# 1584. Min Cost to Connect All Points from collections import defaultdict import heapq """ given a array 'points' representing integer coordinates of some points on a 2d-plane, where 'points[i] = [x[i], y[i]]'. the cost of connecting two points '[x[i], y[i]]' and '[x[j], y[j]]' is the manhattan distance between them: '|x[i], - x[j]| + |y[i] + y[j]|', 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 betwen any two points. """ class Solution(object): def minCostConnectPoints(self, points): manhattan = lambda p1, p2: abs(p1[0] - p2[0]) + abs(p1[1] - p2[1]) n, c = len(points), defaultdict(list) for i in range(n): for j in range(i + 1, n): d = manhattan(points[i], points[j]) c[i].append((d, j)) c[j].append((d, i)) cnt, ans, vis, heap = 1, 0, [0] * n, c[0] vis[0] = 1 heapq.heapify(heap) while heap: d, j = heapq.heappop(heap) if not vis[j]: vis[j], cnt, ans = 1, cnt + 1, ans + d for record in c[j]: heapq.heappush(heap, record) if cnt >= n: break return ans if __name__ == "__main__": obj = Solution() print( obj.minCostConnectPoints([[0, 0], [2, 2], [3, 10], [5, 2], [7, 0]]) ) # expect: 20 print(obj.minCostConnectPoints([[3, 12], [-2, 5], [-4, 1]])) # expect: 18