Your team at amazon is overseeing the design of a new high-efficiency data center at HQ2. A power grid need to be generated for supplying power to N servers. All servers in the grid have to be connected such that they have access to power. The cost of connections between different servers varies. Assume that there are no ties, names of servers are unique, connections are directionless, there is at most one connection between a pair of servers, all costs are greater than zero, and a server does not connect to itself. Write an algorithm to minimize the cost of connecting all servers in the power grid. Input two arguments - num, an Integer representing number of connections. connectons, representing a list of connections where each element of the list consists of two servers and the cost of connection between the servers.

Following are the python program to the given question:

from collections import defaultdict #import package

import heapq as h#import package

def primsMST(gr, st_v): # defining a method primsMST that takes two values in parameters  

   primalMST = defaultdict(set)#defining primalMST as a variable that calls defaultdict method  

   v = set([st_v])# defining a variable v that calls the set method and hold its value

   e_list = [(c, st_v, to)for to, c in gr[st_v].items()]#defining variable e_list that use loop to hold value in list

   h.heapify(e_list)# use package that holds heapify and holds its value

   while e_list:#defining while loop that checks e_list  

       c, s, e = h.heappop(e_list)#holding heapop method value in c,s,and e variable

       if e not in v:#defining if block checks e value is not in v

           v.add(e)# use add method to add value in v

           primalMST[s].add(e)#use primalMST as list that adds value in mwthod

   for nxt, c in gr[e].items():#defining for loop that uses nxt, and c variable that checks value in list

       if nxt not in v:#defining nxt variable that checks value is not in v

           h.heappush(e_list, (c, e, nxt))#add value into the heappush method

   return primalMST#return method value

connects=[['A','B',1],['B','C',4],['B','D',6],['D','E',5],['C','E',1]]#defining a list connects

my_gr=dict()#defining a variable my_gr that holds method dict() value  

for el in connects:#defining a for loop that uses el to count connects list value

   my_gr[el[0]]=dict()#use my_gr as list hold value in dict method

   my_gr[el[1]]=dict()#use my_gr as list hold value in dict method

for el in connects:#defining another for loop that uses el to count connects list

   my_gr[el[0]].update({el[1]:el[2]}) # use update method that update value in my_gr

   my_gr[el[1]].update({el[0]:el[2]})# use update method that update value in my_gr

x=dict(primsMST(my_gr, list(my_gr.keys())[0]))#defining x variable that calls dict method and  hold its value  

a=[]#defining an empty list

for k in x:#defining a for loop that uses k to hold dict method value

   for no in x[k]:#defining a loop that checks list value

       a.append([k,no,my_gr[k][no]])#use a that add value in list  

       print(a)#print list value.

Output:

Please find the attached file.

Program Explanation:

Learn more:

dictionary:

List:

answer would be