Solution Explanation

This problem requires reformatting a table to pivot the month column into separate columns representing each month's revenue. The solution uses SQL's aggregate functions and conditional logic to achieve this.

Approach

The core idea is to use conditional aggregation. We group the data by id (department ID) and then use SUM(CASE WHEN ... THEN ... END) to calculate the revenue for each month. The CASE statement checks the month column and sums the revenue only when it matches the specific month. If a department doesn't have data for a particular month, SUM will return NULL for that month's revenue column.

SQL Code (MySQL)

SELECT
    id,
    SUM(CASE WHEN month = 'Jan' THEN revenue ELSE NULL END) AS Jan_Revenue,
    SUM(CASE WHEN month = 'Feb' THEN revenue ELSE NULL END) AS Feb_Revenue,
    SUM(CASE WHEN month = 'Mar' THEN revenue ELSE NULL END) AS Mar_Revenue,
    SUM(CASE WHEN month = 'Apr' THEN revenue ELSE NULL END) AS Apr_Revenue,
    SUM(CASE WHEN month = 'May' THEN revenue ELSE NULL END) AS May_Revenue,
    SUM(CASE WHEN month = 'Jun' THEN revenue ELSE NULL END) AS Jun_Revenue,
    SUM(CASE WHEN month = 'Jul' THEN revenue ELSE NULL END) AS Jul_Revenue,
    SUM(CASE WHEN month = 'Aug' THEN revenue ELSE NULL END) AS Aug_Revenue,
    SUM(CASE WHEN month = 'Sep' THEN revenue ELSE NULL END) AS Sep_Revenue,
    SUM(CASE WHEN month = 'Oct' THEN revenue ELSE NULL END) AS Oct_Revenue,
    SUM(CASE WHEN month = 'Nov' THEN revenue ELSE NULL END) AS Nov_Revenue,
    SUM(CASE WHEN month = 'Dec' THEN revenue ELSE NULL END) AS Dec_Revenue
FROM Department
GROUP BY id;

This SQL query does the following:

1. SELECT id, ...: Selects the department id and creates columns for each month's revenue.
2. SUM(CASE WHEN month = 'Jan' THEN revenue ELSE NULL END) AS Jan_Revenue: This is repeated for each month. It sums the revenue only if the month is 'Jan', otherwise it uses NULL. The ELSE NULL is crucial; without it, SUM would treat non-matching rows as 0 and not handle missing data properly.
3. FROM Department: Specifies the table to query.
4. GROUP BY id: Groups the results by department id, so we get one row per department.

Time and Space Complexity

• Time Complexity: The time complexity is dominated by the GROUP BY operation. In the worst case, this involves sorting or hashing the input rows, which typically takes O(N log N) or O(N) time, where N is the number of rows in the Department table. The CASE statements within the SUM function adds a constant factor to this time complexity but doesn't alter the overall order.

• Space Complexity: The space complexity is determined by the size of the output table, which depends on the number of distinct departments and the number of months. In the worst case, if each department has data for every month, the space complexity is O(M * D), where M is the number of months (12 in this case) and D is the number of distinct departments. The intermediate space used during the GROUP BY operation also contributes to the space complexity, but is likely smaller than the output size.

This solution efficiently pivots the table using standard SQL features. The alternative approaches would involve more complex joins or subqueries and would likely be less efficient.