mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-10-06 13:49:30 +00:00
9316e7c014
* flake8 --max-line-length=88
* fixup! Format Python code with psf/black push
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
117 lines
3.7 KiB
Python
117 lines
3.7 KiB
Python
import sys
|
|
from collections import defaultdict
|
|
|
|
|
|
def PrimsAlgorithm(l): # noqa: E741
|
|
|
|
nodePosition = []
|
|
|
|
def get_position(vertex):
|
|
return nodePosition[vertex]
|
|
|
|
def set_position(vertex, pos):
|
|
nodePosition[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 deleteMinimum(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)
|
|
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[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 TreeEdges
|
|
|
|
|
|
if __name__ == "__main__":
|
|
# < --------- 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(PrimsAlgorithm(adjlist))
|