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.
#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;
}
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.
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));
}
}
// 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)
# 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++ 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 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# 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.
<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>
# 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.
