/**********************************************************************
* Section : 15
* Machine No. : N
* Roll No. : 18CS100XY
* Name : Soumyajit Dey, Aritra Hazra
* Assignment No : 5a
* Description : Find Binomial Sum using Expansions of Binomial Theorem
**********************************************************************/

#include <stdio.h>

/* calculates m^p */
double power(float m, int p)
{
    double result;
    if (p == 0)
        result = 1.0;
    else if (p == 1)
        return result = m;
    else
    {
        if(p%2)
        {
            result = power(m, p/2);
            result = result * result * m;
        }
        else
        {
            result = power(m, p/2);
            result = result * result;
        }
    }
    return result;
}

/* calculates num! */
long int factorial(int num)
{
    long int fact = 1;
    while(num > 0)
    {
        fact = fact * num;
        num = num - 1;
    }
    return fact;
}

/* calculates nCr = (n!) / (r!(n-r)!) */
long int find_ncr(int n, int r)
{
    return ( factorial(n) / (factorial(r) * factorial(n-r)) );
}

/* calculates the Binomial sum using Binomial Theorem as follows:
(x+y)^n = nC0.x^n.y^0 + ... + nCi.x^(n-i).y^i + ... + nCn.x^0.y^n */
double find_binomial_sum(float x, float y, int n)
{
    int i;
    double sum = 0.0;
    for(i=0; i<=n; ++i)
    {
        sum = sum + find_ncr(n,i) * power(x,n-i) * power(y,i);
    }
    return sum;
}

int main()
{
    float x, y;
    int n;
    
    /* reads user inputs */
    printf("Enter Real x: ");
    scanf("%f", &x);
    printf("Enter Real y: ");
    scanf("%f", &y);
    printf("Enter Integer Exponent (n >= 0): ");
    scanf("%d", &n);
    
    /* displays the Binomial Sum */
    printf("The Binomial Sum: (%f + %f)^%d = %lf\n", x, y, n, find_binomial_sum(x,y,n));

    return 0;
}