题目描述:

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.

Example 1:

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2
3
4
  2
 / \
1   3

Binary tree

1
[2,1,3]

, return true.

Example 2:

1
2
3
4
  1
 / \
2   3

Binary tree

1
[1,2,3]

, return false.

验证一个二叉搜索树是否合法, 使用递归的方法来依次遍历左右子树.

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/**
 * 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 isValidBST(TreeNode* root) {
        if(!root) return true;
        if(root->left && BSTMax(root->left) >= root->val){
            return false;
        }
        if(root->right && BSTMin(root->right) <= root->val){
            return false;
        }
        return isValidBST(root->left) && isValidBST(root->right);
    }
    
    int BSTMax(TreeNode* root){
        if(!root->right){
            return root->val;
        }
        return BSTMax(root->right);
    }
    
    int BSTMin(TreeNode* root){
        if(!root->left){
            return root->val;
        }
        return BSTMin(root->left);
    }
};