LeetCode #1366 — MEDIUM

Rank Teams by Votes

Move from brute-force thinking to an efficient approach using array strategy.

Solve on LeetCode
The Problem

Problem Statement

In a special ranking system, each voter gives a rank from highest to lowest to all teams participating in the competition.

The ordering of teams is decided by who received the most position-one votes. If two or more teams tie in the first position, we consider the second position to resolve the conflict, if they tie again, we continue this process until the ties are resolved. If two or more teams are still tied after considering all positions, we rank them alphabetically based on their team letter.

You are given an array of strings votes which is the votes of all voters in the ranking systems. Sort all teams according to the ranking system described above.

Return a string of all teams sorted by the ranking system.

Example 1:

Input: votes = ["ABC","ACB","ABC","ACB","ACB"]
Output: "ACB"
Explanation: 
Team A was ranked first place by 5 voters. No other team was voted as first place, so team A is the first team.
Team B was ranked second by 2 voters and ranked third by 3 voters.
Team C was ranked second by 3 voters and ranked third by 2 voters.
As most of the voters ranked C second, team C is the second team, and team B is the third.

Example 2:

Input: votes = ["WXYZ","XYZW"]
Output: "XWYZ"
Explanation:
X is the winner due to the tie-breaking rule. X has the same votes as W for the first position, but X has one vote in the second position, while W does not have any votes in the second position. 

Example 3:

Input: votes = ["ZMNAGUEDSJYLBOPHRQICWFXTVK"]
Output: "ZMNAGUEDSJYLBOPHRQICWFXTVK"
Explanation: Only one voter, so their votes are used for the ranking.

Constraints:

  • 1 <= votes.length <= 1000
  • 1 <= votes[i].length <= 26
  • votes[i].length == votes[j].length for 0 <= i, j < votes.length.
  • votes[i][j] is an English uppercase letter.
  • All characters of votes[i] are unique.
  • All the characters that occur in votes[0] also occur in votes[j] where 1 <= j < votes.length.

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: In a special ranking system, each voter gives a rank from highest to lowest to all teams participating in the competition. The ordering of teams is decided by who received the most position-one votes. If two or more teams tie in the first position, we consider the second position to resolve the conflict, if they tie again, we continue this process until the ties are resolved. If two or more teams are still tied after considering all positions, we rank them alphabetically based on their team letter. You are given an array of strings votes which is the votes of all voters in the ranking systems. Sort all teams according to the ranking system described above. Return a string of all teams sorted by the ranking system.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Hash Map

Example 1

["ABC","ACB","ABC","ACB","ACB"]

Example 2

["WXYZ","XYZW"]

Example 3

["ZMNAGUEDSJYLBOPHRQICWFXTVK"]

Related Problems

  • Online Election (online-election)
Step 02

Core Insight

What unlocks the optimal approach

  • Build array rank where rank[i][j] is the number of votes for team i to be the j-th rank.
  • Sort the teams by rank array. if rank array is the same for two or more teams, sort them by the ID in ascending order.
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Upper-end input sizes
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1366: Rank Teams by Votes
class Solution {
    public String rankTeams(String[] votes) {
        int m = votes[0].length();
        int[][] cnt = new int[26][m + 1];
        for (var vote : votes) {
            for (int i = 0; i < m; ++i) {
                ++cnt[vote.charAt(i) - 'A'][i];
            }
        }
        Character[] s = new Character[m];
        for (int i = 0; i < m; ++i) {
            s[i] = votes[0].charAt(i);
        }
        Arrays.sort(s, (a, b) -> {
            int i = a - 'A', j = b - 'A';
            for (int k = 0; k < m; ++k) {
                if (cnt[i][k] != cnt[j][k]) {
                    return cnt[j][k] - cnt[i][k];
                }
            }
            return a - b;
        });
        StringBuilder ans = new StringBuilder();
        for (var c : s) {
            ans.append(c);
        }
        return ans.toString();
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n × m + m^2 × log m)
Space
O(m^2)

Approach Breakdown

BRUTE FORCE
O(n²) time
O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED
O(n) time
O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.