N的指数阶乘

给定一个正整数N ，任务是打印N的指数阶乘。由于输出可能非常大，请打印答案模数1000000007 。

例子：

Input: N = 4  
Output: 262144   

Input: N = 3  
Output: 9  

方法：可以根据以下观察解决给定的问题：

The exponential factorial is defined by the recurrence relation:

• $a_n=n^{a_{n-1}}$.

请按照以下步骤解决问题：

• 初始化一个变量res为1以存储N的指数阶乘。
• 使用变量i在范围[2, N]上进行迭代，并在每次迭代中将res更新为res = i ^res %1000000007。
• 最后，完成上述步骤后，打印res中得到的答案。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to find exponential factorial
// of a given number
int ExpoFactorial(int N)
{
   
    // Stores the exponential factor of N
    int res = 1;
    int mod = 1000000007;
 
    // Iterate over the range [2, N]
    for (int i = 2; i < N + 1; i++)
       
        // Update res
        res = (int)pow(i, res) % mod;
 
    // Return res
    return res;
}
 
// Driver Code
int main()
{
    // Input
    int N = 4;
   
    // Function call
    cout << (ExpoFactorial(N));
   
   // This code is contributed by Potta Lokesh
    return 0;
}
 
// This code is contributed by lokesh potta

Java

// Java program for the above approach
class GFG{
     
// Function to find exponential factorial
// of a given number
static int ExpoFactorial(int N)
{
     
    // Stores the exponential factor of N
    int res = 1;
    int mod = 1000000007;
 
    // Iterate over the range [2, N]
    for(int i = 2; i < N + 1; i++)
     
        // Update res
        res = (int)Math.pow(i, res) % mod;
 
    // Return res
    return res;
}
 
// Driver code
public static void main(String[] args)
{
     
    // Input
    int N = 4;
 
    // Function call
    System.out.println((ExpoFactorial(N)));
}
}
 
// This code is contributed by abhinavjain194

Python3

# Python3 program for the above approach
 
# Function to find exponential factorial
# of a given number
 
 
def ExpoFactorial(N):
    # Stores the exponential factor of N
    res = 1
    mod = (int)(1000000007)
 
    # Iterate over the range [2, N]
    for i in range(2, N + 1):
        # Update res
        res = pow(i, res, mod)
 
    # Return res
    return res
 
 
# Driver Code
 
# Input
N = 4
# Function call
print(ExpoFactorial(N))

C#

// C# program for the above approach
using System;
 
class GFG{
 
// Function to find exponential factorial
// of a given number
static int ExpoFactorial(int N)
{
     
    // Stores the exponential factor of N
    int res = 1;
    int mod = 1000000007;
 
    // Iterate over the range [2, N]
    for(int i = 2; i < N + 1; i++)
     
        // Update res
        res = (int)Math.Pow(i, res) % mod;
 
    // Return res
    return res;
}
 
// Driver Code
public static void Main()
{
    // Input
    int N = 4;
 
    // Function call
    Console.Write(ExpoFactorial(N));
 
}
}
 
// This code is contributed by sanjoy_62.

Javascript

 
// JavaScript program for the above approach
 
 
// Function to find exponential factorial
// of a given number
function ExpoFactorial(N) {
 
    // Stores the exponential factor of N
    let res = 1;
    let mod = 1000000007;
 
    // Iterate over the range [2, N]
    for (let i = 2; i < N + 1; i++)
 
        // Update res
        res = Math.pow(i, res) % mod;
 
    // Return res
    return res;
}
 
// Driver Code
 
// Input
let N = 4;
 
// Function call
document.write((ExpoFactorial(N)));
 
// This code is contributed by _saurabh_jaiswal
 

输出

262144

时间复杂度： O(N*log(N))
辅助空间： O(1)