Solution Explanation for LeetCode Problem 2339: All the Matches of the League

This problem requires generating all possible matches between teams in a league, considering that each pair of teams plays two matches (home and away). The solution uses a self-join on the Teams table.

Approach

The core idea is to join the Teams table with itself. This creates all possible pairings of teams. Since we need two matches for each pair (home and away), we don't need any additional logic to handle this; the self-join implicitly generates all combinations. The WHERE clause ensures that a team doesn't play against itself.

MySQL Solution

SELECT t1.team_name AS home_team, t2.team_name AS away_team
FROM
    Teams AS t1
    JOIN Teams AS t2
WHERE t1.team_name != t2.team_name;

Explanation:

1. SELECT t1.team_name AS home_team, t2.team_name AS away_team: This selects the team_name from the first instance of the Teams table (t1) and names it home_team, and similarly selects the team_name from the second instance (t2) and names it away_team.

2. FROM Teams AS t1 JOIN Teams AS t2: This performs a self-join on the Teams table, aliased as t1 and t2. This generates all possible combinations of teams.

3. WHERE t1.team_name != t2.team_name: This crucial condition filters out cases where a team plays against itself.

Time and Space Complexity Analysis

• Time Complexity: O(n^2), where n is the number of teams. This is because the self-join generates all possible pairs of teams, resulting in a quadratic number of comparisons.

• Space Complexity: O(n^2) in the worst case. The output table can contain up to n*(n-1) rows (all possible matches without self-matches), which is quadratic in terms of n. The space used for intermediate steps during the join operation might also scale similarly. However, the space complexity is often dominated by the size of the output, which is O(n^2).

This solution efficiently and directly addresses the problem statement using a simple and well-understood database operation. The time and space complexity are inherent to the nature of the problem, as we need to consider all possible pairings of teams.