Grokking Graph Algorithms for Coding Interviews
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Min Cost to Connect All Points (medium)
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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] = [x<sub>i</sub>, y<sub>i</sub>].

The cost of connecting two points [x<sub>i</sub>, y<sub>i</sub>] and [x<sub>i</sub>, y<sub>i</sub>] is the Manhattan distance between them: |x<sub>i</sub> - x<sub>i</sub>| + |y<sub>i</sub> - y<sub>i</sub>|, where |val| denotes the absolute value of val.

Return the minimum cost to connect all the points such that each point is connected directly or indirectly to every other point with exactly one simple path between any two points.

Examples

  1. Example 1:
    • Input: points = [[1, 1], [2, 2], [2, 4], [3, 3]]
    • Expected Output: 6
Image
  • Justification: The optimal connections are [(1,1) -> (2,2)], [(2,2) -> (3,3)] and [(2,2) -> (2,4)] with distances 2, 2 and 2 respectively, summing up to 6.
  1. Example 2:
    • Input: points = [[0, 0], [1, 2], [3, 3]]
    • Expected Output: 6
Image
  • Justification: The optimal connections are [(0,0) -> (1,2)] and [(1,2) -> (3,3)] with distances 3 and 3 respectively, summing up to 6.
  1. Example 3:
    • Input: points = [[0, 0], [2, 4], [4, 2], [6, 6]]
    • Expected Output: 16
Image
  • Justification: The optimal connections are [(0,0) -> (2,4)], [(2,4) -> (4,2)] and [(4,2) -> (6,6)] with distances 6, 4 and 6 respectively, summing up to 16.

Constraints:

  • 1 <= points.length <= 1000
  • -10<sup>6</sup> <= x<sub>i</sub>, y<sub>i</sub> <= 10<sup>6</sup>
  • All pairs (x<sub>i</sub>, y<sub>i</sub>) are distinct.

Try it yourself

Try solving this question here:

Python3
Python3
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