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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: $O(1)$