The recursive solution isn't hard to sketch out but I fumbled a bit explaining the complexity.
Start by clarifying the problem and edge cases, then propose a recursive solution that simultaneously traverses both trees, comparing root values and recursively checking each child pair in order. After outlining the algorithm, analyze time and space complexity, and discuss potential optimizations or trade-offs.
Pro tip: Mention that you can short-circuit on the first mismatch to save time, and that the space complexity is O(h) for recursion depth, but can be O(N) in the worst case for skewed trees. Also, note that an iterative approach using a stack can avoid recursion limits.
Restate the problem in your own words, confirm the definition of identical N-ary trees, and ask about constraints (e.g., tree size, recursion depth limits).
Explain that you will recursively compare the roots and then iterate through both children lists simultaneously, ensuring same length and recursive equality.
Discuss base cases: both null, one null, different values, different number of children. Also consider empty trees and single-node trees.
State that time complexity is O(min(N, M)) where N and M are the number of nodes in each tree, as you stop at first mismatch. Space complexity is O(min(H1, H2)) for recursion stack, where H is height.
Mention iterative alternative using stack/queue, potential for early termination, and that the recursive solution is clean but may risk stack overflow for deep trees.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.