Validate binary tree sorted
Last updated: November 13, 2025
Quick Overview
Given a binary tree, write a function to determine if the tree is a valid binary search tree (BST). A valid BST must satisfy the property that for any given node, all values in its left subtree are less than the node's value, and all values in its right subtree are greater. The function should return a boolean indicating whether the tree is a valid BST.
Capital One
November 13, 2025174
15
2,219 solved
Given a binary tree, write a function to determine if the tree is a valid binary search tree (BST). A valid BST must satisfy the property that for any given node, all values in its left subtree are less than the node's value, and all values in its right subtree are greater. The function should return a boolean indicating whether the tree is a valid BST.
Capital One uses this problem in the Take-home Project to evaluate your algorithmic thinking. They expect you to discuss multiple approaches, analyze trade-offs between them, and implement the optimal solution with clean, readable code.
What the Interviewer Expects
- Quickly identify the optimal approach and its theoretical basis
- Handle complex algorithm design with multiple interacting components
- Write concise, elegant code under time pressure
- Prove correctness of your approach and discuss alternative solutions
- Optimize beyond the obvious: discuss constant factor improvements
- Address follow-up variations and explain how the solution generalizes
Key Topics to Cover
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- Can you solve this iteratively instead of recursively (or vice versa)?
- Can you optimize the space complexity of your solution?
- How would your solution change if the input was sorted?
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Problem Analysis
To determine if a binary tree is a valid binary search tree (BST), we can utilize the concept of recursion with bounds. The key property of a BST is that for any given node, all values in its left sub...
Approach
- Start at the root of the binary tree and initialize the valid range as (-infinity, infinity).
- Recursively check each node:
- For the current node, if its value is not within the valid range, ...
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