I jumped straight to a brute force where I recomputed the subtree sum at every node separately.
Use a post-order traversal to compute the sum and count of descendants for each node, then check if the node's value equals the average. Return both the sum and count to the parent to avoid redundant computations. Handle edge cases like leaf nodes (no descendants) and null nodes appropriately.
Pro tip: Clarify with the interviewer whether leaf nodes (with no descendants) should be considered as satisfying the condition vacuously or if they should be excluded. This shows attention to detail and avoids ambiguity.
Ask about the definition of 'descendant' (all nodes in the subtree excluding the node itself) and how to handle leaf nodes and empty trees. Confirm whether the average is computed as sum/count and if integer division is acceptable.
Define a helper function that returns the sum of all node values in the subtree and the number of nodes. For each node, first recursively process left and right children, then compute the average of descendants (excluding the node) and compare with the node's value.
In the helper, if any subtree violates the condition, propagate a failure flag. For a leaf node, there are no descendants, so decide based on clarification whether it's valid. Return the sum and count up the tree.
Explain that the algorithm visits each node once, so time complexity is O(n) where n is the number of nodes. Space complexity is O(h) for the recursion stack, where h is the tree height, which is O(n) in the worst case.
Walk through a simple tree, a tree with a violation, a single-node tree, and an empty tree. Verify that the logic correctly handles these cases and discuss potential pitfalls like integer division or floating-point precision.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.