Python/graphs/minimum_spanning_tree_prims.py

113 lines
3.7 KiB
Python
Raw Normal View History

2018-10-19 12:48:28 +00:00
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
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()]
adjlist[l[0]].append([ l[1], l[2] ])
adjlist[l[1]].append([ l[0], l[2] ])
print(PrimsAlgorithm(adjlist))