---
source:
  platform: leetcode
  problemId: 1584
tags: graphs, prims-algorithm
---

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: 
    
    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
    

**Constraints:**

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

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