/* Homwork two:(Binomial Theorem)
Bethuel Khamala
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.

Solution:
The loop below calculates the binomial coefficients of two numbers i.e, num_1 and num_2.
 */
#include<iostream>
#include <cmath>
using namespace std ;


unsigned int factorial ( unsigned int num )

{
  int i =1, fact;
  fact =i ;
  
 
  while(i<=num)
    {
      fact=fact*i;
      i++;
    }

  return fact ;
 
}




int main()
{

  cout << "Hello this program is a work in progress. The goal is to verify the binomial theorem." << endl ;
  cout << "We break this into a series of subtasks namely compute the binomial coefficients then multiply with the numbers."<<endl; 
  unsigned int num =0 ;
  unsigned int num_1,num_2 ;

  //calculating the bino expansion of two integers
  cout << "Enter the two numbers whose binomial coeff we desire:" << endl;
  cin>>num_1;
  cin>>num_2;
  cout << "You entered the first no. as  "<< num_1 << " and second number as "<<num_2<<endl;
 //double x,y ;
 //unsigned int n ;
 //double sum = pow(x+y,n);
  double bino_coeff = factorial(num_1)/(factorial(num_1-num_2)*factorial(num_2));
  cout << "Bino coeff=" << bino_coeff << endl;
  return 0;
}