Solution Explanation for Winning Candidate

This problem requires finding the name of the candidate with the most votes from two tables: Candidate and Vote. Both solutions leverage SQL's aggregate and join capabilities to achieve this efficiently.

Solution 1: Subquery Approach

This solution uses a subquery to first identify the candidateId with the maximum number of votes and then joins this result with the Candidate table to retrieve the candidate's name.

MySQL Code:

SELECT
    Name
FROM
    (
        SELECT
            CandidateId AS id
        FROM Vote
        GROUP BY CandidateId
        ORDER BY COUNT(id) DESC
        LIMIT 1
    ) AS t
    INNER JOIN Candidate AS c ON t.id = c.id;

Explanation:

1. Inner Subquery:

   • SELECT CandidateId AS id FROM Vote GROUP BY CandidateId: This groups the Vote table by candidateId, effectively counting the votes for each candidate.
   • ORDER BY COUNT(id) DESC: This sorts the grouped results in descending order based on the vote count (COUNT(id)).
   • LIMIT 1: This limits the result set to only the top row, which represents the candidate with the most votes. The AS id renames the CandidateId column to id for easier joining.

2. Outer Query:

   • SELECT Name FROM (...) AS t INNER JOIN Candidate AS c ON t.id = c.id: This joins the result of the subquery (t) with the Candidate table (c) using the id column as the join key. This retrieves the Name of the winning candidate.

Time Complexity: The time complexity is dominated by the sorting in the subquery which is typically O(N log N) where N is the number of votes, although database engines might use optimizations that perform better in practice. The join operation has a time complexity dependent on the database engine's implementation, but it would typically be at most linear in the number of candidates.

Space Complexity: The space complexity is primarily determined by the temporary tables created during the query execution. This depends heavily on the database engine's implementation and optimization strategies. In general it's expected to be linear with respect to the input data size.

Solution 2: Direct Join and Aggregation

This solution directly joins the Candidate and Vote tables, groups the results by candidate, and then orders and limits to find the winner.

MySQL Code:

SELECT name
FROM
    Candidate AS c
    LEFT JOIN Vote AS v ON c.id = v.candidateId
GROUP BY c.id
ORDER BY COUNT(1) DESC
LIMIT 1;

Explanation:

1. Join:

   • Candidate AS c LEFT JOIN Vote AS v ON c.id = v.candidateId: This performs a LEFT JOIN between Candidate and Vote tables using id and candidateId as join keys. A LEFT JOIN ensures that all candidates are included in the result, even those with zero votes.

2. Grouping and Aggregation:

   • GROUP BY c.id: This groups the results by candidate ID.
   • COUNT(1): This counts the number of votes for each candidate (counting 1 for each row in the group). COUNT(1) is often faster than COUNT(*) or COUNT(column_name) in some database systems, because it doesn't need to examine the actual column data.

3. Ordering and Limiting:

   • ORDER BY COUNT(1) DESC: This sorts the results in descending order of vote count.
   • LIMIT 1: This selects only the top row, representing the winning candidate.

Time Complexity: Similar to Solution 1, the time complexity is dominated by the sorting operation, which is typically O(N log N), where N is the number of votes. The grouping and join operations have time complexities that vary depending on the database engine, however they are typically O(N) or better with suitable indexing.

Space Complexity: The space complexity is again influenced by the database engine, but it's expected to be linear in the size of the input.

Both solutions provide correct results. Solution 2 might be slightly more efficient in some database systems due to the direct aggregation and avoidance of a subquery, but the difference might be negligible for smaller datasets. The optimal solution often depends on specific database engine capabilities and the size of the input data. The choice between the two solutions often comes down to readability and personal preference.