[leetcode] 98. Validate Binary Search Tree 解题报告

题目链接：https://leetcode.com/problems/validate-binary-search-tree/

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.

思路：要判断一个树是否是二叉树，要看是否满足三个条件：

1. 左子树包含的节点值都满足小于根节点

2. 右子树包含的节点值都满足大于根节点

3. 左右子树都是二叉排序树

在本题中只需要递归的遍历左右子树即可，给定一个范围空间，表明当前值的合法区间。需要注意的是初始的区间要超出[INT_MIN, INT_MAX]范围，不然会无法判断边界的值。

代码如下：

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    bool DFS(TreeNode* root, long Min, long Max)
    {
        if(!root) return true;
        if(root->val <= Min || root->val >= Max) return false;
        auto left = root->left, right = root->right;
        return DFS(left, Min, root->val) && DFS(right, root->val, Max);
    }
    
    bool isValidBST(TreeNode* root) {
        if(!root) return true;
        return DFS(root, LONG_MIN, LONG_MAX);
    }
};