Rank Teams from Ballot Preferences

## Problem Each vote ranks every team exactly once, from best to worst. Rank teams by these rules: 1. The team with more first-place votes ranks higher. 2. If tied, compare second-place vote counts, then third-place counts, continuing through every position. 3. If every position count ties, the alphabetically smaller team ID ranks higher. Return the team IDs concatenated in final rank order. ### Function Contract Implement `rankTeams(votes)` and return a string. ### Constraints & Assumptions - `1 <= len(votes) <= 1,000`. - `1 <= len(votes[0]) <= 26`. - Every vote contains the same distinct uppercase English letters exactly once, although their order differs. - Team IDs are single uppercase letters. ### Clarifying Questions to Ask - Are all teams present in every vote? Yes. - Does a first differing position decide the comparison? Yes. - Is alphabetical order ascending for a complete tie? Yes. - Can there be only one vote or one team? Yes. ```hint Build one position-count vector per team Sort teams by the negative counts at positions `0..t-1`, followed by the team letter. ``` ### Examples - `votes = ["ABC", "ACB", "ABC", "ACB", "ACB"]` returns `"ACB"`. - `votes = ["WXYZ", "XYZW"]` returns `"XWYZ"`. - `votes = ["ZMNAGUEDSJYLBOPHRQICWFXTVK"]` returns the same string. ### Evaluation Focus - Accumulates counts at every rank position for every team. - Compares count vectors in the correct descending direction and applies alphabetical fallback. - Derives the team set from the ballots rather than assuming all 26 letters. - Runs in `O(v * t + t^2 log t)` time or better for `v` votes and `t` teams. ### Extensions to Discuss 1. How would missing teams on some ballots change the rule? 2. What if team IDs are arbitrary strings rather than letters? 3. How would weighted voters affect the count vectors?