Min Cost to Connect All Points — LeetCode 1584 Python Solution

The problem

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.

Example

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.

Python solution

class Solution:
    def minCostConnectPoints(self, points: List[List[int]]) -> int:
        n = len(points)
        g = [[0] * n for _ in range(n)]
        dist = [inf] * n
        vis = [False] * n
        for i, (x1, y1) in enumerate(points):
            for j in range(i + 1, n):
                x2, y2 = points[j]
                t = abs(x1 - x2) + abs(y1 - y2)
                g[i][j] = g[j][i] = t
        dist[0] = 0
        ans = 0
        for _ in range(n):
            i = -1
            for j in range(n):
                if not vis[j] and (i == -1 or dist[j] < dist[i]):
                    i = j
            vis[i] = True
            ans += dist[i]
            for j in range(n):
                if not vis[j]:
                    dist[j] = min(dist[j], g[i][j])
        return ans

Complexity

Pattern: Union-Find

Merge groups and ask whether two things are connected, both in near-constant time. LeetCode 1584. Min Cost to Connect All Points is filed here because LeetCode tags it Union Find, which is the vocabulary this hub collects.

The union-find guide has the Python template for the pattern and the 83 LeetCode problems that use it.

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