[LeetCode] Validate Binary Search Tree

问题：

Given a binary tree, determine if it is a valid binary search tree (BST).

Assume a BST is defined as follows:

• The left subtree of a node contains only nodes with keys less than the node's key.
• The right subtree of a node contains only nodes with keys greater than the node's key.
• Both the left and right subtrees must also be binary search trees.

分析：

一道简单的递归题。但很容易脑子一热，写出下面这样的代码：

class Solution {public:bool isValidBST(TreeNode *root) {if (!root) return true;if (root->left && root->left->val >= root->val) return false;if (root->right && root->right->val <= root->val) return false;return (isValidBST(root->left) && isValidBST(root->right));}};

这个代码的错误的地方在于，它没有判断一个node的左subtree中是不是所有的node都小于自己；右边也是类似。它仅仅判断了它左右两个children是不是小于自己。这是不够的。正确的代码如下：

class Solution {public:bool isValidBSTHelper(TreeNode *root, int min_val, int max_val) {if (!root)return true;if (root->val >= max_val || root->val <= min_val)return false;return (isValidBSTHelper(root->left, min_val, root->val) && isValidBSTHelper(root->right, root->val, max_val));}bool isValidBST(TreeNode *root) {int max_val = INT_MAX;int min_val = INT_MIN;return isValidBSTHelper(root, min_val, max_val);}};