LeetCode 98: Validate Binary Search Tree — Python Solution

Solve LeetCode 98: Validate Binary Search Tree in Python with a recursive value bounds approach. The key is to make the state invariant explicit, so the implementation and complexity follow naturally.

This guide paraphrases the task and does not reproduce LeetCode’s prompt. Use the official page for the complete statement, examples, constraints, and submission runner.

What the problem is testing

Pass strict lower and upper bounds into each subtree; every node must lie inside its inherited interval.

Algorithm

1. Pass strict lower and upper bounds into each subtree; every node must lie inside its inherited interval.
2. Maintain this invariant: The bounds represent every ancestor constraint that applies to the current subtree.
3. Continue until every input item or reachable state has been resolved, then return the accumulated result.

Python solution

LeetCode provides the list, tree, or graph node definition used by the method.

from collections import Counter, defaultdict, deque, OrderedDict
import random

class Solution:
    def isValidBST(self, root):
        def valid(node, lower, upper):
            if not node: return True
            if not lower < node.val < upper: return False
            return valid(node.left, lower, node.val) and valid(node.right, node.val, upper)
        return valid(root, float("-inf"), float("inf"))

Why this is correct

The proof follows the maintained state: The bounds represent every ancestor constraint that applies to the current subtree. Each iteration preserves that claim while permanently resolving at least one position, node, interval, or search state. When the loop or recursion ends, every candidate required by the problem has therefore been included or ruled out, so the returned value is correct.

Complexity

O(n) time and O(h) recursion space. The stated auxiliary space excludes the returned output unless the output is the data structure being built.

Edge cases

Duplicates are invalid because inequalities are strict.

Tested reference code

This implementation is included in the site’s downloadable 100-solution Python library. The complete suite compiles every solution and runs a behavioral assertion for every problem before publication.

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