Solution Explanation and Code

This problem requires finding the longest winning streak for each player in a database table. The solution uses a window function approach in SQL to efficiently achieve this.

Approach:

The core idea is to group consecutive wins together and then find the maximum length of each group for each player. We achieve this using two window functions in a common table expression (CTE):

1. ROW_NUMBER() OVER (PARTITION BY player_id ORDER BY match_day): This assigns a unique rank to each match for each player based on the match day. This is a sequential numbering of matches for each player.

2. ROW_NUMBER() OVER (PARTITION BY player_id, result ORDER BY match_day): This assigns another unique rank, but this time, it's partitioned by both player_id and result. This means the ranking restarts whenever the result changes (from Win to Draw or Lose, or vice versa).

The difference between these two rank numbers (rk in the query) identifies consecutive wins. Consecutive wins will have the same rk value because the second ranking restarts only when the result is not a win.

MySQL Code Explanation:

WITH
    S AS (
        SELECT
            *,
            ROW_NUMBER() OVER (
                PARTITION BY player_id
                ORDER BY match_day
            ) - ROW_NUMBER() OVER (
                PARTITION BY player_id, result
                ORDER BY match_day
            ) AS rk
        FROM Matches
    ),
    T AS (
        SELECT player_id, SUM(result = 'Win') AS s
        FROM S
        GROUP BY player_id, rk
    )
SELECT player_id, MAX(s) AS longest_streak
FROM T
GROUP BY player_id;

• CTE S: This selects all columns from the Matches table and calculates the rk value as described above. This rk essentially groups consecutive wins.

• CTE T: This groups the results by player_id and rk. It then sums the number of wins (SUM(result = 'Win')) within each group (rk). This sum represents the length of each winning streak for a particular player_id and rk.

• Final SELECT Statement: This selects the player_id and the maximum sum (MAX(s)) from CTE T, grouped by player_id. This gives the longest winning streak for each player.

Time Complexity Analysis:

The time complexity is dominated by the window function operations. Window functions generally have a time complexity of O(N log N) where N is the number of rows in the Matches table in the worst case. However, in practice, optimized database engines often achieve better performance. The grouping and aggregation operations have a complexity related to the size of the intermediate results from the CTEs, which is still proportional to N. Therefore, the overall time complexity can be approximated as O(N log N) or potentially better depending on the database implementation.

Space Complexity Analysis:

The space complexity is determined by the size of the intermediate CTEs (S and T). In the worst case, these CTEs can have a size proportional to the number of rows in the Matches table. Thus, the space complexity is O(N).

Follow Up:

If the requirement was changed to include draws in the streak (longest streak without a loss), the only change needed would be in CTE T by summing all non-loss results: SUM(result != 'Lose') instead of SUM(result = 'Win'). The rest of the logic remains the same.