LeetCode: Validate Binary Search Tree [098]

【题目】

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.

confused what "{1,#,2,3}" means? >
read more on how binary tree is serialized on OJ.

【题意】

给定一棵二叉树，推断是不是合法的二叉搜索树

【思路】

依据二叉搜索树定义，递归推断就可以

【代码】

/**
 * Definition for binary tree
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:

    bool isValid(TreeNode*root, int lowBound, int upBound){
        //每棵树取值都有上边界和下边界
        if(root==NULL)return true;
        //推断节点值是否在合法的取值区间内
        if(!(root->val>lowBound && root->val<upBound))return false;

        //推断左子树是否合法
        if(root->left){
            if(root->left->val >= root->val || !isValid(root->left, lowBound, root->val))return false;
        }
        //推断右子树
        if(root->right){
            if(root->right->val <= root->val || !isValid(root->right, root->val, upBound))return false;
        }

        return true;
    }

    bool isValidBST(TreeNode *root) {
        return isValid(root, INT_MIN, INT_MAX);
    }
};