚" >
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+								          <a href="../binary_search_recur/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 12.2 &amp;nbsp; 分治搜索策略">
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+								            <div class="md-footer__button md-icon">
 								              <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
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+								          <a href="../hanota_problem/" class="md-footer__link md-footer__link--next" aria-label="下一页: 12.4 &amp;nbsp; 汉诺塔问题">
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+								    </div>
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											2023-12-07 20:12:31 +08:00
+								      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </a>
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											2024-04-03 15:44:14 +08:00
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
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-												deploy

											
										
										
											2023-12-07 20:12:31 +08:00
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-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								    </a>
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											2023-12-07 20:12:31 +08:00
-												deploy

											
										
										
											2024-02-23 17:03:55 +08:00
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											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2024-01-25 21:09:11 +08:00
+								      <script src="../../assets/javascripts/bundle.c18c5fb9.min.js"></script>
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											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-09-24 17:12:06 +08:00
+								        <script src="../../javascripts/mathjax.js"></script>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-09-24 17:12:06 +08:00
+								        <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2024-04-26 19:21:13 +08:00
+								        <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js"></script>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
-												deploy

											
										
										
											2023-09-22 13:08:10 +08:00
+								  <script>document$.subscribe(() => {const lightbox = GLightbox({"touchNavigation": true, "loop": false, "zoomable": true, "draggable": false, "openEffect": "zoom", "closeEffect": "zoom", "slideEffect": "none"});})</script></body>
-												deploy

											
										
										
											2023-07-16 04:19:01 +08:00
+								</html>