Solution Explanation for Weather Type in Each Country

This problem requires querying two tables, Countries and Weather, to determine the weather type for each country in November 2019. The weather type is categorized based on the average weather_state for that month: Cold (≤ 15), Hot (≥ 25), or Warm (otherwise).

Approach

1. Filtering Data: We first filter the Weather table to include only records from November 2019. This is crucial for calculating the average weather state for the specified period. The DATE_FORMAT function is used to extract the year and month from the day column.

2. Joining Tables: We perform an INNER JOIN between the Weather and Countries tables using country_id as the join key. This combines the weather data with the country names.

3. Grouping and Averaging: We use GROUP BY country_name to group the results by country. The AVG(weather_state) function calculates the average weather_state for each country in November 2019.

4. Categorizing Weather Type: A CASE statement assigns the appropriate weather type ('Cold', 'Hot', or 'Warm') based on the calculated average weather state.

5. Result: The query returns a table with country_name and weather_type columns, showing the weather type for each country in November 2019.

Code (MySQL)

SELECT
    country_name,
    CASE
        WHEN AVG(weather_state) <= 15 THEN 'Cold'
        WHEN AVG(weather_state) >= 25 THEN 'Hot'
        ELSE 'Warm'
    END AS weather_type
FROM
    Weather AS w
    JOIN Countries USING (country_id)
WHERE DATE_FORMAT(day, '%Y-%m') = '2019-11'
GROUP BY 1;

Time Complexity Analysis

The time complexity of this SQL query depends on the size of the Weather and Countries tables. The DATE_FORMAT function adds a small constant overhead to each row scan. The JOIN operation has a time complexity that's dependent on the join algorithm used by the database system (e.g., hash join, nested loop join). In the best-case scenario (with optimized indexing and efficient join algorithm), the complexity would approach O(N), where N is the number of rows in the Weather table after filtering for November 2019. The GROUP BY and AVG operations also add a cost proportional to the number of groups (countries). In practice, a well-optimized database query will execute this efficiently, making the runtime largely dependent on the database system and the table sizes. The space complexity is primarily determined by the size of the intermediate result sets created during the join and grouping operations; this would again be proportional to the size of the input data.