rectangles-area.sql

/*

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 Dimensional (x_value, y_value).
Write an SQL query to report of all possible rectangles which can be formed by any two points of the table.

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

p1 and p2 are the id of two opposite corners of a rectangle and p1 < p2.
Area of this rectangle is represented by the column area.
Report the query in descending order by area in case of tie in ascending order by p1 and p2.

Points table:
+----------+-------------+-------------+
| id       | x_value     | y_value     |
+----------+-------------+-------------+
| 1        | 2           | 8           |
| 2        | 4           | 7           |
| 3        | 2           | 10          |
+----------+-------------+-------------+

Result table:
+----------+-------------+-------------+
| p1       | p2          | area        |
+----------+-------------+-------------+
| 2        | 3           | 6           |
| 1        | 2           | 2           |
+----------+-------------+-------------+

p1 should be less than p2 and area greater than 0.
p1 = 1 and p2 = 2, has an area equal to |2-4| * |8-7| = 2.
p1 = 2 and p2 = 3, has an area equal to |4-2| * |7-10| = 6.
p1 = 1 and p2 = 3 It's not possible because the rectangle has an area equal to 0.

*/


# V0

# V1
# https://code.dennyzhang.com/rectangles-area
select t1.id as p1, t2.id as p2, abs(t1.x_value-t2.x_value)*abs(t1.y_value-t2.y_value) as area
from Points as t1 inner join Points as t2
on t1.id < t2.id
and t1.x_value != t2.x_value and t1.y_value != t2.y_value
order by area desc, p1, p2

# V2
# Time:  O(n^2)
# Space: O(n^2)
SELECT *
FROM
  (SELECT a.id AS P1,
          b.id AS P2,
          abs(a.x_value - b.x_value) * abs(a.y_value - b.y_value) AS area
   FROM Points a
   INNER JOIN Points b ON a.id < b.id
   ORDER BY area DESC, P1, P2) r
WHERE area > 0;