diff --git a/img/Construct-Binary-Search-Tree-from-Preorder-Traversal.png b/img/Construct-Binary-Search-Tree-from-Preorder-Traversal.png new file mode 100644 index 0000000000000..3423c8333864d Binary files /dev/null and b/img/Construct-Binary-Search-Tree-from-Preorder-Traversal.png differ diff --git a/solution/1008.Construct Binary Search Tree from Preorder Traversal/README.md b/solution/1008.Construct Binary Search Tree from Preorder Traversal/README.md new file mode 100644 index 0000000000000..9a9d0d9670ef7 --- /dev/null +++ b/solution/1008.Construct Binary Search Tree from Preorder Traversal/README.md @@ -0,0 +1,80 @@ +## 先序遍历构造二叉树 + +### 问题描述 + +返回与给定先序遍历 **preorder** 相匹配的二叉搜索树(binary **search** tree)的根结点。 + +**示例1:** + +``` +输入:[8,5,1,7,10,12] +输出:[8,5,10,1,7,null,12] +``` + +![示例1](/img/Construct-Binary-Search-Tree-from-Preorder-Traversal.png) + +**提示:** + +- `1 <= preorder.length <= 100` +- The values of `preorder` are distinct. + +### 解法 + +二叉树类的题目可以考虑使用递归中的分治法,让本次递归的根节点(sub-root)来管理自身子树的生成方式。而本题使用的是**前序遍历法**所生成的数组,则先检查了根节点,再检查左子树,再检查右子树。因此每层递归我们需要确定的是: + +* 本层递归的根节点是什么? +* 根节点确定后,本层递归之后的左子树范围是什么,右子树的范围是什么? + +对于第一个问题,我们知道前序遍历法的根节点一定是当前范围内的第一个元素;而对于第二个问题,我们知道右子树开始于**第一个比当前根节点大的元素**,而左子树结束于该元素的前面一个元素。在解决了这两个问题后,答案已经比较明确了,在每一层递归中,我们需要一个 start 和一个 end 来表示当前的递归所涉及的元素范围: + +* 确定当前的递归是否结束(start > end || start >= end) +* 确定当前递归层的根节点(start) +* 确定左子树的范围(start + 1, leftEnd - 1)和右子树的范围(leftEnd, end) + +因此有如下的递归解法: + +```java +/** + * Definition for a binary tree node. + * public class TreeNode { + * int val; + * TreeNode left; + * TreeNode right; + * TreeNode(int x) { val = x; } + * } + */ +class Solution { + public TreeNode bstFromPreorder(int[] preorder) { + if (preorder == null || preorder.length == 0) { + return null; + } + // 进入分治法的递归 + return helper(preorder, 0, preorder.length - 1); + } + + private TreeNode helper(int[] preorder, int start, int end) { + // System.out.println("start: " + start + " end: " + end); + // 确认递归结束的标志,当 start == end 时,表示该区间只剩下一个 subRoot 节点 + if (start > end) { + return null; + } + if (start == end) { + return new TreeNode(preorder[start]); + } + // 前序遍历,首先遍历到的为根 + TreeNode root = new TreeNode(preorder[start]); + int leftEnd = start; + while (leftEnd <= end) { + if (preorder[leftEnd] > preorder[start]) { + break; + } + leftEnd++; + } + // System.out.println("leftEnd:" + leftEnd + " num: " + preorder[leftEnd]); + root.left = helper(preorder, start + 1, leftEnd - 1); + root.right = helper(preorder, leftEnd, end); + return root; + } +} +``` + diff --git a/solution/1008.Construct Binary Search Tree from Preorder Traversal/Solution.java b/solution/1008.Construct Binary Search Tree from Preorder Traversal/Solution.java new file mode 100644 index 0000000000000..eae491aa6f3bc --- /dev/null +++ b/solution/1008.Construct Binary Search Tree from Preorder Traversal/Solution.java @@ -0,0 +1,42 @@ +/** + * Definition for a binary tree node. + * public class TreeNode { + * int val; + * TreeNode left; + * TreeNode right; + * TreeNode(int x) { val = x; } + * } + */ +class Solution { + public TreeNode bstFromPreorder(int[] preorder) { + if (preorder == null || preorder.length == 0) { + return null; + } + // 进入分治法的递归 + return helper(preorder, 0, preorder.length - 1); + } + + private TreeNode helper(int[] preorder, int start, int end) { + // System.out.println("start: " + start + " end: " + end); + // 确认递归结束的标志,当 start == end 时,表示该区间只剩下一个 subRoot 节点 + if (start > end) { + return null; + } + if (start == end) { + return new TreeNode(preorder[start]); + } + // 前序遍历,首先遍历到的为根 + TreeNode root = new TreeNode(preorder[start]); + int leftEnd = start; + while (leftEnd <= end) { + if (preorder[leftEnd] > preorder[start]) { + break; + } + leftEnd++; + } + // System.out.println("leftEnd:" + leftEnd + " num: " + preorder[leftEnd]); + root.left = helper(preorder, start + 1, leftEnd - 1); + root.right = helper(preorder, leftEnd, end); + return root; + } +} \ No newline at end of file