I went with an iterative postorder traversal using a stack where each frame tracked the node, a child iterator, and the max height seen so far among processed children.
Clarify the problem: this is essentially finding the height of each node from the leaves (leaf height = 0) and grouping nodes by height. Use a post-order traversal or topological peeling (Kahn's algorithm) to compute heights efficiently. Then present the solution with complexity analysis and discuss trade-offs between recursive and iterative approaches.
Pro tip: Mention that this problem is equivalent to finding the 'height' of each node in the tree when rooted at the leaves, and that it can be solved in O(n) time. Also, proactively discuss how to handle large trees to avoid stack overflow by using an iterative approach.
Confirm that the tree is rooted (or unrooted) and that leaves are nodes with no children. Discuss edge cases like empty tree, single node, and skewed trees.
Explain that the height of a node from leaves is the number of edges on the longest downward path to a leaf, with leaves having height 0. This is the key to grouping.
Propose a post-order DFS to compute heights recursively, or an iterative topological peeling (Kahn's algorithm) that removes leaves layer by layer. Discuss trade-offs: recursion is simpler but may cause stack overflow; iterative is more robust for large trees.
During traversal, compute each node's height and add it to a list for that height. Alternatively, during peeling, assign the current layer number as the height.
State that time and space complexity are O(n). Walk through a small example to verify correctness, and mention potential optimizations like using an array of lists for grouping.
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