Solution Explanation

This problem requires calculating the confirmation rate for each user based on data from two tables: Signups and Confirmations. The confirmation rate is the ratio of confirmed messages to the total number of confirmation messages for each user. The solution uses SQL to efficiently perform this calculation.

Approach

The core idea is to join the Signups and Confirmations tables, aggregate the results by user ID, and then compute the confirmation rate. A LEFT JOIN ensures that all users from Signups are included, even if they have no entries in Confirmations. This handles the case where a user has zero confirmation messages, resulting in a confirmation rate of 0.

Steps:

1. Left Join: Perform a LEFT JOIN between Signups and Confirmations using user_id as the join key. This ensures that all users from Signups are included in the result.

2. Conditional Aggregation: Use SUM(action = 'confirmed') to count the number of confirmed messages for each user. The expression action = 'confirmed' evaluates to 1 if true and 0 if false, effectively summing only the confirmed cases. COUNT(*) or COUNT(1) counts the total number of confirmation requests for each user.

3. Handling Zero Divisions: Use IFNULL to handle cases where a user has no confirmation messages. IFNULL(SUM(action = 'confirmed') / COUNT(1), 0) replaces potential division by zero errors with 0.

4. Rounding: Use ROUND(..., 2) to round the confirmation rate to two decimal places, as specified in the problem description.

5. Grouping: Use GROUP BY user_id to group the results by user ID, so the aggregation is done per user.

MySQL Code Explanation

SELECT
    user_id,
    ROUND(IFNULL(SUM(action = 'confirmed') / COUNT(1), 0), 2) AS confirmation_rate
FROM
    SignUps
    LEFT JOIN Confirmations USING (user_id)
GROUP BY 1;

• SELECT user_id, ...: Selects the user_id and the calculated confirmation rate.
• ROUND(IFNULL(SUM(action = 'confirmed') / COUNT(1), 0), 2): This is the core calculation.
  • SUM(action = 'confirmed'): Counts the number of confirmed messages.
  • COUNT(1): Counts the total number of confirmation messages (confirmed or timeout).
  • /: Divides confirmed count by total count to get the rate.
  • IFNULL(..., 0): Handles the case where there are no confirmations (division by zero), setting the rate to 0 in such cases.
  • ROUND(..., 2): Rounds the result to two decimal places.
• FROM SignUps LEFT JOIN Confirmations USING (user_id): Performs a LEFT JOIN between the Signups and Confirmations tables on the user_id column.
• GROUP BY 1: Groups the results by the first column in the SELECT statement, which is user_id.

Time Complexity Analysis

The time complexity of this SQL query is dominated by the LEFT JOIN and GROUP BY operations. In general, a JOIN operation on two tables with m and n rows can have a time complexity of O(mlog(m) + nlog(n)) or even O(mn) in the worst case (depending on the database system and the specific query optimizer used). The GROUP BY operation has a complexity of O(klog(k)), where k is the number of groups (in this case, the number of unique user IDs). Therefore, the overall time complexity is approximately O(max(mlog(m), nlog(n), k*log(k))). The exact complexity depends heavily on the database system's optimization techniques.

The space complexity is determined by the size of the intermediate result set generated by the join and the grouping. In the worst case, it could be proportional to the number of rows in the joined tables, resulting in a space complexity that's approximately O(m + n).

This SQL solution provides an efficient and concise way to calculate the confirmation rate for each user. The use of LEFT JOIN, conditional aggregation, and error handling makes it robust and adaptable to different datasets.