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Problem

Table: Points

+---------------+---------+
| Column Name   | Type    |
+---------------+---------+
| id            | int     |
| x_value       | int     |
| y_value       | int     |
+---------------+---------+
id is the primary key for this table.
Each point is represented as a 2D coordinate (x_value, y_value).

Write an SQL query to report all possible axis-aligned rectangles with a non-zero area that can be formed by any two points from the Points table.

Each row in the result should contain three columns (p1, p2, area) where:

  • p1 and p2 are the id’s of the two points that determine the opposite corners of a rectangle.
  • area is the area of the rectangle and must be non-zero.

Return the result table ordered by area in descending order. If there is a tie, order them by p1 in ascending order. If there is still a tie, order them by p2 in ascending order.

The query result format is in the following table.

Example 1:

img

Input: 
Points table:
+----------+-------------+-------------+
| id       | x_value     | y_value     |
+----------+-------------+-------------+
| 1        | 2           | 7           |
| 2        | 4           | 8           |
| 3        | 2           | 10          |
+----------+-------------+-------------+
Output: 
+----------+-------------+-------------+
| p1       | p2          | area        |
+----------+-------------+-------------+
| 2        | 3           | 4           |
| 1        | 2           | 2           |
+----------+-------------+-------------+
Explanation: 
The rectangle formed by p1 = 2 and p2 = 3 has an area equal to |4-2| * |8-10| = 4.
The rectangle formed by p1 = 1 and p2 = 2 has an area equal to |2-4| * |7-8| = 2.
Note that the rectangle formed by p1 = 1 and p2 = 3 is invalid because the area is 0.

Code

SELECT  pt1.id as P1, pt2.id as P2,
		ABS(pt2.x_value - pt1.x_value)*ABS(pt2.y_value-pt1.y_value) as AREA
FROM Points pt1 JOIN Points pt2 
ON pt1.id<pt2.id
AND pt1.x_value!=pt2.x_value 
AND pt2.y_value!=pt1.y_value
ORDER BY AREA DESC, p1 ASC, p2 ASC;