Solution Explanation for LeetCode Problem 1421: NPV Queries

This problem involves querying two tables, NPV and Queries, to find the Net Present Value (NPV) for each query in the Queries table. The solution uses a LEFT JOIN operation in SQL.

Understanding the Tables:

• NPV Table: Contains id, year, and npv columns representing the inventory ID, year, and its NPV. The combination of id and year is the primary key, ensuring uniqueness.
• Queries Table: Contains id and year columns representing the inventory ID and year for each query. Again, the combination of id and year forms the primary key.

The Approach:

The core idea is to combine the Queries table with the NPV table based on matching id and year values. We use a LEFT JOIN because we want to include all rows from the Queries table, even if there's no matching entry in the NPV table. If there's no match, the npv value from the NPV table will be NULL.

SQL Solution (MySQL):

SELECT q.*, IFNULL(npv, 0) AS npv
FROM
    Queries AS q
    LEFT JOIN NPV AS n USING (id, year);

Code Breakdown:

1. SELECT q.*, IFNULL(npv, 0) AS npv: This selects all columns (*) from the Queries table (aliased as q) and a calculated column named npv. IFNULL(npv, 0) handles cases where the npv from the NPV table is NULL. It replaces NULL with 0, as specified in the problem description.

2. FROM Queries AS q LEFT JOIN NPV AS n USING (id, year): This specifies the join operation.

   • LEFT JOIN: Ensures that all rows from the Queries table are included in the result.
   • NPV AS n: Aliasing the NPV table as n for brevity.
   • USING (id, year): This concisely specifies that the join should be performed on the id and year columns, which are common to both tables.

Time Complexity Analysis:

The time complexity of this SQL query depends heavily on the database engine's optimization strategies and the size of the tables. In a simplified scenario, a LEFT JOIN operation, in the worst case, could have a time complexity of O(m*n), where 'm' is the number of rows in the Queries table and 'n' is the number of rows in the NPV table. However, well-indexed databases typically perform this operation much more efficiently, often closer to O(m + n) or even logarithmic time if appropriate indexes are present on the id and year columns of both tables.

Note: The specific time complexity can vary significantly depending on factors like database indexing, table sizes, and query optimization techniques employed by the database management system. The provided O(m*n) represents a worst-case theoretical upper bound, while in practice, it is usually far more efficient.