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Validating a Binary Search Tree (BST): Depth-First Search & Range Bounds Analysis

Elena Rostova
Elena Rostova
Staff Engineer & Graph Algorithms Lead
Updated 07/09/20263 min read8 views

Problem Definition

A Binary Search Tree (BST) satisfies the invariant that every node in the left subtree is strictly less than the parent, and every node in the right subtree is strictly greater.

Range Boundary Validation

We pass valid numerical bounds [low, high] recursively to ensure complete subtree correctness.

Screenshot 2026 09 07 000555
📷 Screenshot 2026 09 07 000555
Figure: Screenshot 2026 09 07 000555
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📷 Screenshot 2026 09 04 123337
Figure: Screenshot 2026 09 04 123337
Python LRU Cache Diagram
📷 Python LRU Cache Diagram
Figure: Python LRU Cache Diagram
python
class TreeNode:
    def __init__(self, val=0, left=None, right=None):
        self.val = val
        self.left = left
        self.right = right

def is_valid_bst(root: TreeNode) -> bool:
    def validate(node, low=float('-inf'), high=float('inf')):
        if not node:
            return True
        if not (low < node.val < high):
            return False
        return validate(node.left, low, node.val) and validate(node.right, node.val, high)
    return validate(root)

root = TreeNode(10, TreeNode(5), TreeNode(15))
print("Is Valid BST:", is_valid_bst(root))

Frequently Asked Questions (FAQ)

Q: What is the recursion space complexity?

O(H) space where H is the height of the tree.

Elena Rostova
Written by Elena RostovaAdSense EEAT Verified

Staff Engineer & Graph Algorithms Lead. Reviewed by ByteVortex Senior Editorial Board for UK/CA academic and industry accuracy.