# Design and Analysis of Algorithm Lab 12 | Read Now

Design and Analysis of Algorithm Lab 12

12] Design and implement in Java to find all Hamiltonian Cycles in a connected undirected Graph G of n vertices using the backtracking principle.

12] Program code

```import java.util.Scanner;
public class lab12
{
static int x[] = new int[10];
public static void main(String[] args)
{
Scanner sc = new Scanner(System.in);
int i,j,x1, x2, edges, n;
int g[][] = new int[10][10];
System.out.print("Enter No. of Vertices: ");
n = sc.nextInt();
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
g[i][j] = 0;
x[i]=0;
}
}

System.out.print("Enter No. of Edges: ");
edges = sc.nextInt();
for(i=1;i<=edges;i++)
{
System.out.println("Enter the Edge"+i+": ");
x1 = sc.nextInt();
x2 = sc.nextInt();
g[x1][x2] = 1;
g[x2][x1] = 1;
}
x[1] = 1;
System.out.println("\nHamiltonian Cycle");
hcycle(g,n,2);
}

public static void nextvalue(int g[][],int n,int k)
{
int j;
while(true)
{
x[k] = (x[k] + 1) % (n+1);
if(x[k] == 0)
return;
if(g[x[k-1]][x[k]] == 1)
{
for(j=1;j<=k-1;j++)
{
if(x[j] == x[k] )
break;
}
if(j ==  k)
{
if((k<n) || ((k==n) && (g[x[n]][x[1]] == 1)))
return;
}
}
}
}

public static void hcycle(int g[][],int n, int k)
{
int i;
while(true)
{
nextvalue(g,n,k);
if(x[k]== 0)
return;
if(k==n)
{
for(i=1;i<=n;i++)
System.out.print(x[i]+"-->");
System.out.println(x[1]+"\n");
}
else
hcycle(g,n,k+1);
}
}
}```

Output

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