Solution Explanation for LeetCode 534: Game Play Analysis III

This problem requires calculating the cumulative sum of games played for each player up to a given date. We can achieve this efficiently using SQL window functions or with a self-join.

Approach 1: Using Window Functions (Most Efficient)

This approach leverages the power of SQL window functions for a concise and efficient solution. The SUM() OVER() function calculates the running total.

MySQL Code:

SELECT
    player_id,
    event_date,
    SUM(games_played) OVER (PARTITION BY player_id ORDER BY event_date) AS games_played_so_far
FROM Activity;

Explanation:

• SELECT player_id, event_date: Selects the player ID and event date.
• SUM(games_played) OVER (PARTITION BY player_id ORDER BY event_date): This is the core of the solution.
  • PARTITION BY player_id: This divides the data into groups based on each player. The running sum is calculated separately for each player.
  • ORDER BY event_date: Within each player's group, the rows are ordered by the event date, ensuring the running sum is calculated correctly in chronological order.
  • SUM(games_played): This calculates the sum of games_played for each row, considering the PARTITION BY and ORDER BY clauses. The OVER clause makes it a running sum (cumulative sum).
• AS games_played_so_far: This renames the resulting column for clarity.

Time Complexity: O(N log N) - due to sorting within partitions. The exact complexity depends on the database engine's implementation of window functions. In practice it's very efficient. Space Complexity: O(N) - The space used depends on the size of the input table and intermediate results.

Approach 2: Self-Join (Less Efficient)

This approach uses a self-join to compare each row with all previous rows for the same player. While functional, it's generally less efficient than the window function approach, especially for large datasets.

MySQL Code:

SELECT
    t1.player_id,
    t1.event_date,
    SUM(t2.games_played) AS games_played_so_far
FROM
    Activity AS t1
INNER JOIN Activity AS t2 ON t1.player_id = t2.player_id AND t1.event_date >= t2.event_date
GROUP BY t1.player_id, t1.event_date;
 

Explanation:

• Activity AS t1: Aliases the Activity table as t1 (the main table).
• INNER JOIN Activity AS t2 ON t1.player_id = t2.player_id AND t1.event_date >= t2.event_date: This joins t1 with itself (t2). The join condition ensures that we only include rows from t2 where the player ID is the same and the event date is on or before the event date in t1.
• SUM(t2.games_played): Calculates the sum of games_played from all matching rows in t2 (all games played up to the current date).
• GROUP BY t1.player_id, t1.event_date: Groups the results by player ID and event date, ensuring a single row for each player-date combination with the total games played.

Time Complexity: O(N^2) in the worst case (all dates for one player). The database optimizer might improve this in practice, but it's fundamentally less efficient than the window function method. Space Complexity: O(N) - depends on the size of the table and intermediate results.

In summary: The window function approach (Solution 1) is the preferred and more efficient method for solving this problem due to its optimized implementation in most database systems. The self-join approach (Solution 2) works but is less efficient for larger datasets. Solution 3 is functionally equivalent to Solution 2 but uses a CROSS JOIN instead of an INNER JOIN, which can be slightly less efficient due to producing more intermediate results before the GROUP BY clause.