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chapter_divide_and_conquer/build_binary_tree_problem/index.html
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<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（即引用）是在向上“归”的过程中建立的。</p>
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<p><img alt="构建二叉树的递归过程" src="../build_binary_tree_problem.assets/built_tree_step1.png" /></p>
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<p><img alt="built_tree_step9" src="../build_binary_tree_problem.assets/built_tree_step9.png" /></p>
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<p><img alt="built_tree_step10" src="../build_binary_tree_problem.assets/built_tree_step10.png" /></p>
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<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><img alt="built_tree_overall" src="../build_binary_tree_problem.assets/built_tree_overall.png" /></p>
<p align="center"> 图 12-9 &nbsp; built_tree_overall </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> 。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>