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

In the case of code 2 though n will eventualy reach a point at which it doesnt satisfy n>0 and the method will stop calling itself recursivly

to make it look similar you can replace condition if (n == 0 || n == 1) with if (n < 2)

Also i don't see how the line `return fibonacci (n-1) + fibonacci (n-2) would work since fibbonacci n-2 has to contain in some sense fibonacci n-1 in order to wrok but it isn't there yet.

I suspect you wanted to write: "since fibbonacci n-1 has to contain in some sense fibonacci n-2"
If I'm right, then you will see from the example below, that actually fibonacci (n-2) will be called twice for every recursion level (fibonacci(1) in the example):
1. when executing fibonacci (n-2) on the current step
2. when executing fibonacci ((n-1)-1) on the next step

(Also take a closer look at the Spike's comment)

Suppose you call fibonacci(3), then call stack for fibonacci will be like this:
(Veer provided more detailed explanation)

n=3. fibonacci(3)  
n=3. fibonacci(2) // call to fibonacci(n-1)
   n=2. fibonacci(1) // call to fibonacci(n-1)
      n=1. returns 1
   n=2. fibonacci(0) // call to fibonacci(n-2)
      n=0. returns 1
   n=2. add up, returns 2
n=3. fibonacci(1) //call to fibonacci(n-2)
   n=1. returns 1
n=3. add up, returns 2 + 1

Note, that adding up in fibonacci(n) takes place only after all functions for smaller args return (i.e. fibonacci(n-1), fibonacci(n-2)... fibonacci(2), fibonacci(1), fibonacci(0))

To see what is going on with call stack for bigger numbers you could run this code.

public static String doIndent( int tabCount ){
    String one_tab = new String("   ");
    String result = new String("");
    for( int i=0; i < tabCount; ++i )
       result += one_tab;
    return result;
}

public static int fibonacci( int n, int recursion_level )
{
    String prefix = doIndent(recursion_level) + "n=" + n + ". ";

    if (n == 0 || n == 1){
        System.out.println( prefix + "bottommost level, returning 1" );
        return 1;
    }
    else{
        System.out.println( prefix + "left fibonacci(" + (n-1) + ")" );
        int n_1 = fibonacci( n-1, recursion_level + 1 );

        System.out.println( prefix + "right fibonacci(" + (n-2) + ")" );
        int n_2 = fibonacci( n-2, recursion_level + 1 );

        System.out.println( prefix + "returning " + (n_1 + n_2) );
        return n_1 + n_2;
    }
}

public static void main( String[] args )
{
    fibonacci(5, 0);
}