Implement tree column grouping and minimal parentheses fixes

Part A — Binary tree column grouping: Given the root of a binary tree, group node values by their vertical columns from leftmost to rightmost using x-coordinates (left child: x-1, right child: x+ 1). Within each column, list nodes in top-to-bottom order; if two nodes share the same row and column, order them by left-to-right encounter. Return a list of columns (each a list of integers). Describe your algorithm, the data structures used, and analyze time and space complexity. Follow-ups: ( 1) How would you stream results without storing the entire traversal? ( 2) How would you change tie-breaking to use node values instead? ( 3) Discuss handling trees with up to 100,000 nodes. Part B — Minimal deletions for balanced parentheses: Given a string s of lowercase letters and parentheses '()' only, remove the fewest parentheses so the string is balanced. Return any valid resulting string. Provide an O(n) time solution and prove correctness. Follow-ups: ( 1) Can you do it in a single pass? ( 2) Can you achieve O( 1) extra space if in-place edits are allowed?)