# Prims algorithm
from collections import defaultdict
from heapq import *
def prim( nodes, edges ):
conn = defaultdict( list )
for n1,n2,c in edges:
conn[ n1 ].append( (c, n1, n2) )
conn[ n2 ].append( (c, n2, n1) )
mst = []
used = set( nodes[ 0 ] )
usable_edges = conn[ nodes[0] ][:]
heapify( usable_edges )
while usable_edges:
cost, n1, n2 = heappop( usable_edges )
if n2 not in used:
used.add( n2 )
mst.append( ( n1, n2, cost ) )
for e in conn[ n2 ]:
if e[ 2 ] not in used:
heappush( usable_edges, e )
return mst
#test
nodes = list("ABCDEFG")
edges = [ ("A", "B", 7), ("A", "D", 5),
("B", "C", 8), ("B", "D", 9),
("B", "E", 7), ("C", "E", 5),
("D", "E", 15), ("D", "F", 6),
("E", "F", 8), ("E", "G", 9),
("F", "G", 11)]
print "prim:", prim( nodes, edges )
from collections import defaultdict
from heapq import *
def prim( nodes, edges ):
conn = defaultdict( list )
for n1,n2,c in edges:
conn[ n1 ].append( (c, n1, n2) )
conn[ n2 ].append( (c, n2, n1) )
mst = []
used = set( nodes[ 0 ] )
usable_edges = conn[ nodes[0] ][:]
heapify( usable_edges )
while usable_edges:
cost, n1, n2 = heappop( usable_edges )
if n2 not in used:
used.add( n2 )
mst.append( ( n1, n2, cost ) )
for e in conn[ n2 ]:
if e[ 2 ] not in used:
heappush( usable_edges, e )
return mst
#test
nodes = list("ABCDEFG")
edges = [ ("A", "B", 7), ("A", "D", 5),
("B", "C", 8), ("B", "D", 9),
("B", "E", 7), ("C", "E", 5),
("D", "E", 15), ("D", "F", 6),
("E", "F", 8), ("E", "G", 9),
("F", "G", 11)]
print "prim:", prim( nodes, edges )