### Problem Description –

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.

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

**Note:** The longest distance among all the points are less than 10000.

#### Difficulty Level – Medium

#### Problem Link – https://leetcode.com/problems/shortest-distance-in-a-plane/

### Solution –

```
SELECT
MIN(ROUND(SQRT(POWER(p2.x - p1.x, 2) + POWER(p2.y - p1.y, 2)),2)) as shortest
FROM point_2d as p1 JOIN point_2d as p2
ON p1.x != p2.x OR p1.y != p2.y
```

The distance between two points (x1, y1) and (x2, y2) on a plane can be calculated by pythagorean theorem.

```
WITH result AS(
SELECT
p1.x AS x1,
p1.y AS y1,
p2.x AS x2,
p2.y AS y2,
SQRT(POWER(p2.x - p1.x, 2) + POWER(p2.y - p1.y, 2)) distance
FROM point_2d as p1 JOIN point_2d as p2
ON p1.x != p2.x OR p1.y != p2.y
)
SELECT *
FROM result
```

We can see that the minimum distance is 1. Now, all we have to do is round the numbers to two decimal palces and use the MIN() function to select the answer.