Group a tree by vertical columns

Q: Group a tree by vertical columns

This question evaluates understanding of binary tree traversal, spatial coordinate mapping, ordering and tie-breaking rules, and the use of auxiliary data structures to group nodes by vertical columns.

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Question

Given the root of a binary tree, produce a vertical listing of nodes: assign each node an x-coordinate (root at x=0; left child x−1; right child x+ 1). For each x from smallest to largest, list node values from top to bottom; when multiple nodes share the same (x, depth), order them by their left-to-right appearance in level order. Return a list of columns (each a list of values). Describe your traversal strategy, tie-breaking, and data structures. Analyze time and space complexity.

Group a tree by vertical columns

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