Recursive Function

Question

Given the following recursive function:

// Pre-condition: y is non-negative.
int mysterious(int x, int y) {
    if (y == 0) return x;
    return 2*mysterious(x, y-1);
}

What is the return value of mysterious(3, 2)?

Here is my call stack:

return 2*mysterious(3, 2-1) => 2*3 => 6, 2*1 => mysterious(6,2)
return 2*mysterious(6, 2-1) => 6*2 => 12, 2*2 => mysterious(12, 2)

But it seems like y will never reach 0. What am I doing wrong?

Answer 1

mysterious(3, 2)

= 2 * mysterious(3, 1)
= 2 * 2 * mysterious(3, 0)
= 2 * 2 * 3
= 12

Answer 2

if you expand that call you effectively have

(2*(2*(3))) == 12

Y only ever decreases (by 1 each call) so the function is clearly recursive and should terminate for y>=0

Answer 3

Each time mysterious is called (once by you, twice by recursion), y is decremented by 1.

So, you get (in mysterious)

3 2
3 1
3 0

the final value is 12 (3*2*2)

Answer 4

mysterious(3, 2)
    y(==2) is not 0 therefore it 
    returns 2 * mysterious(3, 1)
        mysterious(3,1)
            y(==1) is not 0 so it 
            returns 2 * mysterious(3 , 0)
                mysterious(3 , 0) 
                    return 3 because y == 0
            2 * 3 = 6
    2 * 6 = 12

x is never modified, but with each recursive call y is reduced by one and when reaches the ground clause ( if y == 0 ) it returns x (which from the first call is 3)

Answer 5

It's nothing else than

x * 2**y

or

mysterious(x, y) == x*pow(2, y)

so it could be very well defined for any value of y