Prim's Algorithm for Minimum Spanning Tree

# 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 )