## 613. Shortest Distance in a Line

Table `point` holds the x coordinate of some points on x-axis in a plane, which are all integers.

Write a query to find the shortest distance between two points in these points.

```| x   |
|-----|
| -1  |
| 0   |
| 2   |
```

The shortest distance is '1' obviously, which is from point '-1' to '0'. So the output is as below:

```| shortest|
|---------|
| 1       |
```

Note: Every point is unique, which means there is no duplicates in table `point`.

Follow-up: What if all these points have an id and are arranged from the left most to the right most of x axis?

b'
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## Solution

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

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Intuition

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

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Algorithm

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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.\nOne trick here is to add the condition in the join to avoid calculating the distance between a point with itself.

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`SELECT\n    p1.x, p2.x, ABS(p1.x - p2.x) AS distance\nFROM\n    point p1\n        JOIN\n    point p2 ON p1.x != p2.x\n;\n`
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Note: The columns p1.x, p2.x are only for demonstrating purpose, so they are not actually needed in the end.

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

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`| x  | x  | distance |\n|----|----|----------|\n| 0  | -1 | 1        |\n| 2  | -1 | 3        |\n| -1 | 0  | 1        |\n| 2  | 0  | 2        |\n| -1 | 2  | 3        |\n| 0  | 2  | 2        |\n`
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At last, use `MIN()` to select the smallest value in the distance column.

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MySQL

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`SELECT\n    MIN(ABS(p1.x - p2.x)) AS shortest\nFROM\n    point p1\n        JOIN\n    point p2 ON p1.x != p2.x\n;\n`
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'