Solution Explanation for LeetCode 512: Game Play Analysis II

This problem requires finding the device used for the first login of each player in the Activity table. Two efficient approaches are presented: using a subquery and using a window function.

Approach 1: Subquery

This approach leverages a subquery to determine the earliest login date for each player and then joins this information back to the original table to retrieve the corresponding device ID.

Steps:

1. Inner Query: A subquery is used to find the minimum event_date for each player_id. This is achieved using GROUP BY player_id and MIN(event_date). The result is a table with player_id and the corresponding minimum event_date.

2. Outer Query: The outer query joins the results of the inner query back to the original Activity table. The WHERE clause ensures that only rows matching both player_id and the minimum event_date (found in the subquery) are selected.

3. Result: The outer query returns player_id and device_id for each player's first login.

MySQL Code:

SELECT
    player_id,
    device_id
FROM Activity
WHERE
    (player_id, event_date) IN (
        SELECT
            player_id,
            MIN(event_date) AS event_date
        FROM Activity
        GROUP BY 1
    );

Time Complexity: O(N log N), where N is the number of rows in the Activity table. This is primarily due to the sorting implied by the MIN aggregate function within the subquery. The IN operator can also contribute to the complexity depending on the database's optimization strategies.

Space Complexity: O(N) in the worst case, mainly due to the intermediate table created by the subquery. However, depending on the database's optimization, this might be less.

Approach 2: Window Function

This approach utilizes the power of window functions to assign a rank to each login event for each player, ordered by date. The first login gets rank 1.

Steps:

1. Common Table Expression (CTE): A CTE named T is created using the WITH clause. Within this CTE:

   • The RANK() window function assigns a rank to each row within each partition (player). The partitioning is done using PARTITION BY player_id, and the ranking is based on event_date using ORDER BY event_date. This assigns rank 1 to the earliest login for each player.
   • The CTE essentially adds a rk column representing the rank of each login event.

2. Main Query: The main query selects player_id and device_id from the CTE T. The WHERE clause filters the results, selecting only rows where rk = 1 (i.e., the first login).

MySQL Code:

WITH
    T AS (
        SELECT
            *,
            RANK() OVER (
                PARTITION BY player_id
                ORDER BY event_date
            ) AS rk
        FROM Activity
    )
SELECT player_id, device_id
FROM T
WHERE rk = 1;

Time Complexity: O(N log N). The RANK() window function involves sorting within each partition, which contributes to the logarithmic time complexity.

Space Complexity: O(N) in the worst case, to store the intermediate results of the CTE. Again, the database may optimize this.

Comparison:

Both approaches achieve the same result. The window function approach might be slightly more efficient in some database systems due to potential query optimization, although the asymptotic complexity remains the same for both. The subquery approach is generally more portable across different SQL dialects, while window functions have become a standard feature in most modern database systems. The choice depends on familiarity and specific database optimization capabilities.