Solution Explanation

This problem requires finding the airport(s) with the maximum total number of flights, considering both departures and arrivals. The solution uses SQL to efficiently process the data.

Approach

The solution employs a two-step approach using Common Table Expressions (CTEs):

1. Unioning Departure and Arrival Airports: A CTE named T is created to combine departure and arrival airports into a single table. This is done using a UNION operation on the Flights table. The UNION ensures that each airport's total traffic is counted regardless of whether it's a departure or arrival airport.

2. Aggregating and Finding the Maximum: Another CTE, P, groups the data by airport ID (departure_airport) and sums the flights_count for each airport. This gives the total traffic for each airport. Finally, the main query selects the departure_airport (renamed as airport_id) from P where the cnt (total flights) is equal to the maximum cnt found in P. This ensures that all airports with the maximum traffic are returned.

Time Complexity Analysis

• CTE T: The UNION operation has a time complexity of O(N), where N is the number of rows in the Flights table. This is because it needs to scan and combine the rows from both parts of the UNION.

• CTE P: The GROUP BY operation in CTE P has a time complexity that is dependent on the sorting algorithm used. In a well-optimized database system, this typically involves techniques like hash-based grouping which would make the time complexity O(N) on average. Worst case could be O(N log N) depending on the specific database implementation.

• Final Query: Selecting from CTE P based on the maximum value requires another scan of P, which is O(N).

Therefore, the overall time complexity of the solution is dominated by the GROUP BY operation and UNION, resulting in a time complexity of O(N) on average, assuming optimized database operations, or potentially O(N log N) in a less optimized database system. The space complexity is also O(N) in the worst case due to the intermediate results stored in CTEs, which could occupy space proportional to the size of the input table.

Code in Different Languages (MySQL)

The provided solution is already in MySQL. Other database systems (like PostgreSQL, SQL Server, etc.) would have similar syntax, but might differ in specific function names or keyword usage. The core logic remains the same. Here's the MySQL code again for clarity:

WITH
    T AS (
        SELECT * FROM Flights
        UNION
        SELECT arrival_airport, departure_airport, flights_count FROM Flights
    ),
    P AS (
        SELECT departure_airport, SUM(flights_count) AS cnt
        FROM T
        GROUP BY 1
    )
SELECT departure_airport AS airport_id
FROM P
WHERE cnt = (SELECT MAX(cnt) FROM P);

Note: If you wanted to handle ties differently (e.g., only return one airport even if there are ties), you could adjust the final SELECT statement to use LIMIT 1 and an appropriate ORDER BY clause to specify which airport should be selected in case of a tie.