Solution Explanation

This problem requires generating a summary report of user spending on different platforms (desktop and mobile). The solution uses SQL queries to process the Spending table and produce the desired output.

Approach

The solution employs a common table expression (CTE) approach in MySQL to achieve the desired result efficiently. It breaks down the problem into two main CTEs:

1. P (Platforms): This CTE generates all possible combinations of spend_date and platform ('desktop', 'mobile', 'both'). This ensures that all dates are included in the final output, even if there are no transactions for a particular platform on that date. A UNION is used to combine the distinct dates for each platform and 'both'.

2. T (Transactions): This CTE groups the Spending data by user_id and spend_date. It calculates the total amount spent (amount) by each user on each date. The IF statement determines whether a user used only one platform ('desktop' or 'mobile') or both.

The final SELECT statement joins P and T using spend_date and platform. IFNULL handles cases where there's no matching entry in T, setting total_amount to 0. COUNT(t.user_id) counts the unique users for each platform and date. The result is grouped by spend_date and platform to get the final aggregated results.

Time Complexity Analysis

• The P CTE has a time complexity that is proportional to the number of distinct spend_date values in the Spending table, let's call this N. The UNION operations contribute to this complexity.
• The T CTE has a time complexity that depends on the total number of rows in the Spending table. This will be dominated by the GROUP BY operation, which is typically O(M log M) or O(M) depending on the database's implementation (where M is the number of rows).
• The final SELECT statement joins P and T, which in the worst case is O(N * M). However, this is likely optimized by the database engine. The GROUP BY operation in this final select contributes additional cost, similar to the T CTE.

Therefore, the overall time complexity is dominated by the GROUP BY operations and potentially the join in the final SELECT statement, making it approximately O(max(M log M, N * M)), where M is the number of rows in the Spending table and N is the number of distinct spend dates. In practice, this would likely be close to linear in the size of the Spending table, given database optimization.

Space Complexity Analysis

The space complexity is primarily determined by the size of the CTEs P and T.

• P's size is proportional to the number of distinct spend_date values multiplied by the number of platforms (3). This is O(N).
• T's size is proportional to the number of unique (user_id, spend_date) combinations, which is at most M.

Thus the overall space complexity is O(M + N), where M is the number of rows and N is the number of unique spend dates.

MySQL Code

WITH
    P AS (
        SELECT DISTINCT spend_date, 'desktop' AS platform FROM Spending
        UNION
        SELECT DISTINCT spend_date, 'mobile' FROM Spending
        UNION
        SELECT DISTINCT spend_date, 'both' FROM Spending
    ),
    T AS (
        SELECT
            user_id,
            spend_date,
            SUM(amount) AS amount,
            IF(COUNT(platform) = 1, platform, 'both') AS platform
        FROM Spending
        GROUP BY 1, 2
    )
SELECT
    p.*,
    IFNULL(SUM(amount), 0) AS total_amount,
    COUNT(t.user_id) AS total_users
FROM
    P AS p
    LEFT JOIN T AS t USING (spend_date, platform)
GROUP BY 1, 2;

No other language implementations are provided as the problem specifically involves SQL database querying.