612_Shortest Distance in a Plane

[medium]

Table point_2d holds the coordinates (x,y) of some unique points (more than two) in a plane.

Write a query to find the shortest distance between these points rounded to 2 decimals.

| x  | y  |
|----|----|
| -1 | -1 |
| 0  | 0  |
| -1 | -2 |

The shortest distance is 1.00 from point (-1,-1) to (-1,2). So the output should be:

| shortest |
|----------|
| 1.00     |

Solution 1: using join

SELECT round(sqrt(min(power(p1.x-p2.x, 2) + power(p1.y-p2.y, 2))), 2) AS shortest
FROM point_2d p1 JOIN point_2d p2 ON (p1.x, p1.y) != (p2.x, p2.y);

Solution 2: using subquery

SELECT min(dist) AS shortest
FROM (
    SELECT p.x, p.y, 
        (SELECT round(min(sqrt(power(p.x - x, 2) + power(p.y - y, 2))), 2)
        FROM point_2d
        WHERE (x, y) != (p.x, p.y)) AS dist
    FROM point_2d AS p
) AS t;