import sys from collections import defaultdict class Heap: def __init__(self): self.node_position = [] def get_position(self, vertex): return self.node_position[vertex] def set_position(self, vertex, pos): self.node_position[vertex] = pos def top_to_bottom(self, heap, start, size, positions): if start > size // 2 - 1: return else: if 2 * start + 2 >= size: smallest_child = 2 * start + 1 else: if heap[2 * start + 1] < heap[2 * start + 2]: smallest_child = 2 * start + 1 else: smallest_child = 2 * start + 2 if heap[smallest_child] < heap[start]: temp, temp1 = heap[smallest_child], positions[smallest_child] heap[smallest_child], positions[smallest_child] = ( heap[start], positions[start], ) heap[start], positions[start] = temp, temp1 temp = self.get_position(positions[smallest_child]) self.set_position( positions[smallest_child], self.get_position(positions[start]) ) self.set_position(positions[start], temp) self.top_to_bottom(heap, smallest_child, size, positions) # Update function if value of any node in min-heap decreases def bottom_to_top(self, 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] self.set_position(position[parent], index) else: heap[index] = val position[index] = temp self.set_position(temp, index) break index = parent else: heap[0] = val position[0] = temp self.set_position(temp, 0) def heapify(self, heap, positions): start = len(heap) // 2 - 1 for i in range(start, -1, -1): self.top_to_bottom(heap, i, len(heap), positions) def delete_minimum(self, heap, positions): temp = positions[0] heap[0] = sys.maxsize self.top_to_bottom(heap, 0, len(heap), positions) return temp def prisms_algorithm(adjacency_list): """ >>> adjacency_list = {0: [[1, 1], [3, 3]], ... 1: [[0, 1], [2, 6], [3, 5], [4, 1]], ... 2: [[1, 6], [4, 5], [5, 2]], ... 3: [[0, 3], [1, 5], [4, 1]], ... 4: [[1, 1], [2, 5], [3, 1], [5, 4]], ... 5: [[2, 2], [4, 4]]} >>> prisms_algorithm(adjacency_list) [(0, 1), (1, 4), (4, 3), (4, 5), (5, 2)] """ heap = Heap() visited = [0] * len(adjacency_list) nbr_tv = [-1] * len(adjacency_list) # 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 vertex in range(len(adjacency_list)): distance_tv.append(sys.maxsize) positions.append(vertex) heap.node_position.append(vertex) tree_edges = [] visited[0] = 1 distance_tv[0] = sys.maxsize for neighbor, distance in adjacency_list[0]: nbr_tv[neighbor] = 0 distance_tv[neighbor] = distance heap.heapify(distance_tv, positions) for _ in range(1, len(adjacency_list)): vertex = heap.delete_minimum(distance_tv, positions) if visited[vertex] == 0: tree_edges.append((nbr_tv[vertex], vertex)) visited[vertex] = 1 for neighbor, distance in adjacency_list[vertex]: if ( visited[neighbor] == 0 and distance < distance_tv[heap.get_position(neighbor)] ): distance_tv[heap.get_position(neighbor)] = distance heap.bottom_to_top( distance, heap.get_position(neighbor), distance_tv, positions ) nbr_tv[neighbor] = vertex return tree_edges if __name__ == "__main__": # pragma: no cover # < --------- Prims Algorithm --------- > edges_number = int(input("Enter number of edges: ").strip()) adjacency_list = defaultdict(list) for _ in range(edges_number): edge = [int(x) for x in input().strip().split()] adjacency_list[edge[0]].append([edge[1], edge[2]]) adjacency_list[edge[1]].append([edge[0], edge[2]]) print(prisms_algorithm(adjacency_list))