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> |
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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__ |
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__ |
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