/* Homwork two:(Binomial Theorem)
We know (x+y)^3 = x^3 + 3xy^2 + 3 x^2y + y^3
Now, we want this to be verified via a simple program which takes in two numbers x and y and an exponent say n.
Then returns (x+y)^n. 
Next, we want a loop which calculates the binomial rule for this i.e., we want x^n + n xy^(n-1) + ...
Need the task for calculating the binomial coefficients first.
for which, we need the factorial of a whole number set up right.
 */
#include<iostream>
#include <cmath>
using namespace std ;


unsigned int factorial ( unsigned int num )

{
  int i =1, fact;
  //fact =i ;

  while(i <= num)
    {
	
  cout << "Iteration number " << i << endl;
	if (i ==1)
         {  fact = 1 ; //initialization
	 cout << "We are on iteration number = "<< i << endl; 
 	}
	
      fact=fact*i;
      i++;
    }

 return fact ;	
 
}


int main()
{

  cout << "Hi!" << endl ; 
  unsigned int num = 1;

  //Input the number and save it.
  cout<<"Enter the no."<<endl;
  cin>> num;
  cout << "You typed "<< num << endl;

  //Calculate the factorial using loop
  cout << "the factorial is: "<< factorial(num)<< endl;

  return 0;
}