Solution Explanation for LeetCode Problem 618: Students Report By Geography

This problem requires pivoting a table to display student names organized by continent. The solution uses a window function to rank students within each continent and then conditional aggregation to construct the final report.

Approach

The solution employs a two-step process:

1. Ranking within Continents: A Common Table Expression (CTE) named T is created using the ROW_NUMBER() window function. This function assigns a unique rank to each student within their respective continent, ordered alphabetically by name. This ensures that students from the same continent are listed in the correct order.

2. Conditional Aggregation: The main query then uses MAX(IF(...)) to conditionally select student names based on their continent. The GROUP BY rk clause groups the results by rank, creating rows corresponding to the ranked positions. If a continent has fewer students than others, NULL values will be filled for the missing ranks.

Time and Space Complexity Analysis

• Time Complexity: The time complexity is dominated by the sorting and ranking operations within the window function. In general, window functions have a time complexity of O(N log N) where N is the number of rows in the Student table. The subsequent aggregation has a time complexity that depends on the database engine's implementation but would be O(N) in the ideal case. Therefore, the overall time complexity can be considered O(N log N).

• Space Complexity: The space complexity is mainly determined by the size of the CTE T. In the worst case, this would be O(N) to store the ranked data. The final result set will have at most max(number_of_students_per_continent) rows, which is also bounded by O(N).

Code Implementation (MySQL)

WITH
    T AS (
        SELECT
            *,
            ROW_NUMBER() OVER (
                PARTITION BY continent
                ORDER BY name
            ) AS rk
        FROM Student
    )
SELECT
    MAX(IF(continent = 'America', name, NULL)) AS 'America',
    MAX(IF(continent = 'Asia', name, NULL)) AS 'Asia',
    MAX(IF(continent = 'Europe', name, NULL)) AS 'Europe'
FROM T
GROUP BY rk;

This MySQL query directly implements the two-step approach described above. It uses standard SQL syntax, making it relatively portable to other SQL-based database systems. The use of IF and MAX for conditional aggregation is a common technique for pivoting data in SQL.

Note: Other SQL dialects might offer slightly different syntax or functions for achieving the same outcome (e.g., CASE statements instead of IF in some systems), but the underlying logic remains the same. The core idea is to rank students within continents and then perform conditional aggregation to pivot the data.