How does the recursion here work?

Question

Code 1:

public static int fibonacci (int n){ 
    if (n == 0 || n == 1) { 
        return 1; 
    } else { 
        return fibonacci (n-1) + fibonacci (n-2)         


        

Answer 1

I'll explain what your PC is doing when executing that piece of code with an example:

Imagine you're standing in a very big room. In the room next to this room you have massive amounts of paper, pens and tables. Now we're going to calculate fibonacci(3):

We take a table and put it somewhere in the room. On the table we place a paper and we write "n=3" on it. We then ask ourselves "hmm, is 3 equal to 0 or 1?". The answer is no, so we will do "return fibonacci (n-1) + fibonacci (n-2);".

There's a problem however, we have no idea what "fibonacci (n-1)" and "fibonacci (n-2)" actually do. Hence, we take two more tables and place them to the left and right of our original table with a paper on both of them, saying "n=2" and "n=1".

We start with the left table, and wonder "is 2 equal to 0 or 1?". Of course, the answer is no, so we will once again place two tables next to this table, with "n=1" and "n=0" on them.

Still following? This is what the room looks like:

n=1

n=2 n=3 n=1

n=0

We start with the table with "n=1", and hey, 1 is equal to 1, so we can actually return something useful! We write "1" on another paper and go back to the table with "n=2" on it. We place the paper on the table and go to the other table, because we still don't know what we're going to do with that other table.

"n=0" of course returns 1 as well, so we write that on a paper, go back to the n=2 table and put the paper there. At this point, there are two papers on this table with the return values of the tables with "n=1" and "n=0" on them, so we can compute that the result of this method call is actually 2, so we write it on a paper and put it on the table with "n=3" on it.

We then go to the table with "n=1" on it all the way to the right, and we can immediately write 1 on a paper and put it back on the table with "n=3" on it. After that, we finally have enough information to say that fibonacci(3) returns 3.

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It's important to know that the code you are writing is nothing more than a recipe. All the compiler does is transform that recipe in another recipe your PC can understand. If the code is completely bogus, like this:

    public static int NotUseful()
    {
        return NotUseful();
    }

will simply loop endlessly, or as in my example, you'll keep on placing more and more tables without actually getting anywhere useful. Your compiler doesn't care what fibonacci(n-1) or fibonacci(n-2) actually do.