chore(Java) : add prims algorithm (#945)

algorithms/Java/README.md

@@ -16,6 +16,7 @@
 ## Graphs
 
 - [Dijkstras](graphs/Dijkstras.java)
+- [Prims](graphs/Prims.java)
 
 ## Linked Lists
 

algorithms/Java/graphs/Prims.java

@@ -0,0 +1,81 @@
+/**
+Approach-
+It starts with an empty spanning tree. The idea is to maintain two sets of vertices. 
+The first set contains the vertices already included in the MST, the other set contains the vertices not yet included. 
+At every step, it considers all the edges that connect the two sets and picks the minimum weight edge from these edges. 
+After picking the edge, it moves the other endpoint of the edge to the set containing MST. 
+*/
+
+/* 
+Time complexity -
+Time Complexity: O(V^2)
+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.  
+In this implementation, we are always considering the spanning tree to start from the root of the graph.
+
+Auxiliary Space: O(V)
+*/
+
+import java.util.Scanner;
+public class Prims{
+	public static void main(String[] args) {
+		int w[][]=new int[10][10];
+		int min,mincost=0, u, v, flag=0;
+		int sol[]=new int[10];
+		System.out.println("Enter the number of vertices");
+		Scanner sc=new Scanner(System.in);
+		int n=sc.nextInt();
+		System.out.println("Enter the weighted graph");
+		for(int i=1;i<=n;i++)
+			for(int j=1;j<=n;j++)
+				w[i][j]=sc.nextInt();
+		System.out.println("Enter the source vertex");
+		int s=sc.nextInt();
+		for(int i=1;i<=n;i++) // Initialise the solution matrix with 0
+			sol[i]=0;
+		sol[s]=1; // mark the source vertex
+		int count=1;
+		while (count<=n-1)
+		{
+			min=99; // If there is no edger between any two vertex its cost is assumed to be 99
+			for(int i=1;i<=n;i++)
+				for(int j=1;j<=n;j++)
+					if(sol[i]==1&&sol[j]==0) //this will check the edge if not already traversed will be considered
+						if(i!=j && w[i][j]<min)
+						{
+							min=w[i][j]; //cost of the edge
+							u=i;
+							v=j;
+						}
+			sol[v]=1;
+			mincost += min; //mincost of whole graph
+			count++;
+			System.out.println(u+"->"+v+"="+min);
+		}
+
+		for(i=1;i<=n;i++)
+			if(sol[i]==0)
+				flag=1;
+		if(flag==1)
+		System.out.println("No spanning tree");
+		else
+		System.out.println("The cost of minimum spanning tree is"+mincost);
+		sc.close();
+		}
+}
+
+/* Let us create the following graph
+        2 3
+        (0)--(1)--(2)
+        | / \ |
+        6| 8/ \5 |7
+        | /     \ |
+        (3)-------(4)
+            9         
+         { 
+            { 99, 2, 99, 6, 99 },
+            { 2, 99, 3, 8, 5 },
+            { 99, 3, 99, 99, 7 },
+            { 6, 8, 99, 99, 9 },
+            { 99, 5, 7, 9, 99 } 
+         };
+*/