Hyperfactorial of a number

Given a number, the task is to find the hyperfactorial of a number.

The result of multiplying a given number of consecutive integers from 1 to the given number, each raised to its own power is called hyperfactorial of a number.

H(n)= 1 ^ 1 * 2 ^ 2 * 3 ^ 3 * . . . . . * n ^ n

Examples:



Input : 2
Output : 4

Input : 4
Output : 27648
H(4) = 1^1 * 2^2 * 3^3 * 4^4 = 27648

A naive approach is two use two loops, one to find the summation of i^i and the other to find i^i. But the time complexity will be O(n2).

An efficient approach is to use the inbuilt pow() function or the O(log n) method to find i^i and then add it.

Below is the implementation of the above approach.

C++

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/// C++ program to find the hyperfactorial 
// of a number 
#include <bits/stdc++.h>
  
using namespace std;
#define ll long long 
  
// function to calculate the value of hyperfactorial
ll boost_hyperfactorial(ll num)
{
    // initialise the val to 1
    ll val = 1;
    for (int i = 1; i <= num; i++) {
        val = val * pow(i,i); 
    }
    // returns the hyperfactorial of a number
    return val;
}
  
// Driver code
int main()
{
    int num = 5;
    cout << boost_hyperfactorial(num);
    return 0;
}

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Java

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// Java program to find the 
// hyperfactorial of a number 
  
// function to calculate the 
// value of hyperfactorial
class GFG
{
static long boost_hyperfactorial(long num)
{
    // initialise the val to 1
    long val = 1;
    for (int i = 1; i <= num; i++) 
    {
        val = val * (long)Math.pow(i, i); 
    }
      
    // returns the hyperfactorial 
    // of a number
    return val;
}
  
// Driver code
public static void main(String args[])
{
    int num = 5;
    System.out.println(boost_hyperfactorial(num));
}
}
  
// This code is contributed 
// by chandan_jnu

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Python3

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# Python3 program to find the 
# hyperfactorial of a number 
  
# function to calculate the
# value of hyperfactorial
def boost_hyperfactorial(num):
  
    # initialise the 
    # val to 1
    val = 1;
    for i in range(1, num + 1):
        val = val * pow(i, i); 
      
    # returns the hyperfactorial
    # of a number
    return val;
  
# Driver code
num = 5;
print(boost_hyperfactorial(num));
  
# This code is contributed
# by mits

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C#

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// C# program to find the 
// hyperfactorial of a number 
using System;
  
class GFG
{
  
// function to calculate the 
// value of hyperfactorial
static long boost_hyperfactorial(long num)
{
    // initialise the val to 1
    long val = 1;
    for (long i = 1; i <= num; i++) 
    {
        val = val * (long)Math.Pow(i, i);
    }
      
    // returns the hyperfactorial 
    // of a number
    return val;
}
  
// Driver code
public static void Main()
{
    int num = 5;
    Console.WriteLine(boost_hyperfactorial(num));
}
}
  
// This code is contributed 
// by chandan_jnu

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PHP

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<?php
// PHP program to find the 
// hyperfactorial of a number 
  
// function to calculate the
// value of hyperfactorial
function boost_hyperfactorial($num)
{
    // initialise the 
    // val to 1
    $val = 1;
    for ($i = 1; $i <= $num; $i++) 
    {
        $val = $val * pow($i, $i); 
    }
      
    // returns the hyperfactorial
    // of a number
    return $val;
}
  
// Driver code
$num = 5;
echo boost_hyperfactorial($num);
  
// This code is contributed
// by Akanksha Rai(Abby_akku)
?>

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Output:

86400000

Time-complexity:O(N * log N)

Since hyper-factorials of number can be huge, hence the numbers will overflow. We can use boost libraries in C++ or BigInteger in Java to store the hyper-factorial of a number N.

C++

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// C++ program to find the hyperfactorial 
// of a number using boost libraries 
#include <bits/stdc++.h>
#include <boost/multiprecision/cpp_int.hpp>
  
using namespace boost::multiprecision;
using namespace std;
  
// function to calculate the value of hyperfactorial
int1024_t boost_hyperfactorial(int num)
{
    // initialise the val to 1
    int1024_t val = 1;
    for (int i = 1; i <= num; i++) {
        for (int j = 1; j <= i; j++) {
            // 1^1*2^2*3^3....
            val *= i;
        }
    }
    // returns the hyperfactorial of a number
    return val;
}
  
// Driver code
int main()
{
    int num = 5;
    cout << boost_hyperfactorial(num);
    return 0;
}

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Java

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// Java program to find the hyperfactorial 
// of a number using boost libraries 
  
import java.io.*;
  
class GFG {
  
// function to calculate the value of hyperfactorial
static int boost_hyperfactorial(int num)
{
    // initialise the val to 1
    int val = 1;
    for (int i = 1; i <= num; i++) {
        for (int j = 1; j <= i; j++) {
            // 1^1*2^2*3^3....
            val *= i;
        }
    }
    // returns the hyperfactorial of a number
    return val;
}
  
// Driver code
  
  
    public static void main (String[] args) {
    int num = 5;
    System.out.println( boost_hyperfactorial(num));
    }
}
// This code is contributed 
// by chandan_jnu

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Python3

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# Python3 program to find the hyperfactorial 
# of a number using boost libraries 
  
# function to calculate the value of hyperfactorial 
def boost_hyperfactorial(num):
      
    # initialise the val to 1 
    val = 1
    for i in range(1,num+1): 
        for j in range(1,i+1): 
              
            # 1^1*2^2*3^3.... 
            val *= i; 
              
    # returns the hyperfactorial of a number 
    return val; 
  
# Driver code 
num = 5
print( boost_hyperfactorial(num)); 
  
# This code is contributed by mits

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C#

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// C# program to find the hyperfactorial 
// of a number using boost libraries 
using System;
  
class GFG 
{
  
// function to calculate the
// value of hyperfactorial
static int boost_hyperfactorial(int num)
{
    // initialise the val to 1
    int val = 1;
    for (int i = 1; i <= num; i++) 
    {
        for (int j = 1; j <= i; j++)
        {
            // 1^1*2^2*3^3....
            val *= i;
        }
    }
      
    // returns the hyperfactorial
    // of a number
    return val;
}
  
// Driver code
public static void Main ()
{
    int num = 5;
    Console.WriteLine(boost_hyperfactorial(num));
}
}
  
// This code is contributed 
// by chandan_jnu

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PHP

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<?php
// PHP program to find the hyperfactorial 
// of a number using boost libraries 
  
// function to calculate the value 
// of hyperfactorial
function boost_hyperfactorial($num)
{
    // initialise the val to 1
    $val = 1;
    for ($i = 1; $i <= $num; $i++)
    {
        for ($j = 1; $j <= $i; $j++) 
        {
            // 1^1*2^2*3^3....
            $val *= $i;
        }
    }
      
    // returns the hyperfactorial 
    // of a number
    return $val;
}
  
// Driver code
$num = 5;
echo boost_hyperfactorial($num);
  
// This code is contributed 
// by Mukul Singh
?>

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Output:

86400000


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