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:Â
Input : 2Â
Output : 4Input : 4Â
Output : 27648Â
H(4) = 1^1 * 2^2 * 3^3 * 4^4 = 27648Â
A naive approach is using 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).Â
An efficient approach is to use the inbuilt pow() function or O(log n) method to find i^i and then add it.Â
Below is the implementation of the above approach.Â
C++
/// C++ program to find the hyperfactorial // of a number #include <bits/stdc++.h>Â
using namespace std;#define ll long long Â
// function to calculate the value of hyperfactorialll 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;}Â
// Driver codeint main(){Â Â Â Â int num = 5;Â Â Â Â cout << boost_hyperfactorial(num);Â Â Â Â return 0;} |
Java
// Java program to find the // hyperfactorial of a number Â
// function to calculate the // value of hyperfactorialclass 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;}Â
// Driver codepublic static void main(String args[]){Â Â Â Â int num = 5;Â Â Â Â System.out.println(boost_hyperfactorial(num));}}Â
// This code is contributed // by chandan_jnu |
Python3
# Python3 program to find the # hyperfactorial of a number Â
# function to calculate the# value of hyperfactorialdef boost_hyperfactorial(num):Â
    # 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;Â
# Driver codenum = 5;print(boost_hyperfactorial(num));Â
# This code is contributed# by mits |
C#
// C# program to find the // hyperfactorial of a number using System;Â
class GFG{Â
// function to calculate the // value of hyperfactorialstatic 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;}Â
// Driver codepublic static void Main(){Â Â Â Â int num = 5;Â Â Â Â Console.WriteLine(boost_hyperfactorial(num));}}Â
// This code is contributed // by chandan_jnu |
PHP
<?php// PHP program to find the // hyperfactorial of a number Â
// function to calculate the// value of hyperfactorialfunction 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 $val;}Â
// Driver code$num = 5;echo boost_hyperfactorial($num);Â
// This code is contributed// by Akanksha Rai(Abby_akku)?> |
Javascript
<script>Â
// Javascript program to find the// hyperfactorial of a numberÂ
// function to calculate the// value of hyperfactorialfunction boost_hyperfactorial(num){    // initialise the    // val to 1    let val = 1;    for (let i = 1; i <= num; i++)    {        val = val * Math.pow(i, i);    }         // returns the hyperfactorial    // of a number    return val;}Â
// Driver codelet num = 5;document.write(boost_hyperfactorial(num));Â
// This code is contributed// by gfgkingÂ
</script> |
Output:Â
86400000
Â
Time complexity:O(N * log N)Â
Auxiliary Space: O(1)
Since hyper-factorials of numbers 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++
// C++ program to find the hyperfactorial // of a number using boost libraries #include <bits/stdc++.h>#include <boost/multiprecision/cpp_int.hpp>Â
using namespace boost::multiprecision;using namespace std;Â
// function to calculate the value of hyperfactorialint1024_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;}Â
// Driver codeint main(){Â Â Â Â int num = 5;Â Â Â Â cout << boost_hyperfactorial(num);Â Â Â Â return 0;} |
Java
// Java program to find the hyperfactorial // of a number Â
import java.io.*;Â
class GFG {Â
// function to calculate the value of hyperfactorialstatic 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;}Â
// Driver codeÂ
Â
    public static void main (String[] args) {    int num = 5;    System.out.println( boost_hyperfactorial(num));    }}// This code is contributed // by chandan_jnu |
Python3
# Python3 program to find the hyperfactorial # of a number Â
# 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; Â
# Driver code num = 5; print( boost_hyperfactorial(num)); Â
# This code is contributed by mits |
C#
// C# program to find the hyperfactorial // of a number using boost libraries using System;Â
class GFG {Â
// function to calculate the// value of hyperfactorialstatic 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;}Â
// Driver codepublic static void Main (){Â Â Â Â int num = 5;Â Â Â Â Console.WriteLine(boost_hyperfactorial(num));}}Â
// This code is contributed // by chandan_jnu |
PHP
<?php// PHP program to find the hyperfactorial // of a number using boost libraries Â
// function to calculate the value // of hyperfactorialfunction 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 $val;}Â
// Driver code$num = 5;echo boost_hyperfactorial($num);Â
// This code is contributed // by Mukul Singh?> |
Javascript
<script>Â
// Javascript program to find the hyperfactorial // of a number using boost libraries Â
// function to calculate the value of hyperfactorialfunction boost_hyperfactorial(num){    // initialise the val to 1    var val = 1;    for (var i = 1; i <= num; i++) {        for (var j = 1; j <= i; j++) {            // 1^1*2^2*3^3....            val *= i;        }    }    // returns the hyperfactorial of a number    return val;}Â
// Driver codevar num = 5;document.write( boost_hyperfactorial(num));Â
Â
</script> |
Output:Â
86400000
Â
Time Complexity: O(N2), where N is the given number.
Auxiliary Space: O(1)
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