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Min Cost to Connect All Points

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Problem statement

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.

Function

minCostConnectPoints(points: int[][]) → int

Examples

Example 1

points = [[0,0],[2,2],[3,10],[5,2],[7,0]]return = 20
Example 1 illustration
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

points = [[3,12],[-2,5],[-4,1]]return = 18
The points can be connected in various ways to get the minimum cost of 18.

Constraints

  • 1 <= points.length <= 1000
  • -10^6 <= xi, yi <= 10^6
  • All pairs (xi, yi) are distinct.

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public int minCostConnectPoints(int[][] points) {
  // write your code here (You many want to refer to LC1584 :)
}
points[[0,0],[2,2],[3,10],[5,2],[7,0]]
expected20
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