Hypercube Graph (original) (raw)

Last Updated : 8 Feb, 2023

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++ `

// C++ program to find vertices in a hypercube // graph of order n #include 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

// 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

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#

// 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

JavaScript

`

Iterative Approach

C++ `

// 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__

Java

/*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));
}

}

Python3

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#

// 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__

JavaScript

// 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__

`

Java Using Math.pow()

C++ `

#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__

Java

/*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));
}

}

Python3

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__

C#

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__

JavaScript

// 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__

`