Recursive Program to find Factorial of a large number

Given a large number N, the task is to find the factorial of N using recursion.

Factorial of a non-negative integer is the multiplication of all integers smaller than or equal to n. For example factorial of 6 is 6*5*4*3*2*1 which is 720.

Examples:

Input : N = 100
Output : 933262154439441526816992388562667004-907159682643816214685929638952175999-932299156089414639761565182862536979-208272237582511852109168640000000000-00000000000000

Input : N = 50
Output : 3041409320171337804361260816606476884-4377641568960512000000000000

Iterative Approach: The iterative approach is discussed in Set 1 of this article. Here, we have discussed the recursive approach.

Recursive Approach: To solve this problem recursively, the algorithm changes in the way that calls the same function recursively and multiplies the result by the number n. Follow the steps below to solve the problem:

• If n is less than equal to 2, then multiply n by 1 and store the result in a vector.
• Otherwise, call the function multiply(n, factorialRecursiveAlgorithm(n – 1)) to find the answer.

Below is the implementation of the above approach.

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// MUltiply the number x with the number
// represented by res array
vector<int> multiply(long int n, vector<int> digits)
{

    // Initialize carry
    long int carry = 0;

    // One by one multiply n with
    // individual digits of res[]
    for (long int i = 0; i < digits.size(); i++) {
        long int result
          = digits[i] * n + carry;

        // Store last digit of 'prod' in res[]
        digits[i] = result % 10;

        // Put rest in carry
        carry = result / 10;
    }

    // Put carry in res and increase result size
    while (carry) {
        digits.push_back(carry % 10);
        carry = carry / 10;
    }

    return digits;
}

// Function to recursively calculate the
// factorial of a large number
vector<int> factorialRecursiveAlgorithm(
  long int n)
{
    if (n <= 2) {
        return multiply(n, { 1 });
    }

    return multiply(
      n, factorialRecursiveAlgorithm(n - 1));
}

// Driver Code
int main()
{
    long int n = 50;

    vector<int> result
      = factorialRecursiveAlgorithm(n);

    for (long int i = result.size() - 1; i >= 0; i--) {
        cout << result[i];
    }

    cout << "\n";

    return 0;
}

Java

// Java program for the above approach
import java.util.*;
class GFG{

// MUltiply the number x with the number
// represented by res array
static Integer []multiply(int n, Integer []digits)
{

    // Initialize carry
    int carry = 0;

    // One by one multiply n with
    // individual digits of res[]
    for (int i = 0; i < digits.length; i++) {
        int result
          = digits[i] * n + carry;

        // Store last digit of 'prod' in res[]
        digits[i] = result % 10;

        // Put rest in carry
        carry = result / 10;
    }

    // Put carry in res and increase result size
    LinkedList<Integer> v = new LinkedList<Integer>();
    v.addAll(Arrays.asList(digits));
    while (carry>0) {
        v.add(new Integer(carry % 10));
        carry = carry / 10;
    }

    return v.stream().toArray(Integer[] ::new);
}

// Function to recursively calculate the
// factorial of a large number
static Integer []factorialRecursiveAlgorithm(
  int n)
{
    if (n <= 2) {
        return multiply(n, new Integer[]{ 1 });
    }

    return multiply(
      n, factorialRecursiveAlgorithm(n - 1));
}

// Driver Code
public static void main(String[] args)
{
    int n = 50;

    Integer []result
      = factorialRecursiveAlgorithm(n);

    for (int i = result.length - 1; i >= 0; i--) {
        System.out.print(result[i]);
    }

    System.out.print("\n");

}
}

// This code is contributed by 29AjayKumar

C#

// C# program for the above approach
using System;
using System.Collections.Generic;
using System.Linq;
class GFG
{

    // MUltiply the number x with the number
    // represented by res array
    static int[] multiply(int n, int[] digits)
    {

        // Initialize carry
        int carry = 0;

        // One by one multiply n with
        // individual digits of res[]
        for (int i = 0; i < digits.Length; i++)
        {
            int result
              = digits[i] * n + carry;

            // Store last digit of 'prod' in res[]
            digits[i] = result % 10;

            // Put rest in carry
            carry = result / 10;
        }

        // Put carry in res and increase result size
        LinkedList<int> v = new LinkedList<int>();
        foreach (int i in digits)
        {
            v.AddLast(i);
        }
        while (carry > 0)
        {
            v.AddLast((int)(carry % 10));
            carry = carry / 10;
        }

        return v.ToArray();
    }

    // Function to recursively calculate the
    // factorial of a large number
    static int[] factorialRecursiveAlgorithm(
      int n)
    {
        if (n <= 2)
        {
            return multiply(n, new int[] { 1 });
        }

        return multiply(
          n, factorialRecursiveAlgorithm(n - 1));
    }

    // Driver Code
    public static void Main()
    {
        int n = 50;
        int[] result = factorialRecursiveAlgorithm(n);
        for (int i = result.Length - 1; i >= 0; i--)
        {
            Console.Write(result[i]);
        }

        Console.Write("\n");

    }
}

// This code is contributed by gfgking

Python3

# Python 3 program for the above approach

# MUltiply the number x with the number
# represented by res array


def multiply(n, digits):

    # Initialize carry
    carry = 0

    # One by one multiply n with
    # individual digits of res[]
    for i in range(len(digits)):
        result = digits[i] * n + carry

        # Store last digit of 'prod' in res[]
        digits[i] = result % 10

        # Put rest in carry
        carry = result // 10

    # Put carry in res and increase result size
    while (carry):
        digits.append(carry % 10)
        carry = carry // 10

    return digits


# Function to recursively calculate the
# factorial of a large number
def factorialRecursiveAlgorithm(n):
    if (n <= 2):
        return multiply(n, [1])

    return multiply(
        n, factorialRecursiveAlgorithm(n - 1))


# Driver Code
if __name__ == "__main__":

    n = 50

    result = factorialRecursiveAlgorithm(n)

    for i in range(len(result) - 1, -1, -1):
        print(result[i], end="")

Javascript

<script>
// javascript program for the above approach
// MUltiply the number x with the number
// represented by res array
function multiply(n, digits)
{

    // Initialize carry
    var carry = 0;

    // One by one multiply n with
    // individual digits of res
    for (var i = 0; i < digits.length; i++) {
        var result
          = digits[i] * n + carry;

        // Store last digit of 'prod' in res
        digits[i] = result % 10;

        // Put rest in carry
        carry = parseInt(result / 10);
    }

    // Put carry in res and increase result size
    while (carry>0) {
        digits.push(carry % 10);
        carry = parseInt(carry / 10);
    }

    return digits;
}

// Function to recursively calculate the
// factorial of a large number
function factorialRecursiveAlgorithm(
  n)
{
    if (n <= 2) {
        return multiply(n, [ 1 ]);
    }

    return multiply(
      n, factorialRecursiveAlgorithm(n - 1));
}

// Driver Code
    var n = 50;

    var result = factorialRecursiveAlgorithm(n);

    for (var i = result.length - 1; i >= 0; i--) {
        document.write(result[i]);
    }

    document.write("<br>");

// This code is contributed by shikhasingrajput
</script>

Output

30414093201713378043612608166064768844377641568960512000000000000

Time Complexity: O(n*log(n))
Auxiliary Space: O(K), where K is the maximum number of digits in the output