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krahets
2023-08-30 02:52:29 +08:00
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chapter_divide_and_conquer/build_binary_tree_problem.md
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=== "<9>"
![built_tree_step9](build_binary_tree_problem.assets/built_tree_step9.png)
=== "<10>"
![built_tree_step10](build_binary_tree_problem.assets/built_tree_step10.png)
<p align="center"> 图 12-8 &nbsp; 构建二叉树的递归过程 </p>
每个递归函数内的前序遍历 `preorder` 和中序遍历 `inorder` 的划分结果如图 12-9 所示。
![built_tree_overall](build_binary_tree_problem.assets/built_tree_overall.png)
<p align="center"> 图 12-9 &nbsp; built_tree_overall </p>
设树的节点数量为 $n$ ，初始化每一个节点（执行一个递归函数 `dfs()` ）使用 $O(1)$ 时间。**因此总体时间复杂度为 $O(n)$** 。
哈希表存储 `inorder` 元素到索引的映射，空间复杂度为 $O(n)$ 。最差情况下，即二叉树退化为链表时，递归深度达到 $n$ ，使用 $O(n)$ 的栈帧空间。**因此总体空间复杂度为 $O(n)$** 。