## Solution

#### Approach: Using ABS() and MIN() functions [Accepted]

Intuition

Calculate the distances between each two points first, and then display the minimum one.

Algorithm

To get the distances of each two points, we need to join this table with itself and use ABS() function since the distance is nonnegative. One trick here is to add the condition in the join to avoid calculating the distance between a point with itself.

SELECT
p1.x, p2.x, ABS(p1.x - p2.x) AS distance
FROM
point p1
JOIN
point p2 ON p1.x != p2.x
;


Note: The columns p1.x, p2.x are only for demonstrating purpose, so they are not actually needed in the end.

Taking the sample data for example, the output would be as below.

| x  | x  | distance |
|----|----|----------|
| 0  | -1 | 1        |
| 2  | -1 | 3        |
| -1 | 0  | 1        |
| 2  | 0  | 2        |
| -1 | 2  | 3        |
| 0  | 2  | 2        |


At last, use MIN() to select the smallest value in the distance column.

MySQL

SELECT
MIN(ABS(p1.x - p2.x)) AS shortest
FROM
point p1
JOIN
point p2 ON p1.x != p2.x
;