import sys
from collections import defaultdict
def prisms_algorithm(l):
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)
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))]
distance_tv = []
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 _ 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__":
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()]
adjlist[l[0]].append([l[1], l[2]])
adjlist[l[1]].append([l[0], l[2]])
print(prisms_algorithm(adjlist))