Solution Explanation for Finding Missing IDs

This problem requires finding missing customer IDs within a given range in a database table. The range is determined by the maximum customer_id present in the Customers table. We need to identify IDs within this range that are not present as customer_id values in the table.

Approach

The solution uses a recursive common table expression (CTE) in MySQL to generate a sequence of numbers from 1 to 100. This sequence covers the potential range of customer IDs. We then filter this sequence to include only those numbers that:

1. Are less than the maximum customer_id in the Customers table (to stay within the relevant range).
2. Are not present in the customer_id column of the Customers table (identifying the missing IDs).

MySQL Code Explanation

WITH RECURSIVE
    t AS (
        SELECT
            1 AS n
        UNION ALL
        SELECT
            n + 1
        FROM t
        WHERE n < 100
    )
SELECT
    n AS ids
FROM t
WHERE
    n < (
        SELECT
            MAX(customer_id)
        FROM Customers
    )
    AND n NOT IN (
        SELECT
            customer_id
        FROM Customers
    );

• WITH RECURSIVE t AS (...): This defines a recursive CTE named t. Recursive CTEs are used to generate series of data.
• SELECT 1 AS n UNION ALL SELECT n + 1 FROM t WHERE n < 100: This is the core of the recursion. It starts with n = 1 and recursively adds 1 to n until n reaches 100. This generates a sequence of numbers from 1 to 100. The UNION ALL combines the initial SELECT with the subsequent recursive SELECTs.
• SELECT n AS ids FROM t WHERE ...: This selects the generated numbers (n) and renames the column to ids.
• n < (SELECT MAX(customer_id) FROM Customers): This condition filters the sequence to include only numbers less than the maximum customer_id found in the Customers table.
• AND n NOT IN (SELECT customer_id FROM Customers): This crucial condition filters out numbers that are already present as customer_id values in the Customers table, leaving only the missing IDs.

Time Complexity Analysis

The time complexity is dominated by the recursive CTE, which generates a sequence of numbers from 1 to 100. This takes O(100) time, which is essentially O(1) – constant time since the range is fixed. The NOT IN subquery has a time complexity that depends on the size of the Customers table, which is at most O(N) where N is the number of rows in the Customers table. However, given that the problem states the maximum customer_id will not exceed 100, N is also bounded by a constant. Therefore, the overall time complexity is considered O(1).

Space Complexity Analysis

The space complexity is determined by the size of the CTE t, which stores 100 numbers. This is O(1) space complexity due to the constant size. The space used by other parts of the query is also constant, so the overall space complexity is O(1).