How do you determine if a binary tree is height-balanced?
Direct Answer
This problem checks your recursive thinking skills and understanding of tree properties. It is crucial for roles involving hierarchical data processing.
Why Interviewers Ask This
Balanced trees are fundamental to efficient database indexing and search algorithms used in financial systems. Interviewers want to verify that you understand recursion depth and subtree validation. They are looking for candidates who can write clean, recursive code without stack overflow risks.
How to Answer This Question
Define what balanced means: the height difference between left and right subtrees must not exceed one. Propose a helper function that returns both the height and balance status. Explain why returning a single boolean is inefficient compared to returning height. Discuss base cases for leaf nodes and null pointers explicitly.
Key Points to Cover
- Define height difference constraint
- Recursive traversal strategy
- Return height alongside balance check
- Base case handling for leaves
Sample Answer
A binary tree is height-balanced if for every node, the height difference between its left and right subtrees is no more than one. I would implement a recursive function that calculates the height of each subtree. If any…
Common Mistakes to Avoid
- Calculating height separately for each node causing O(n^2)
- Not handling null nodes correctly
- Confusing balanced with complete binary trees
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