// Md Al Masum Bhuiyan


/*This code is for finding the value of (x + y )^n using
the binomial coeffecient (for any positive integer n) */






#include<iostream>
#include <cmath>
using namespace std ;


int facto (int num ) // factorial function

{
    int i =1, fact;
    fact = i;
    
    while(i<=num)
    {
        fact=fact*i; // the definition of factorial
        i++;
    }
    return fact ;
}

int binom (int num, int num1) //  Binomial function
{
    float bin;
    int x = facto(num); // calling factorial function
    int y = facto(num1);
    int z = facto(num-num1);
    
    bin=  x/(y * z); // The Binomial coeffecient

return bin;
}

int main()
{
    int n,i;
    double x,y;
    double sum =0;
    double rslt = 0;

        cout << "Enter the number of n : " << endl;
        cin >> n;
        cout << "Enter the number of x : " << endl;
        cin >> x;
        cout << "Enter the number of y : " << endl;
        cin >> y;
    
    while (( x == 0 && y == 0 && n == 0 ) || (n < 0)) // invalid input
    {
        cout << "Invalid input. Please try again. \n ";
        cout << "Enter the number of n : " << endl;
        cin >> n;
        cout << "Enter the number of x : " << endl;
        cin >> x;
        cout << "Enter the number of y : " << endl;
        cin >> y;
    }

    for (i=0; i<=n; i++)
    {
        rslt = binom(n,i) * pow(x,(n-i)) * pow(y,i); //  The Binomial theorem
        sum = sum + rslt;
    }
    cout << " By the binomial theorem, the result of (x+y)^n is : " << sum << endl; // Final result
    return 0;
    
}