import sys from collections import defaultdict def PrimsAlgorithm(l): nodePosition = [] def getPosition(vertex): return nodePosition[vertex] def setPosition(vertex, pos): nodePosition[vertex] = pos def topToBottom(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 = getPosition(positions[m]) setPosition(positions[m], getPosition(positions[start])) setPosition(positions[start], temp) topToBottom(heap, m, size, positions) # Update function if value of any node in min-heap decreases def bottomToTop(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] setPosition(position[parent], index) else: heap[index] = val position[index] = temp setPosition(temp, index) break index = parent else: heap[0] = val position[0] = temp setPosition(temp, 0) def heapify(heap, positions): start = len(heap) // 2 - 1 for i in range(start, -1, -1): topToBottom(heap, i, len(heap), positions) def deleteMinimum(heap, positions): temp = positions[0] heap[0] = sys.maxsize topToBottom(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) nodePosition.append(x) TreeEdges = [] 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 = deleteMinimum(Distance_TV, Positions) if visited[vertex] == 0: TreeEdges.append((Nbr_TV[vertex], vertex)) visited[vertex] = 1 for v in l[vertex]: if visited[v[0]] == 0 and v[1] < Distance_TV[ getPosition(v[0]) ]: Distance_TV[ getPosition(v[0]) ] = v[1] bottomToTop(v[1], getPosition(v[0]), Distance_TV, Positions) Nbr_TV[ v[0] ] = vertex return TreeEdges # < --------- Prims Algorithm --------- > n = int(raw_input("Enter number of vertices: ")) e = int(raw_input("Enter number of edges: ")) adjlist = defaultdict(list) for x in range(e): l = [int(x) for x in input().split()] adjlist[l[0]].append([ l[1], l[2] ]) adjlist[l[1]].append([ l[0], l[2] ]) print(PrimsAlgorithm(adjlist))