Solution Explanation

This problem requires generating league statistics based on match results. The solution involves several steps: calculating points for each team based on match outcomes, aggregating team statistics (matches played, points, goals for, goals against, and goal difference), and finally, ordering the results based on specified criteria.

Approach

The solution uses a Common Table Expression (CTE) to simplify the process.

1. CTE (Scores): This CTE calculates the points earned by each team for each match. It uses UNION ALL to combine results for home and away teams. The CASE statement determines points awarded (3 for a win, 1 for a draw, 0 for a loss). Goals scored and conceded are also tracked.

2. Main Query: The main query joins the Scores CTE with the Teams table using team_id. This links match results with team names. Aggregate functions (COUNT, SUM) are applied to compute the required statistics for each team.

3. Ordering: The final ORDER BY clause sorts the results first by points (descending), then by goal_diff (descending), and finally by team_name (ascending) to handle ties according to the problem's specifications.

Time Complexity Analysis

• CTE (Scores): The CTE involves two SELECT statements within a UNION ALL. The time complexity for each SELECT is proportional to the number of rows in the Matches table (let's call it M). Thus, the complexity of the CTE is O(M).

• Main Query: The JOIN operation between Scores and Teams takes O(M + T), where T is the number of rows in the Teams table (typically much smaller than M). Aggregation using SUM and COUNT takes O(M) time.

• Overall: The dominant factor in the time complexity is the processing of the Matches table, which is O(M). Therefore, the overall time complexity of the solution is O(M), where M is the number of matches.

Space Complexity Analysis

The space complexity is dominated by the intermediate CTE Scores. The size of Scores is at most twice the size of the Matches table (because of the UNION ALL). Thus, the space complexity is O(M), where M is the number of matches.

Code in MySQL

WITH
    Scores AS (
        SELECT
            home_team_id AS team_id,
            CASE
                WHEN home_team_goals > away_team_goals THEN 3
                WHEN home_team_goals < away_team_goals THEN 0
                ELSE 1
            END AS score,
            home_team_goals AS goals,
            away_team_goals AS away_goals
        FROM Matches
        UNION ALL
        SELECT
            away_team_id AS team_id,
            CASE
                WHEN home_team_goals > away_team_goals THEN 0
                WHEN home_team_goals < away_team_goals THEN 3
                ELSE 1
            END AS score,
            away_team_goals AS goals,
            home_team_goals AS away_goals
        FROM Matches
    )
SELECT
    team_name,
    COUNT(1) AS matches_played,
    SUM(score) AS points,
    SUM(goals) AS goal_for,
    SUM(away_goals) AS goal_against,
    (SUM(goals) - SUM(away_goals)) AS goal_diff
FROM
    Scores AS s
    JOIN Teams AS t ON s.team_id = t.team_id
GROUP BY s.team_id
ORDER BY points DESC, goal_diff DESC, team_name;

This MySQL solution directly implements the approach described above. Other SQL dialects might have slightly different syntax, but the core logic remains the same. There's no equivalent direct translation into languages like Python or Java since these are procedural and don't directly support SQL-style queries. You would need to use a database connector library to interact with a MySQL database from those languages.