Question

Preferably in python but java is good too

Task 1: Minimum Spanning Trees For this warm-up task you are to implement any efficient minimum spanning tree algorithm that takes a sequence of edge-weighted graphs and outputs the minimum cost weight of a spanning tree of each Input Format For this assignment we use adjacency matrices with positive integer weights. Here a zero entry at row i and column J indicates that no edge i] exists in the graph. The first line consists of an integer n < 1000 denoting the order of the graph. This is then followed by n lines of n white-space separated integers denoting edge weights The sequence of graphs is terminated by a value n 0, which is not processed 3 0 1 3 1 02 3 2 0 4 0 270 2 0 5 1 7 5 0 3 0 1 3 0 0 1 04 0 0 10 3 0 3 0 0 3 0 0 0 2 4 00 0 2 0 0 3 0 2 0 1 0 0 2 0 1 0 0 OutputFormat Output should be one line for each input graph indicating the minimum cost weighted tree. The sample output for the previous input cases is as follows. 3 6

Answer 1

It is a python program I used Prim's algorithm

Solution:

import sys

class Graph():

    def __init__(self, vertices):
        self.V = vertices
        self.graph = [[0 for column in range(vertices)]
                    for row in range(vertices)]


    def printMST(self, parent):
        self.tree=0
        for i in range(1,self.V):
            self.tree=self.tree+self.graph[i][parent[i]]
        print("Minimum weighted tree's weight:",self.tree)


    def minKey(self, key, mstSet):


        min = sys.maxsize

        for v in range(self.V):
            if key[v] < min and mstSet[v] == False:
                min = key[v]
                min_index = v

        return min_index


    def primMST(self):


        key = [sys.maxsize] * self.V
        parent = [None] * self.V

        key[0] = 0
        mstSet = [False] * self.V

        parent[0] = -1

        for cout in range(self.V):


            u = self.minKey(key, mstSet)


            mstSet[u] = True


            for v in range(self.V):
                 #write below if in single line in your ide
                if self.graph[u][v] > 0 and mstSet[v] == False and key[v] > self.graph[u][v]:
                        key[v] = self.graph[u][v]
                        parent[v] = u

        self.printMST(parent)

n=int(input('Enter order of the graph:'))
g = Graph(n)
matrix=[]
for i in range(n):
    row=[]
    x=input()
    row=x.split()
    for j in range(n):
        row[j]=int(row[j])
    matrix.append(row)

g.graph = matrix

g.primMST();