I knew vertical order traversal cold but the weighting part tripped me up for a bit.
Clarify the definition of column weight and how it's computed, then use a BFS/DFS to group nodes by column index while tracking weights. Finally, sort the columns by weight and output the nodes in that order.
Pro tip: Discuss trade-offs between BFS and DFS for vertical order, and mention that if weights are dynamic, a priority queue might be needed; also, confirm if nodes within a column should be sorted by row or value.
Ask how column weight is defined (e.g., sum of node values, count of nodes) and whether ties in weight should be broken by column index or another rule.
Use BFS or DFS to traverse the tree, maintaining a map from column index to a list of nodes and a running weight for each column.
During traversal, update the weight for each column and append nodes to the corresponding list, ensuring order within a column (e.g., by row).
Extract the column indices and their weights, sort them by weight (and tie-breaker if specified), then output the nodes in that order.
Discuss time and space complexity, and handle edge cases like empty tree, negative weights, or columns with equal weights.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.