Validate Binary Search Tree

Problem

Given the root of a binary tree, determine if it is a valid binary search tree (BST).

A valid 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:

Input: root = [2,1,3]
Output: true

Example 2:

Input: root = [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.

Constraints:

The number of nodes in the tree is in the range [1, $10^4$}].
$-2^{31}$ <= Node.val <= $2^{31}$ - 1

Solution

• left 노드는 항상 상위 노드보다 작아야 하고, right 노드는 항상 상위보다 커야 한다

Code

// https://leetcode.com/problems/validate-binary-search-tree/description/
/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode() : val(0), left(nullptr), right(nullptr) {}
 *     TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
 *     TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
 * };
 */
class Solution
{
public:
    bool isPossible(TreeNode *root, long long l, long long r)
    {
        if (root == nullptr)
            return true;
        if (root->val < r && root->val > l)
            return isPossible(root->left, l, root->val) && isPossible(root->right, root->val, r);
        else
            return false;
    }

    bool isValidBST(TreeNode *root)
    {
        long long int min = -1000000000000;
        long long int max = 1000000000000;

        return isPossible(root, min, max);
    }
};

Testcase

false case

true case