Find sum of factorials till N factorial (1! + 2! + 3! + … + N!)
Given a positive integer N. The task is to compute the sum of factorial from 1! to N!, 1! + 2! + 3! + … + N!.
Examples:
Input: N = 5
Output: 153
Explanation: 1! + 2! + 3! + 4! + 5! = 1 + 2 + 6 + 24 + 120 = 153.Input: N = 1
Output: 1
Naive Approach: The basic way to solve this problem is to find the factorial of all numbers till 1 to N and calculate their sum.
C++
#include<bits/stdc++.h> using namespace std; // Function to find the factorial of a number int findFact( int num) { // Base case: 0! and 1! are both 1 if (num == 0 || num == 1) return 1; // Initialize result to 1 and multiply by each number from 2 to num long long result = 1; for ( int i = 2; i <= num; i++) { result *= i; } // Return the factorial result return result; } // Function to find the sum of factorials from 1! to N! int findFactSum( int N) { // Initialize sum to 0 int sum = 0; // Iterate from 1 to N and add the factorial of each number to the sum for ( int i = 1; i <= N; i++) { sum += findFact(i); } // Return the sum of factorials return sum; } int main() { // Example usage with N = 5 int N = 5; // Display the sum of factorials from 1! to N! cout << findFactSum(N) << endl; return 0; } |
Java
public class Main { // Function to find the factorial of a number public static long findFact( int num) { // Base case: 0! and 1! are both 1 if (num == 0 || num == 1 ) return 1 ; // Initialize result to 1 and multiply by each number from 2 to num long result = 1 ; for ( int i = 2 ; i <= num; i++) { result *= i; } // Return the factorial result return result; } // Function to find the sum of factorials from 1! to N! public static long findFactSum( int N) { // Initialize sum to 0 long sum = 0 ; // Iterate from 1 to N and add the factorial of each number to the sum for ( int i = 1 ; i <= N; i++) { sum += findFact(i); } // Return the sum of factorials return sum; } public static void main(String[] args) { // Example usage with N = 5 int N = 5 ; // Display the sum of factorials from 1! to N! System.out.println(findFactSum(N)); } } //This code is contributed by Monu. |
C#
using System; class Program { // Function to find the factorial of a number static long FindFact( int num) { // Base case: 0! and 1! are both 1 if (num == 0 || num == 1) return 1; // Initialize result to 1 and multiply by each number from 2 to num long result = 1; for ( int i = 2; i <= num; i++) { result *= i; } // Return the factorial result return result; } // Function to find the sum of factorials from 1! to N! static long FindFactSum( int N) { // Initialize sum to 0 long sum = 0; // Iterate from 1 to N and add the factorial of each number to the sum for ( int i = 1; i <= N; i++) { sum += FindFact(i); } // Return the sum of factorials return sum; } static void Main( string [] args) { // Example usage with N = 5 int N = 5; // Display the sum of factorials from 1! to N! Console.WriteLine(FindFactSum(N)); } } |
Javascript
// Function to find the factorial of a number function findFact(num) { // Base case: 0! and 1! are both 1 if (num === 0 || num === 1) return 1; // Initialize result to 1 and multiply by each number from 2 to num let result = 1; for (let i = 2; i <= num; i++) { result *= i; } // Return the factorial result return result; } // Function to find the sum of factorials from 1! to N! function findFactSum(N) { // Initialize sum to 0 let sum = 0; // Iterate from 1 to N and add the factorial of each number to the sum for (let i = 1; i <= N; i++) { sum += findFact(i); } // Return the sum of factorials return sum; } // Main function to test above function // Example usage with N = 5 let N = 5; // Display the sum of factorials from 1! to N! console.log(findFactSum(N)); // This Code is contributed by Yash Agarwal(yashagarwal2852002) |
Python3
# Python code # Function to find the factorial of a number def find_fact(num): # Base case: 0! and 1! are both 1 if num = = 0 or num = = 1 : return 1 # Initialize result to 1 and multiply by each number from 2 to num result = 1 for i in range ( 2 , num + 1 ): result * = i # Return the factorial result return result # Function to find the sum of factorials from 1! to N! def find_fact_sum(N): # Initialize sum to 0 sum_result = 0 # Iterate from 1 to N and add the factorial of each number to the sum for i in range ( 1 , N + 1 ): sum_result + = find_fact(i) # Return the sum of factorials return sum_result # Example usage with N = 5 N = 5 # Display the sum of factorials from 1! to N! print (find_fact_sum(N)) # This code is contributed by shivamgupta310570 |
Output
153
Time Complexity: O(N^2)
Auxiliary Space: O(1)
Approach: An efficient approach is to calculate factorial and sum in the same loop making the time O(N). Traverse the numbers from 1 to N and for each number i:
- Multiply i with previous factorial (initially 1).
- Add this new factorial to a collective sum
At the end, print this collective sum. Below is the implementation of the above approach.
C++
// C++ program to compute sum of series // 1! + 2! + 3! + ... + N! #include <iostream> 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. |
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
<script> // 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 </script> |
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 |
Output
153
Time Complexity: O(N)
Auxiliary Space: O(1), since no extra space has been taken.
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