求阶乘之和，直到 N 阶乘 (1! + 2! + 3! + ... + N!)

给定一个正整数N 。任务是从 1 计算阶乘之和！到 N!, 1! + 2！ + 3！ + ... + N！ .

例子：

Input: N = 5
Output: 153
Explanation: 1! + 2! + 3! + 4! + 5! = 1 + 2 + 6 + 24 + 120 = 153.

Input: N = 1
Output: 1

朴素方法：解决这个问题的基本方法是找到所有数字的阶乘，直到 1 到 N 并计算它们的总和。
时间复杂度：O(N^2)
辅助空间：O(1)

方法：一种有效的方法是在同一循环中计算阶乘和求和，使时间为 O(N)。遍历从 1 到 N 的数字，对于每个数字 i：

• 将 i 与先前的阶乘（最初为 1）相乘。
• 将此新阶乘添加到集体总和中

最后，打印这个集体总和。

下面是上述方法的实现。

C++

// C++ program to compute sum of series
// 1! + 2! + 3! + ... + N!
#include 
using namespace std;
  
// Function to return sum
// of 1!, 2! upto N!
int findFactSum(int N)
{
    // Initializing the variables
    int f = 1, Sum = 0;
  
    // Calculate the factorial and sum
    // in the same loop
    for (int i = 1; i <= N; i++) {
  
        f = f * i;
        Sum += f;
    }
  
    // Return Sum as the final result.
    return Sum;
}
  
// Driver Code
int main()
{
    int N = 5;
  
    // Function call
    cout << findFactSum(N);
  
    return 0;
}

Java

// Java code to implement above approach
class GFG {
  
    // Function to return sum
    // of 1!, 2! upto N!
    static int findFactSum(int N)
    {
  
        // Initializing the variables
        int f = 1, Sum = 0;
  
        // Calculate the factorial and sum
        // in the same loop
        for (int i = 1; i <= N; i++) {
  
            f = f * i;
            Sum += f;
        }
  
        // Return Sum as the final result.
        return Sum;
    }
  
    // Driver code
    public static void main(String[] args)
    {
        int N = 5;
        System.out.print(findFactSum(N));
    }
}
  
// This code is contributed ukasp.

Python3

# python program to compute sum of series
# 1! + 2! + 3! + ... + N!
  
# Function to return sum
# of 1!, 2! upto N!
def findFactSum(N):
  
    # Initializing the variables
    f = 1
    Sum = 0
  
    # Calculate the factorial and sum
    # in the same loop
    for i in range(1, N + 1):
        f = f * i
        Sum += f
  
    # Return Sum as the final result.
    return Sum
  
# Driver Code
if __name__ == "__main__":
    N = 5
  
    # Function call
    print(findFactSum(N))
  
    # This code is contributed by rakeshsahni

C#

// C# code to implement above approach
using System;
class GFG
{
  
  // Function to return sum
  // of 1!, 2! upto N!
  static int findFactSum(int N)
  {
  
    // Initializing the variables
    int f = 1, Sum = 0;
  
    // Calculate the factorial and sum
    // in the same loop
    for (int i = 1; i <= N; i++) {
  
      f = f * i;
      Sum += f;
    }
  
    // Return Sum as the final result.
    return Sum;
  }
  
  // Driver code
  public static void Main()
  {
    int N = 5;
    Console.Write(findFactSum(N));
  
  }
}
  
// This code is contributed by Samim Hossain Mondal.

Javascript

    // JavaScript code for the above approach
  
    // Function to return sum
    // of 1!, 2! upto N!
    function findFactSum(N)
    {
      
      // Initializing the variables
      let f = 1, Sum = 0;
  
      // Calculate the factorial and sum
      // in the same loop
      for (let i = 1; i <= N; i++) {
  
        f = f * i;
        Sum += f;
      }
  
      // Return Sum as the final result.
      return Sum;
    }
  
    // Driver Code
    let N = 5;
  
    // Function call
    document.write(findFactSum(N));
  
  // This code is contributed by Potta Lokesh
  

输出：

153

时间复杂度：O(N)
辅助空间：O(1)