#include <iostream>
using namespace std;

// (2) Write a function called sum_m_to_n() that returns
//     the sum of integers from m to n.
int sum_m_to_n( int m, int n )
{
    int sum = 0;
    for ( int i = m ; i <= n ; i++ )
    {
        sum += i;
    }
    return sum;
}

// (1) Write a function called sum_1_to_n() that returns
//     the sum of integers from 1 to the given value n.
int sum_1_to_n( int n )
{
    // just call the function above!
    return sum_m_to_n( 1, n );
#if 0
    int sum = 0;
    for ( int i = 1 ; i <= n ; i++ )
    {
        sum += i;
    }
    return sum;
#endif
}

// (3) Write a function called m_to_the_n() that returns
//     the value m raised to the nth power.  Do NOT
//     use the pow() function -- write your own!
double m_to_the_n( double m, int n )
{
    double answer = 1;
    for ( int i = 0 ; i < n ; i++ )
    {
        answer *= m;   // m * m * m * ...
    }
    return answer;
}

// (4) Write a function called factorial() that returns
//     the factorial n! of given integer value n.
//        (n! is n * (n-1) * (n-2) * ... * 1)
int factorial( int n )
{
    int answer = 1;
    for ( int i = n ; i >= 1 ; i-- )
    {
        answer *= i;
    }
    return answer;
}

int factorial_using_recursion( int n )
{
    if ( n == 0 )
    {
        return 1;
    }
    else   // n > 0
    {
        return n * factorial_using_recursion( n - 1 );
    }
}


int main()
{
    // test the factorial function:
    int x = 6;
    int result = factorial_using_recursion( x );
    cout << x << "! is " << result << endl;


    // test function (2):
    int m = 3, n = 6;
    int sum = sum_m_to_n( m, n );
    cout << "Sum of " << m << " to " << n
         << " is " << sum << endl;

    return 0;
}