Solution Explanation

This problem requires sorting the Olympic table based on a multi-level priority system: gold medals, then silver medals, then bronze medals, and finally lexicographical order of country names. The SQL query directly addresses this.

SQL Solution (MySQL)

SELECT *
FROM Olympic
ORDER BY gold_medals DESC, silver_medals DESC, bronze_medals DESC, country ASC;

Explanation:

The ORDER BY clause specifies the sorting criteria. Each comma-separated expression represents a level of sorting priority.

• gold_medals DESC: Countries are primarily sorted in descending order of gold medals. More gold medals result in a higher rank.
• silver_medals DESC: If there's a tie in gold medals, the countries are sorted in descending order of silver medals.
• bronze_medals DESC: If there's a tie in both gold and silver medals, the countries are sorted in descending order of bronze medals.
• country ASC: Finally, if there's a tie in gold, silver, and bronze medals, the countries are sorted in ascending order alphabetically by their names (country).

This approach directly translates the problem's sorting rules into a concise SQL query.

Time Complexity Analysis

The time complexity of the SQL query is dependent on the database system's sorting algorithm. Generally, well-optimized database systems use efficient sorting algorithms (often variations of merge sort or quicksort) that have an average time complexity of O(N log N), where N is the number of rows in the Olympic table. In the worst case, it could be O(N^2), but this is unlikely with optimized database implementations. The space complexity depends on the specific implementation but is generally proportional to the size of the table (O(N) in the worst case if it needs to create a temporary sorted copy). However, in practice this is optimized through in-place algorithms or indexing.