一个数的超数
原文:https://www.geeksforgeeks.org/hyperfactorial-of-a-number/
给定一个数，任务是找到一个数的超导数。 给定数量的从 1 到给定数量的连续整数相乘的结果，每个整数的幂都被称为一个数的超工厂。
H(n)= 1 ^ 1 * 2 ^ 2 * 3 ^ 3 * . . . . . * n ^ n
示例:
输入:2 T3】输出: 4
输入: 4 输出:27648 h(4)= 1^1 * 2^2 * 3^3 * 4^4 = 27648
一种简单的方法是使用两个循环，一个寻找 i^i 的和，另一个寻找 i^i.，但是时间复杂度是 O(n)。 一种高效的方法是使用内置的 pow() 函数或 O(log n)方法找到 i^i，然后添加它。 以下是上述办法的实施情况。
C++
/// 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;
}
Java 语言(一种计算机语言，尤用于创建网站)
// 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
Python 3
# 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
C
// 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
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?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)
?>
java 描述语言
<script>
// Javascript program to find the
// hyperfactorial of a number
// function to calculate the
// value of hyperfactorial
function 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;
}
// Driver code
let num = 5;
document.write(boost_hyperfactorial(num));
// This code is contributed
// by gfgking
</script>
Output:
86400000
时间复杂度: O(N * log N) 由于数字的超阶乘可能很大，因此数字会溢出。我们可以用 C++中的 boost 库或者 Java 中的big integer来存储一个数 n 的超阶乘。
C++
// 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;
}
Java 语言(一种计算机语言，尤用于创建网站)
// 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
Python 3
# 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
C
// 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
服务器端编程语言（Professional Hypertext Preprocessor 的缩写）
<?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
?>
java 描述语言
<script>
// Javascript 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
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;
}
// Driver code
var num = 5;
document.write( boost_hyperfactorial(num));
</script>
Output:
86400000
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