import sys from collections import defaultdict def prisms_algorithm(l): # noqa: E741 node_position = [] def get_position(vertex): return node_position[vertex] def set_position(vertex, pos): node_position[vertex] = pos def top_to_bottom(heap, start, size, positions): if start > size // 2 - 1: return else: if 2 * start + 2 >= size: m = 2 * start + 1 else: if heap[2 * start + 1] < heap[2 * start + 2]: m = 2 * start + 1 else: m = 2 * start + 2 if heap[m] < heap[start]: temp, temp1 = heap[m], positions[m] heap[m], positions[m] = heap[start], positions[start] heap[start], positions[start] = temp, temp1 temp = get_position(positions[m]) set_position(positions[m], get_position(positions[start])) set_position(positions[start], temp) top_to_bottom(heap, m, size, positions) # Update function if value of any node in min-heap decreases def bottom_to_top(val, index, heap, position): temp = position[index] while index != 0: if index % 2 == 0: parent = int((index - 2) / 2) else: parent = int((index - 1) / 2) if val < heap[parent]: heap[index] = heap[parent] position[index] = position[parent] set_position(position[parent], index) else: heap[index] = val position[index] = temp set_position(temp, index) break index = parent else: heap[0] = val position[0] = temp set_position(temp, 0) def heapify(heap, positions): start = len(heap) // 2 - 1 for i in range(start, -1, -1): top_to_bottom(heap, i, len(heap), positions) def delete_minimum(heap, positions): temp = positions[0] heap[0] = sys.maxsize top_to_bottom(heap, 0, len(heap), positions) return temp visited = [0 for i in range(len(l))] nbr_tv = [-1 for i in range(len(l))] # Neighboring Tree Vertex of selected vertex # Minimum Distance of explored vertex with neighboring vertex of partial tree # formed in graph distance_tv = [] # Heap of Distance of vertices from their neighboring vertex positions = [] for x in range(len(l)): p = sys.maxsize distance_tv.append(p) positions.append(x) node_position.append(x) tree_edges = [] visited[0] = 1 distance_tv[0] = sys.maxsize for x in l[0]: nbr_tv[x[0]] = 0 distance_tv[x[0]] = x[1] heapify(distance_tv, positions) for i in range(1, len(l)): vertex = delete_minimum(distance_tv, positions) if visited[vertex] == 0: tree_edges.append((nbr_tv[vertex], vertex)) visited[vertex] = 1 for v in l[vertex]: if visited[v[0]] == 0 and v[1] < distance_tv[get_position(v[0])]: distance_tv[get_position(v[0])] = v[1] bottom_to_top(v[1], get_position(v[0]), distance_tv, positions) nbr_tv[v[0]] = vertex return tree_edges if __name__ == "__main__": # pragma: no cover # < --------- Prims Algorithm --------- > n = int(input("Enter number of vertices: ").strip()) e = int(input("Enter number of edges: ").strip()) adjlist = defaultdict(list) for x in range(e): l = [int(x) for x in input().strip().split()] # noqa: E741 adjlist[l[0]].append([l[1], l[2]]) adjlist[l[1]].append([l[0], l[2]]) print(prisms_algorithm(adjlist))