You are given input as order of graph n (highest number of edges connected to a node), you have to find the number of vertices in a Hypercube graph of order n.
Examples:
Input : n = 3 Output : 8 Input : n = 2 Output : 4
In hypercube graph Q(n), n represents the degree of the graph. Hypercube graph represents the maximum number of edges that can be connected to a graph to make it an n degree graph, every vertex has the same degree n and in that representation, only a fixed number of edges and vertices are added as shown in the figure below:
All hypercube graphs are Hamiltonian, hypercube graph of order n has (2^n) vertices, , for input n as the order of graph we have to find the corresponding power of 2.
Recursive Approach
// C++ program to find vertices in a hypercube
// graph of order n
#include <iostream>
using namespace std;
// function to find power of 2
int power(int n)
{
if (n == 1)
return 2;
return 2 * power(n - 1);
}
// driver program
int main()
{
// n is the order of the graph
int n = 4;
cout << power(n);
return 0;
}
// Java program to find vertices in
// a hypercube graph of order n
class GfG
{
// Function to find power of 2
static int power(int n)
{
if (n == 1)
return 2;
return 2 * power(n - 1);
}
// Driver program
public static void main(String []args)
{
// n is the order of the graph
int n = 4;
System.out.println(power(n));
}
}
// This code is contributed by Rituraj Jain
# Python3 program to find vertices in a hypercube
# graph of order n
# function to find power of 2
def power(n):
if n==1:
return 2
return 2*power(n-1)
# Driver code
n =4
print(power(n))
# This code is contributed by Shrikant13
// C# program to find vertices in
// a hypercube graph of order n
using System;
class GfG
{
// Function to find power of 2
static int power(int n)
{
if (n == 1)
return 2;
return 2 * power(n - 1);
}
// Driver code
public static void Main()
{
// n is the order of the graph
int n = 4;
Console.WriteLine(power(n));
}
}
// This code is contributed by Mukul Singh
<?php
// PHP program to find vertices in
// a hypercube graph of order n
{
// Function to find power of 2
function power($n)
{
if ($n == 1)
return 2;
return 2 * power($n - 1);
}
// Driver Code
{
// n is the order of the graph
$n = 4;
echo(power($n));
}
}
// This code is contributed by Code_Mech
?>
<script>
// Javascript program to find vertices in a hypercube
// graph of order n
// function to find power of 2
function power(n)
{
if (n == 1)
return 2;
return 2 * power(n - 1);
}
// driver program
// n is the order of the graph
var n = 4;
document.write( power(n));
</script>
Output
16
Iterative Approach
// C++ program to find vertices in
// a hypercube graph of order n
#include <bits/stdc++.h>
using namespace std;
// Function to find power of 2
int power(int n)
{
if (n == 0)
return 0;
int pow = 1;
for (int i = 1; i <= n; i++)
{
pow *= 2;
}
return pow;
}
int main()
{
// n is the order of the graph
int n = 4;
cout << power(n);
return 0;
}
// This code is contributed by akashish__
/*package whatever //do not write package name here */
import java.io.*;
// Java program to find vertices in
// a hypercube graph of order n
class GFG {
// Function to find power of 2
static int power(int n)
{
if(n==0) return 0;
int pow = 1;
for(int i=1;i<=n;i++){
pow *= 2;
}
return pow;
}
public static void main (String[] args) {
// n is the order of the graph
int n = 4;
System.out.println(power(n));
}
}
# Python program to find vertices in
# a hypercube graph of order n
# Function to find power of 2
def power(n):
if n == 0:
return 0
pow = 1
for i in range(1, n+1):
pow *= 2
return pow
# n is the order of the graph
n = 4
print(power(n))
# This code is contributed by akashish__
// C# program to find vertices in
// a hypercube graph of order n
using System;
public class GFG {
// Function to find power of 2
public static int power(int n)
{
if (n == 0)
return 0;
int pow = 1;
for (int i = 1; i <= n; i++) {
pow *= 2;
}
return pow;
}
static public void Main()
{
// n is the order of the graph
int n = 4;
Console.WriteLine(power(n));
}
}
// This code is contributed by akashish__
// Function to find power of 2
function power(n) {
if (n === 0) return 0;
let pow = 1;
for (let i = 1; i <= n; i++) {
pow *= 2;
}
return pow;
}
// n is the order of the graph
const n = 4;
console.log(power(n));
// This code is contributed by akashish__
Output
16
Java Using Math.pow()
#include <bits/stdc++.h>
using namespace std;
// Function to find power of 2
int power(int n) { return pow(2, n); }
int main()
{
// n is the order of the graph
int n = 4;
cout << power(n) << endl;
return 0;
}
// This code is contributed by akashish__
/*package whatever //do not write package name here */
import java.io.*;
// Java program to find vertices in
// a hypercube graph of order n
class GFG {
// Function to find power of 2
static int power(int n)
{
return (int)Math.pow(2,n);
}
public static void main (String[] args) {
// n is the order of the graph
int n = 4;
System.out.println(power(n));
}
}
# Function to find power of 2
def power(n):
return pow(2, n)
# n is the order of the graph
n = 4
print(power(n))
# contributed by akashish__
using System;
// Java program to find vertices in
// a hypercube graph of order n
public class GFG {
// Function to find power of 2
static int power(int n) { return (int)Math.Pow(2, n); }
static public void Main()
{
// n is the order of the graph
int n = 4;
Console.WriteLine(power(n));
}
}
// This code is contributed by akashish__
// Function to find power of 2
function power(n) { return Math.pow(2, n); }
// n is the order of the graph
let n = 4;
console.log(power(n));
// contributed by akashish__
Output
16