## Validate Binary Search Tree

07/11/2016 Tree Depth First Search

## Question

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


Binary tree [2,1,3], return true.

Example 2:

   1
/ \
2   3


Binary tree [1,2,3], return false.

## Solution

Result: Accepted Time: 8 ms

Here should be some explanations.

/**
* Definition for a binary tree node.
* struct TreeNode {
*     int val;
*     struct TreeNode *left;
*     struct TreeNode *right;
* };
*/
bool is_set;
int before = INT_MIN;
bool dfs(struct TreeNode * root)
{
if(root == NULL) return true;
if(dfs(root->left))
{
if(is_set && root -> val <= before)
return false;
is_set = true;
before = root->val;
return dfs(root->right);
}
return false;
}
bool isValidBST(struct TreeNode* root){
is_set = false;
return dfs(root);
}


Complexity Analytics

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$