#include <iostream>

/***************************************************
 * Problem:
 *
 * This program calculates the binomial coefficient
 *
 *                  n!
 *     n choose k = -----------.
 *                 k!(n - k)!
 *
 * Unfortunately, the program does not work correctly
 * for some values of 'n' and 'k'. For example,
 *
 *     13 choose 1
 *
 * should equal 13, but this program produces an
 * incorrect result.
 *
 * One approach to debugging is to add logging
 * statements that display intermediate values as
 * the program executes.
 *
 * C++ provides std::clog for diagnostic information.
 * This is useful because it distinguishes logging
 * from the normal output of the program:
 *
 *     std::cout   normal program output
 *     std::clog   diagnostic or logging output
 *     std::cerr   error messages
 *
 * For example, you could add
 *
 *     std::clog << "n = " << n << std::endl;
 *
 * to see the value of 'n' at a particular point in
 * the execution.
 *
 * Add logging statements to this program to determine
 * why it produces the wrong answer for some inputs.
 *
 * Consider logging:
 *
 *     1. the arguments passed to factorial(...),
 *     2. the value of 'result' during each iteration,
 *     3. the three factorials calculated in main().
 *
 * You do not have to fix the problem. Your goal is
 * to use logging to determine where the calculation
 * first goes wrong.
 ***************************************************/

// Function declarations
int main();
int factorial( int n );

// Function definitions
int main() {
    int n{};

    std::cout << "Enter a non-negative integer: ";
    std::cin  >> n;

    int k{};

    std::cout << "Enter another non-negative integer: ";
    std::cin  >> k;

    if ( (n < 0) || (k < 0) || (k > n) ) {
        return 0;
    }

    std::clog << "Calculating "
              << n << " choose " << k << std::endl;

    int nf{ factorial( n ) };
    int kf{ factorial( k ) };
    int nkf{ factorial( n - k ) };

    std::clog << "n!       = " << nf << std::endl;
    std::clog << "k!       = " << kf << std::endl;
    std::clog << "(n - k)! = " << nkf << std::endl;

    std::cout << n << " choose " << k
              << " = " << nf/kf/nkf << std::endl;

    return 0;
}

int factorial( int n ) {
    std::clog << "factorial(" << n << ")" << std::endl;

    int result{ 1 };

    for ( int k{ 1 }; k <= n; ++k ) {
        result *= k;

        std::clog << "    k = " << k
                  << ", result = " << result
                  << std::endl;
    }

    return result;
}