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Factorial Program in C++

C++ Factorial Program:

The product of all positive descending integers is the factorial of n. n! denotes the factorial of n. For instance:

5! = 5*4*3*2*1=120
4! = 4*3*2*1=24

In Combinations and Permutations, the factorial is commonly utilized (mathematics). The factorial program may be written in a variety of ways in C++. Let's look at the three different approaches to create a factorial program.

  • Looping Factorial Program
  • Recursive factorial program

Looping Factorial Program in C++:

#include <iostream> 
#include <stdlib>
#include <bits/stdc++.h> 
using namespace std;  
int main()  
{  
   int i,factorial=1,number;    
  cout<<"enter any Number: ";    
 cin>>number;    
  for(i=1;i<=number;i++){    
  factorial=factorial*i;    
  }    
  cout<<"Factorial of " <<number<<" is: "<<fact<<endl;  
  return 0;  
}  

OUTPUT:

Enter any Number: 4  
Factorial of 4 is:  24
………………………………
Process executed in 1.212 seconds
Press any key continue.

Explanation

In the above program in C++, we are iterating in for loop and signing factorial multiply by the number itself.

Let's look at a recursive factorial program in C++.

#include<iostream> 
#include<bits/stdc++.h>
#include<stdlib>   
using namespace std;      
int main()    
{    
int factorial(int);    
int fact,value;    
cout<<"enter any number: ";    
cin>>value;    
fact=factorial(value);    
cout<<"Factorial of a number is: "<<fact<<endl;    
return 0;    
}    
int factorial(int i)    
{    
if(i<0)    
return(-1); /*Wrong value*/      
if(i==0)    
return(1);  /*Terminating condition*/    
else    
{    
return(i*factorial(i-1));        
}    
}  

OUTPUT:

Enter any number: 8
Factorial of a number is: 40320
……………………………………………….
Process executed in 1.11 seconds
Press any key to continue.

Explanation

In the above program in C++, we have used a recursive version to find the factorial of the given number. In the return statement we are making call to factorial function recursively.

Using while loop for finding the factorial of a number in C++:

// C++ program for factorial of a number
#include <iostream>
#include <bits/stdc++.h>
#include <stdlib>
using namespace std; 
// function to find factorial of given
// number using while loop
unsigned int factorial(unsigned int a)
{
	if(a == 0)
		return 1;
	int x = a, fact = 1;
	while (a / x != a) {
		fact = fact * x;
		x--;
	}
	return fact;
}
// Driver code
int main()
{
	int num = 5;
	cout << "Factorial of "
		<< num << " is "
		<< factorial(num) << endl;
	return 0;
}

OUTPUT:

Factorial of 8 is 40302
………………………………...
Process Executed in 0.1212 seconds
Press nay key to continue.

Explanation

In the above program in C++, we are using loops for finding out the factorial. In the line number eleven we are using while loop for finding out the factorial.

Let us see the factorial of a large number in C++:

// C++ program to compute factorial of big numbers
#include<iostream>
#include<bits/sdtc++.h>
#include<stdlib>
using namespace std; 
// Maximum number of digits in output
#define MAX 500


int multiply(int a, int res[], int res_size); 
// This function finds factorial of large numbers
// and prints them
void factorial(int n)
{
	int res[MAX]; 
	// Initialize result
	res[0] = 1;
	int res_size = 1; 
	// Apply simple factorial formula n! = 1 * 2 * 3 * 4...*n
	for (int a=2; a<=n; a++)
		res_size = multiply(a, res, res_size); 
	cout << "Factorial of given number is \n";
	for (int b=res_size-1; b>=0; b--)
		cout << res[b];
}
// This function multiplies x with the number
// represented by res[].
// res_size is size of res[] or number of digits in the
// number represented by res[]. This function uses simple
// school mathematics for multiplication.
// This function may value of res_size and returns the
// new value of res_size
int multiply(int a, int res[], int res_size)
{
	int carry = 0; // Initialize carry
	// One by one multiply n with individual digits of res[]
	for (int b=0; b<res_size; b++)
	{
		int prod = res[b] * a + carry; 
		// Store last digit of 'prod' in res[]
		res[b] = prod % 10; 
		// Put rest in carry
		carry = prod/10;
	}
	// Put carry in res and increase result size
	while (carry)
	{
		res[res_size] = carry%10;
		carry = carry/10;
		res_size++;
	}
	return res_size;
}
// Driver program
int main()
{
	factorial(200);
	return 0;
}

OUTPUT:

Factorial of given number is
788657867364790503552363213932185062295135977687173263294742533244359449963403342920304284011984623904177212138919638830257642790242637105061926624952829931113462857270763317237396988943922445621451664240254033291864131227428294853277524242407573903240321257405579568660226031904170324062351700858796178922222789623703897374720000000000000000000000000000000000000000000000000
--------------------------------
Process exited after 0.07152 seconds with return value 0
Press any key to continue . . 

Explanation

In the above program in C++, factorial function takes n as parameter in that we are applying simple factorial formula and in the multiply function what we doing is One by one multiplying n with individual digits of res [].

Let us see another method of linked list to find the factorial:

#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = a; i <= b; i++)
using namespace std;
class Node {
public:
	int data;
	Node* prev;
	Node(int n)
	{
		data = n;
		prev = NULL;
	}
};
void Multiply(Node* tail, int n)
{
	Node *temp = tail,
		*prevNode = tail; // Temp variable for keeping tail
	int carry = 0;
	while (temp != NULL) {
		int data = temp->data * n + carry;
		temp->data = data % 10; // stores the last digit
		carry = data / 10;
		prevNode = temp;
		temp = temp->prev; // Moving temp by 1 prevNode will
						// now denote temp
	}
	// If carry is greater than 0 then we create another
	// node for it.
	while (carry != 0) {
		prevNode->prev = new Node((int)(carry % 10));
		carry /= 10;
		prevNode = prevNode->prev;
	}
}
void print(Node* tail)
{
	if (tail == NULL) // Using tail recursion
		return;
	print(tail->prev);
	cout
		<< tail->data; // Print linked list in reverse order
}
// Driver code
int main()
{
	int n = 20;
	Node tail(1); // Create a node and initialise it by 1
	rep(i, 2, n)
		Multiply(&tail, i); // Run a loop from 2 to n and
							// multiply with tail's i
	print(&tail); // Print the linked list
	cout << endl;
	return 0;
}

OUTPUT:

243290200817123640000

Explanation

In the above program in C++, we have used linked list and in the multiply function we are taking tail node pointer and size n to calculate the factorial and after that printing it back to the console.

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