Solution Explanation

This problem involves querying two tables, Friends and Activities, to find activities that have neither the maximum nor minimum number of participants. The solution uses a common table expression (CTE) in MySQL to achieve this efficiently.

Approach:

1. Count Participants per Activity: A CTE named t is created to count the number of participants for each activity. This is done by grouping the Friends table by the activity column and using COUNT(1) to get the count for each group. The result includes the activity name and the participant count (cnt).

2. Find Minimum and Maximum Participant Counts: The main query then selects activities from t. The WHERE clause filters these activities based on their participant count (cnt). It checks if cnt is greater than the minimum count and less than the maximum count obtained using subqueries: (SELECT MIN(cnt) FROM t) and (SELECT MAX(cnt) FROM t). This ensures that only activities with counts strictly between the minimum and maximum are selected.

MySQL Code:

WITH
    t AS (
        SELECT activity, COUNT(1) AS cnt
        FROM Friends
        GROUP BY activity
    )
SELECT activity
FROM t
WHERE cnt > (SELECT MIN(cnt) FROM t) AND cnt < (SELECT MAX(cnt) FROM t);

Time Complexity Analysis:

• The CTE (t) has a time complexity of O(N log N) where N is the number of rows in the Friends table due to the GROUP BY operation which generally involves sorting.
• The subqueries to find the minimum and maximum counts are O(M) where M is the number of distinct activities (which is usually much smaller than N).
• The final SELECT statement has a time complexity of O(M) to filter the results.

Therefore, the overall time complexity is dominated by the GROUP BY operation in the CTE, resulting in a time complexity of O(N log N). The space complexity is O(M) to store the intermediate results in the CTE. Note that the exact time complexity of the GROUP BY operation might vary depending on the specific database implementation and optimization techniques employed. In practice, it often performs better than a naive O(N²) approach.

Other Languages (Conceptual):

While the problem is primarily SQL-based, the same logic could be implemented in other languages using a procedural approach. This would involve:

1. Reading the Friends table data.
2. Creating a dictionary or hashmap to store the activity name as keys and the participant count as values.
3. Finding the minimum and maximum participant counts.
4. Iterating through the dictionary/hashmap and selecting activities whose counts are strictly between the minimum and maximum.

The time complexity of this approach would be similar, with the most time-consuming step being counting the participants for each activity (which is comparable to the GROUP BY operation in SQL).