My first instinct was to track a global variable and do a standard DFS, which ended up being the right call.
Use a recursive depth-first search (DFS) that traverses from the root to each leaf, maintaining the current path sum. At each leaf, compare the current sum with the maximum found so far, and return the overall maximum. This approach naturally handles the N-ary tree structure by iterating over all children.
Pro tip: Clarify edge cases upfront: what if the tree is empty? What if node values can be negative? This shows attention to detail and prevents incorrect assumptions. Also, mention that the algorithm runs in O(N) time and O(H) space, where H is the tree height, which is optimal.
Ask about input constraints: can node values be negative? Is the tree guaranteed non-empty? What should be returned for an empty tree? Confirm that a leaf is a node with no children.
Select DFS (recursive or iterative) because it naturally tracks the path from root to leaf. Explain that BFS would require storing path sums for each node, which is less efficient.
Define a helper function that takes a node and the sum so far. If the node is a leaf, update the global maximum. Otherwise, recurse on each child with the updated sum.
State that the time complexity is O(N) since each node is visited once, and space complexity is O(H) for the recursion stack. Mention that this is optimal and no further optimization is needed.
Walk through a small example, including negative values, to verify correctness. Discuss potential pitfalls like integer overflow if sums can be large.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.