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Validate the Binary Search Tree Property DSA Interview

Given the root of a binary tree, determine whether it satisfies the binary search tree ordering property across every subtree, not just immediate parent-child pairs.

Mock Interview with AI

1. Problem Statement

You are given the root of a binary tree. Determine whether every subtree satisfies the binary search tree property: every node in a left subtree is less than its ancestor, and every node in a right subtree is greater.

2. Live Coding Format

Choose Python, JavaScript, Java, or C++, then solve while explaining your reasoning to the live interviewer.

Validation uses handwritten tests only. The MVP does not compile or run code, and it does not provide AI algorithm completion.

3. Key Focus Areas

1
Problem clarification and contract
2
Approach exploration and optimality
3
Think-aloud communication and pacing
4
Implementation correctness
5
Code quality and language fluency
6
Handwritten tests and dry run
7
Debugging and self-correction
8
Complexity analysis
9
Follow-up performance

4. What Strong Candidates Should Demonstrate

✓Clarify the strictness of the ordering property and duplicate-value policy before coding.
✓Explain a naive local-check baseline and improve to a bounded-range recursive traversal.
✓Think aloud while implementing careful recursive range tracking.
✓Validate with explicit expected outputs and a top-to-bottom handwritten dry run.
✓Analyze time and space complexity and handle a bounded follow-up modification.

Evaluation Guide

This is an evaluation framework, not a single model answer. Strong designs may make different choices when their assumptions and trade-offs are explicit.

Problem clarification and contract

10%

Senior signals

✓Clarifies whether duplicate values are allowed and, if so, on which side they belong, and confirms an empty tree is valid.
✓Confirms the property must hold for every subtree, not just immediate parent-child comparisons.

Staff-level signals

◆Raises how extreme integer values should be handled without relying on language-specific sentinel overflow.

Common red flags

×Codes immediately while assuming only immediate parent-child comparisons are needed.

Approach exploration and optimality

20%

Senior signals

✓Explains a naive baseline that only compares each node to its direct children, identifies why this misses violations from a deeper ancestor, and improves to a recursive traversal that carries a valid (low, high) range down the tree.
✓Alternatively explains an in-order traversal that checks values are strictly increasing, and can justify why either approach is correct.

Staff-level signals

◆Discusses how to avoid sentinel overflow issues when bounding with actual minimum/maximum representable values.

Common red flags

×Starts implementation without explaining an approach even after one interviewer prompt.
×Proposes checking only immediate children without recognizing the ancestor-violation gap.

Think-aloud communication and pacing

10%

Senior signals

✓Explains the plan before coding and narrates how the valid range narrows while recursing while implementing.
✓Paces the core solution to leave time for validation and the follow-up.

Common red flags

×Writes substantial code silently and cannot explain what the code is doing.

Implementation correctness

25%

Senior signals

✓Implements a correct recursive (or iterative in-order) check that enforces the full ancestor-derived range or strictly increasing in-order sequence.
✓Handles an empty tree, a single node, a left-skewed or right-skewed tree, and a deep violation from a non-immediate ancestor.
✓Provides a convincing invariant argument for the range-narrowing recursion or in-order strictly-increasing check.

Common red flags

×Only compares nodes to immediate children, missing violations introduced by a grandparent or higher ancestor.
×Final code contains a material correctness bug that the candidate does not identify.

Code quality and language fluency

15%

Senior signals

✓Produces readable, language-appropriate code with clear parameter names for the current bounds or previous in-order value.

Common red flags

×Contains boundary-comparison errors (using <= where < is required, or vice versa) or syntax-level incoherence that prevents credible reasoning.

Handwritten validation, dry run, and debugging

10%

Senior signals

✓Provides explicit inputs and expected outputs before tracing the code from top to bottom, including a tree diagram.
✓Covers an empty tree, a single node, a deep ancestor violation, and duplicate values under the confirmed policy.
✓Finds and fixes an error independently, then re-validates the affected path.

Common red flags

×Claims the code works without a representative trace.

Complexity analysis and follow-up

10%

Senior signals

✓States linear time in the number of nodes and space proportional to tree height for the recursion stack, comparing it with the naive local-check baseline.

Staff-level signals

◆Discusses the difference between balanced and skewed tree height for the space bound.

Common red flags

×Cannot state the complexity of the implemented solution.
×Fails a reasonable follow-up despite having at least five minutes and receiving bounded clarification.

Trade-offs to articulate

Checking only immediate parent-child pairs is fast but incorrect, since it misses violations from higher ancestors.
A bounded-range recursive traversal is correct and linear time, using space proportional to tree height.
An in-order traversal checking strictly increasing order is equally correct but may require storing the previous value across recursive calls or using an explicit stack.

Practice follow-up questions

1.Coding follow-up: modify the solution to find the size of the largest subtree within the given tree that itself satisfies the binary search tree property, given that the whole tree may not be valid.
2.Verbal extension: how would the approach change if the tree were extremely unbalanced and recursion depth became a concern?

Want interactive feedback?

Practice this problem in the live coding workspace while the interviewer probes your clarification, algorithm, implementation, complexity, and handwritten tests.

Start Interview

Core Concepts

TreesBinary Search TreesRecursionComplexity Analysis