#include <stdio.h>
#include <cs50.h>
// Global Variables can be invoked by any function 
int steps = 0;

// Prototypes 
int fact(int n); 
void collatz (int n);

int main(void) 
{ 
	// Fact 
    int x = get_int("Fact of "); 
    printf("fact of %i equals %i\n", x, fact(x));
    
    // Collatz
    int y = get_int("Collatz of ");
    collatz(y); // counts steps
    printf("Collatz steps of %i: %i\n", y, steps);
}

// instead of a for loop 
int fact(int n) // works thanks to the execution stack 
{ 
    // base case 
    if (n == 1) return 1; // last tab

    // recursive case
    else
    {
        return n * fact(n - 1); // close current tab but open a new one
    }
} // in this function you accumulate the closed tabs, for instance, 3 * 2 * 1

void collatz (int n) // for counting number of steps 
{ 
    if (n < 1) 
    { 
        printf("Error: y must be bigger than zero\n"); 
        return; // error 
    } 
    if (n == 1) // zero steps 
    { 
        return; // close tab 
    } 
    else if (n % 2 == 0) // remainder of n divided by 2 
    { 
        steps++; // add a step 
        collatz(n / 2); // open a simple tab 
    } 
    else 
    { 
        steps++; // add a step 
        collatz (3 * n + 1); // open an advanced tab 
    } 
    return; // close simple or advanced tab 
}