Classic recursion problem but I kept second-guessing myself on what counts as balanced.
Clarify the definition of height-balanced (typically, for every node, the heights of left and right subtrees differ by at most 1). Then propose a post-order DFS that returns the height of each subtree and a boolean indicating balance, computing both in a single pass to achieve O(n) time. If needed, discuss the naive O(n^2) approach and why it's suboptimal.
Pro tip: Mention that you can avoid repeated height calculations by returning a sentinel value (e.g., -1) when an imbalance is detected, allowing early termination. This shows you understand optimization and can handle edge cases efficiently.
Confirm the definition of height-balanced: for every node, the height difference between left and right subtrees is at most 1. Also clarify input/output expectations and edge cases (empty tree, single node).
Explain a straightforward solution: for each node, compute the height of left and right subtrees recursively, and check the balance condition. Note that this is O(n^2) due to repeated height computations.
Describe a post-order DFS that returns the height of the subtree and a boolean indicating whether it's balanced. Alternatively, return -1 if unbalanced to short-circuit. This achieves O(n) time and O(h) space.
Trace the algorithm on a small tree (e.g., a balanced tree and an unbalanced one) to demonstrate correctness and how early termination works.
State time and space complexity: O(n) time, O(h) space for recursion stack. Discuss edge cases: empty tree (balanced), single node (balanced), skewed tree (unbalanced).
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