98. Validate Binary Search Tree

• Difficulty: Medium

• Topics: Tree, Depth-first Search

• Similar Questions:

  • Binary Tree Inorder Traversal

  • Find Mode in 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.

Example 1:

    2
   / \
  1   3

Input: [2,1,3]
Output: true

Example 2:

    5
   / \
  1   4
     / \
    3   6

Input: [5,1,4,null,null,3,6]
Output: false
Explanation: The root node's value is 5 but its right child's value is 4.

Solutions:

/**
 * 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) {
        return isValidBSTHelper(root, NULL, NULL);
    }

    bool isValidBSTHelper(TreeNode* root, TreeNode*left, TreeNode* right) {
        if (root == NULL)   return true;
        if (left && root->val <= left->val || right && root->val >= right->val) return false;
        return isValidBSTHelper(root->left, left, root) && isValidBSTHelper(root->right, root, right);
    }
};