# 612. Shortest Distance in a Plane

## Description

Table: Point2D

+-------------+------+
| Column Name | Type |
+-------------+------+
| x           | int  |
| y           | int  |
+-------------+------+
(x, y) is the primary key column (combination of columns with unique values) for this table.
Each row of this table indicates the position of a point on the X-Y plane.


The distance between two points p1(x1, y1) and p2(x2, y2) is sqrt((x2 - x1)2 + (y2 - y1)2).

Write a solution to report the shortest distance between any two points from the Point2D table. Round the distance to two decimal points.

The result format is in the following example.

Example 1:

Input:
Point2D table:
+----+----+
| x  | y  |
+----+----+
| -1 | -1 |
| 0  | 0  |
| -1 | -2 |
+----+----+
Output:
+----------+
| shortest |
+----------+
| 1.00     |
+----------+
Explanation: The shortest distance is 1.00 from point (-1, -1) to (-1, 2).


## Solutions

• # Write your MySQL query statement below

SELECT
ROUND(
SQRT(
MIN(POW(a.x-b.x,2) + POW(a.y-b.y,2))
)
,2
) shortest
FROM point_2d a
CROSS JOIN point_2d b
WHERE NOT (a.x = b.x AND a.y = b.y)
-- where (a.x != b.x and a.y != b.y) -- this will not work, it will remove all pairs where x is the same and y is the same

--

SELECT ROUND(SQRT(POW(p1.x - p2.x, 2) + POW(p1.y - p2.y, 2)), 2) AS shortest
FROM
Point2D AS p1
JOIN Point2D AS p2 ON p1.x != p2.x OR p1.y != p2.y
ORDER BY 1
LIMIT 1;