Return the Top Two Teams by Points, Goal Difference, and Tie Breakers

Problem Statement

You are given the results of a round-robin tournament with n teams numbered from 0 to n - 1. You are given an integer n and a 2D integer array matches, where each element matches[i] = [teamA, teamB, scoreA, scoreB] denotes a match played between teamA and teamB, with teamA scoring scoreA goals and teamB scoring scoreB goals.

Points are awarded as follows:

• Win: 3 points to the winning team, 0 points to the losing team.
• Draw: 1 point to each team if scoreA == scoreB.

Teams should be ranked according to the following tie-breaking rules, in order of priority:

1. Total points earned (higher is better)
2. Goal difference (total goals scored - total goals conceded, higher is better)
3. Total goals scored (higher is better)
4. Team index (smaller index is better)

Return an array containing the indices of the top two teams: [first_place_index, second_place_index].

Function Signature

def get_top_two_teams(n: int, matches: list[list[int]]) -> list[int]:
    pass

Input Format

• n: An integer representing the number of teams.
• matches: A list of lists of four integers [teamA, teamB, scoreA, scoreB].

Output Format

• Return a list of two integers [top1, top2].

Constraints

• 2 <= n <= 10^4
• 1 <= len(matches) <= 10^5
• 0 <= teamA, teamB < n and teamA != teamB
• 0 <= scoreA, scoreB <= 100

Examples

Example 1

Input: n = 3, matches = [
    [0, 1, 2, 1],
    [1, 2, 3, 0],
    [0, 2, 1, 1]
]
Output: [0, 1]

Explanation:

• Team 0: beats Team 1 (3 pts, +1 GD, 2 GF), ties Team 2 (1 pt, 0 GD, 1 GF) -> Total: 4 pts, GD = +1, GF = 3.
• Team 1: loses to Team 0 (0 pts, -1 GD, 1 GF), beats Team 2 (3 pts, +3 GD, 3 GF) -> Total: 3 pts, GD = +2, GF = 4.
• Team 2: loses to Team 1 (0 pts, -3 GD, 0 GF), ties Team 0 (1 pt, 0 GD, 1 GF) -> Total: 1 pt, GD = -3, GF = 1. Ranked: Team 0 (4 pts), Team 1 (3 pts). Top two are [0, 1].

Example 2

Input: n = 3, matches = [
    [0, 1, 2, 2],
    [1, 2, 1, 1],
    [0, 2, 0, 0]
]
Output: [0, 1]

Explanation:

• Team 0: 2 draws -> 2 pts, GD = 0, GF = 2.
• Team 1: 2 draws -> 2 pts, GD = 0, GF = 3.
• Team 2: 2 draws -> 2 pts, GD = 0, GF = 1. All have 2 points and 0 GD. Team 1 has 3 GF (1st place). Team 0 has 2 GF (2nd place). Thus, [1, 0] is returned.

Edge Cases

• Teams that play no matches retain 0 points, 0 GD, and 0 GF.
• Complete ties between teams are resolved by smaller team index.