# 1584. Min Cost to Connect All Points

<https://leetcode.com/problems/min-cost-to-connect-all-points>

## Description

You are given an array `points` representing integer coordinates of some points on a 2D-plane, where `points[i] = [xi, yi]`.

The cost of connecting two points `[xi, yi]` and `[xj, yj]` is the **manhattan distance** between them: `|xi - xj| + |yi - yj|`, where `|val|` denotes the absolute value of `val`.

Return *the minimum cost to make all points connected.* All points are connected if there is **exactly one** simple path between any two points.

**Example 1:**

![](https://assets.leetcode.com/uploads/2020/08/26/d.png)

```
**Input:** points = [[0,0],[2,2],[3,10],[5,2],[7,0]]
**Output:** 20
**Explanation:**![](https://assets.leetcode.com/uploads/2020/08/26/c.png)
We can connect the points as shown above to get the minimum cost of 20.
Notice that there is a unique path between every pair of points.
```

**Example 2:**

```
**Input:** points = [[3,12],[-2,5],[-4,1]]
**Output:** 18
```

**Example 3:**

```
**Input:** points = [[0,0],[1,1],[1,0],[-1,1]]
**Output:** 4
```

**Example 4:**

```
**Input:** points = [[-1000000,-1000000],[1000000,1000000]]
**Output:** 4000000
```

**Example 5:**

```
**Input:** points = [[0,0]]
**Output:** 0
```

**Constraints:**

* `1 <= points.length <= 1000`
* `-106 <= xi, yi <= 106`
* All pairs `(xi, yi)` are distinct.

## ac

```java
```