I knew BFS was the right approach but spent too long debating whether to use DFS first.
Use a BFS traversal while tracking each node's column index, storing nodes in a hash map keyed by column. After traversal, sort the columns and output nodes in the order they were visited within each column to ensure top-to-bottom ordering.
Pro tip: Clarify whether nodes in the same column and row should be ordered left-to-right by their parent's column; if so, use a min-heap or sort by row and value. Also, mention that BFS naturally preserves top-to-bottom order, but if using DFS, you must track depth to sort correctly.
Ask about ordering within the same column and row, and confirm handling of empty tree or single node. Discuss whether to return a list of lists or another format.
Select BFS (level-order) with a queue storing (node, column) pairs, and a hash map (dictionary) mapping column index to a list of node values. Alternatively, use DFS with depth tracking if preferred.
Process nodes level by level, updating the column index for children (-1 for left, +1 for right). Append node values to the corresponding column list in the map.
Extract keys from the map, sort them in ascending order, and build the result list by iterating through sorted columns. Ensure nodes within each column are in top-to-bottom order (BFS naturally provides this).
State time complexity O(N log N) due to sorting columns (or O(N) if using ordered map), and space O(N). Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.