Game Play Analysis V - Solution & Explanation

Problem Overview: The table Activity stores player login activity with columns player_id, device_id, event_date, and games_played. The goal is to compute the fraction of players who return exactly one day after their first login. The result is grouped by each player's install date (their first recorded login).

Approach 1: Subquery + Self Join (O(n) time, O(n) space)

Start by finding each player's install date using MIN(event_date) grouped by player_id. This produces a derived table where every player has a single install date. Next, join this result back to the Activity table and check whether the player has another record where event_date = install_date + INTERVAL 1 DAY. Counting these matches gives the number of players who returned the next day. Finally, group by install_date and divide the number of returning players by the total number of installs for that date. The database performs a linear scan with aggregation, giving O(n) time complexity and O(n) intermediate storage for grouped results.

This approach relies on core database operations: grouping, joins, and date arithmetic. The key insight is separating the "first login" computation from the "next-day return" check. Once the install date is known, verifying retention becomes a simple equality condition.

Approach 2: Window Function Strategy (O(n) time, O(n) space)

Another solution uses window functions available in modern SQL engines. Use MIN(event_date) OVER (PARTITION BY player_id) to compute each player's install date directly inside the query without a separate aggregation table. Then filter rows where event_date = install_date + INTERVAL 1 DAY to identify returning players. Aggregate results by install date and compute the retention fraction using COUNT(DISTINCT player_id). Window functions simplify query structure and often reduce nesting while still scanning the dataset once.

This approach highlights advanced SQL features and is useful when multiple per-player metrics must be computed simultaneously. Engines optimize window partitions efficiently, keeping complexity at O(n).

Recommended for interviews: The subquery + join approach is typically expected. It clearly separates install-date computation from retention analysis and demonstrates strong fundamentals in database aggregation and join logic. Window functions are more concise but depend on familiarity with analytic SQL features.