82 lines
2.4 KiB
Java
82 lines
2.4 KiB
Java
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/**
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Approach-
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It starts with an empty spanning tree. The idea is to maintain two sets of vertices.
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The first set contains the vertices already included in the MST, the other set contains the vertices not yet included.
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At every step, it considers all the edges that connect the two sets and picks the minimum weight edge from these edges.
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After picking the edge, it moves the other endpoint of the edge to the set containing MST.
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*/
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/*
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Time complexity -
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Time Complexity: O(V^2)
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If the input graph is represented using an adjacency list, then the time complexity of Prim’s algorithm can be reduced to O(E log V) with the help of a binary heap.
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In this implementation, we are always considering the spanning tree to start from the root of the graph.
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Auxiliary Space: O(V)
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*/
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import java.util.Scanner;
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public class Prims{
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public static void main(String[] args) {
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int w[][]=new int[10][10];
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int min,mincost=0, u, v, flag=0;
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int sol[]=new int[10];
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System.out.println("Enter the number of vertices");
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Scanner sc=new Scanner(System.in);
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int n=sc.nextInt();
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System.out.println("Enter the weighted graph");
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for(int i=1;i<=n;i++)
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for(int j=1;j<=n;j++)
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w[i][j]=sc.nextInt();
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System.out.println("Enter the source vertex");
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int s=sc.nextInt();
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for(int i=1;i<=n;i++) // Initialise the solution matrix with 0
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sol[i]=0;
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sol[s]=1; // mark the source vertex
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int count=1;
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while (count<=n-1)
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{
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min=99; // If there is no edger between any two vertex its cost is assumed to be 99
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for(int i=1;i<=n;i++)
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for(int j=1;j<=n;j++)
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if(sol[i]==1&&sol[j]==0) //this will check the edge if not already traversed will be considered
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if(i!=j && w[i][j]<min)
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{
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min=w[i][j]; //cost of the edge
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u=i;
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v=j;
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}
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sol[v]=1;
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mincost += min; //mincost of whole graph
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count++;
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System.out.println(u+"->"+v+"="+min);
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}
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for(i=1;i<=n;i++)
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if(sol[i]==0)
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flag=1;
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if(flag==1)
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System.out.println("No spanning tree");
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else
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System.out.println("The cost of minimum spanning tree is"+mincost);
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sc.close();
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}
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}
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/* Let us create the following graph
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2 3
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(0)--(1)--(2)
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| / \ |
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6| 8/ \5 |7
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| / \ |
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(3)-------(4)
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9
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{
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{ 99, 2, 99, 6, 99 },
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{ 2, 99, 3, 8, 5 },
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{ 99, 3, 99, 99, 7 },
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{ 6, 8, 99, 99, 9 },
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{ 99, 5, 7, 9, 99 }
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};
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*/
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