#include <iostream>
using namespace std;

//this function will calculate base raised to the power exp, recursively
//in our example, base = 2, exp = 4, 2 raised to exp 4 = 16
int pow(int base, int exp)
{
    //if (exp<1)
    // error!
    if(exp ==1)
        return base;
    else
        return pow(base, exp-1)*base;
}

int iterativePow(int base, int exp)
{
    int answer=1;
    for(int i = 1; i <= exp; i++)
    {
        answer *= base;
    }
    return answer;
}


int factorial(int n)
{
    //error if n<0
    //base case:
    if (n == 0 )
        return 1;
    else
        return n * factorial(n-1);

}

int fibonacci(int n)
{
    if(n==0) //base case
        return 0;
    else if (n==1) //base case
        return 1;
    else
        return fibonacci(n-1)+fibonacci(n-2);
}

//answer to exercise 5 in book
//recursive multiplication
int mult(int x, int y)
{
    //problem:  if x < 1
    //base case
    if (x==1)
        return y;
    else
        return y + mult(x-1, y);
}

int main()
{
    int ans=pow(2, 4);
    cout<<"2 raised to the power of 4 = " << ans<<" (recursively)"<<endl;

    ans = iterativePow(2, 4);
    cout<<"2 raised to the power of 4 = " << ans<<" (iteratively)"<<endl<<endl;

    ans = pow(2, 20);
    cout<<"2 raised to the power of 20 = " << ans<<endl<<endl;


    ans = fibonacci(7);
    cout<<"7th fibonacci number = "<< ans<<endl;

    ans = fibonacci(15);
    cout<<"15th fibonacci number = "<< ans<<endl<<endl;

    ans =mult(7, 4);
    cout<<"7 * 4 = "<< ans<<endl<<endl;

    ans =mult(4, 7);
    cout<<"4 * 7 = "<< ans<<endl<<endl;


    ans =mult(7, 0);
    cout<<"7 * 0 = "<< ans<<endl<<endl;

}