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:

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


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.

## Solution: Minimum Spanning Tree

Kruskal’s algorithm
Time complexity: O(n^2logn)
Space complexity: O(n^2)
using vector of vector, array, pair of pair, or tuple might lead to TLE…

## C++

Prim’s Algorithm
ds[i] := min distance from i to ANY nodes in the tree.

Time complexity: O(n^2) Space complexity: O(n)

## C++

If you like my articles / videos, donations are welcome.

Buy anything from Amazon to support our website

Paypal
Venmo
huahualeetcode