[Leetcode 76] 98 Validate Binary Search Tree

Problem:

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.

Analysis:

Tree problem always related to its recursive property. Here to judge whether a binary tree is a binary search tree, the condition is as follows.

　　　root

　　/　　　

left　　　　　right

left sub-tree's nodes' value should all less than the root's value

right sub-tree's nodes' valu should all greater than the root's value

And do it recursively. 

For the left-subtree, the max value is root->val and for right-subtree, the min value is root->val

Here the construction of initial max and min value is a little tricky by using the bit operation. 

Code:

/**
 * 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 isValidBST(TreeNode *root) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int max = (1<<31)-1;
        int min = (1<<31);
        
        return judge(root, max, min);
    } 
    
private:
    bool judge(TreeNode *n, int max, int min) {
        if (n == NULL)
            return true;
            
        if (n->val < max && n->val > min)
            return judge(n->left, n->val, min) && judge(n->right, max, n->val);
        else
            return false;
    }
};