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'''

This Prim's Algorithm Code is for finding weight of minimum spanning tree

of a connected graph.

For argument graph, it should be a dictionary type

such as

graph = {

'a': [ [3, 'b'], [8,'c'] ],

'b': [ [3, 'a'], [5, 'd'] ],

'c': [ [8, 'a'], [2, 'd'], [4, 'e'] ],

'd': [ [5, 'b'], [2, 'c'], [6, 'e'] ],

'e': [ [4, 'c'], [6, 'd'] ]

}

where 'a','b','c','d','e' are nodes (these can be 1,2,3,4,5 as well)

'''

import heapq # for priority queue

# prim's algo. to find weight of minimum spanning tree

def prims_minimum_spanning(graph_used):

vis=[]

s=[[0,1]]

prim = []

mincost=0

while(len(s)>0):

v=heapq.heappop(s)

x=v[1]

if(x in vis):

continue

mincost += v[0]

prim.append(x)

vis.append(x)

for j in graph_used[x]:

i=j[-1]

if(i not in vis):

heapq.heappush(s,j)

return mincost