The basic column-tracking part I got pretty fast, just assign an index to each node and collect values by column.
Use BFS to traverse the tree level by level, tracking each node's column index (root at 0, left child -1, right child +1). Store nodes in a hash map keyed by column, appending values as encountered; then output columns from min to max. BFS naturally ensures top-to-bottom and left-to-right ordering within each column.
Pro tip: Clarify the tie-breaking rule upfront: if two nodes share the same row and column, BFS order ensures left-to-right. Mention that DFS with sorting could work but BFS is more efficient and directly satisfies the ordering constraints.
Confirm the ordering rules: columns left to right, within column top to bottom, and same row/column left to right. Ask about empty tree, single node, and nodes with same column but different depths.
Use a queue for level-order traversal, storing each node with its column index. Initialize root at column 0; left child gets col-1, right child col+1.
Use a hash map (or dictionary) mapping column index to a list of node values. Append values as nodes are dequeued, which preserves top-to-bottom and left-to-right order.
Determine the min and max column indices, then iterate from min to max, appending each column's list to the result. Return the list of lists.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.