Add Hamiltonean cycles

Backtracking/Hamiltonean Cycles/Code.java

@@ -0,0 +1,102 @@
+//A Hamiltonian cycle is a cycle in an undirected or directed graph that visits each vertex exactly once.
+// import visualization libraries {
+import org.algorithm_visualizer.*;
+import java.util.Random;
+// }
+
+class Main {
+    // define tracer variables {
+    GraphTracer graphTracer=new GraphTracer("GraphTracer");
+    LogTracer logTracer = new LogTracer("Console");
+    // }
+    int n=8;
+    int x[];
+    int found=0;
+    int vis[];
+    int[][] adjacencyMatrix;
+    void ham(int k) {
+		while(true)
+		{
+			nextVal(k);
+			if(x[k]==-1)
+				return;
+			if(k==n-1)
+			{
+			    graphTracer.visit(x[0],x[k]);
+				graphTracer.delay();
+				found=1;
+				//Printint the cycle{
+				for(int i=0;i<n;i++)
+					logTracer.print((x[i])+"  ");
+				logTracer.println(0);
+				//}
+				graphTracer.leave(x[0],x[k]);
+			}
+			else
+				ham(k+1);
+		}
+	}
+	void nextVal(int k)
+	{
+		while(true) {
+			int i=0;
+			if(vis[k]==1)
+			    graphTracer.leave(x[k],x[k-1]);
+			vis[k]=0;
+			x[k]=(x[k]+1)%(n+1);
+			if(x[k]==n)
+			{
+				x[k]=-1;
+				return;
+			}
+			graphTracer.visit(x[k],x[k-1]);
+		    graphTracer.delay();
+		    vis[k]=1;
+			if (adjacencyMatrix[x[k-1]][x[k]]==1)
+			{
+				for(i=0;i<k;i++)
+					if(x[i]==x[k])
+						break;
+				if(i==k)
+					if(k<n-1 || k==n-1 && adjacencyMatrix[x[k]][x[0]]==1)
+						return;
+			}
+		}
+	}
+
+    Main() {
+        //initializing{
+        adjacencyMatrix=new int[n][n];
+        x=new int[n];
+        vis=new int[n];
+        Random r=new Random();
+        for(int i=1;i<n;i++)
+			x[i]=-1;
+        //}
+
+        //Randomizing adjacancy matrix and displaying on log screen{
+        logTracer.println("The adjacancy Matrix is");
+        for(int i=0;i<n;i++){
+            for(int j=0;j<n;j++){
+                adjacencyMatrix[i][j]=r.nextInt(2);
+                logTracer.print(adjacencyMatrix[i][j]+"  ");
+            }
+            logTracer.println("");
+        }
+        //}
+
+        // visualize {
+        Layout.setRoot(new VerticalLayout(new Commander[]{graphTracer, logTracer}));
+        graphTracer.set(adjacencyMatrix);
+        // }
+
+        logTracer.println("the possible solutios are");
+        ham(1);
+        if(found==0)
+            logTracer.println("No cycles are found Try with a different graph ");
+    }
+
+    public static void main(String[] args) {
+        new Main();
+    }
+}