Need to explain with Fibonacci

Question

I have seen many examples of Fibonacci here on Stack Overflow but I have found no answer for my question. So, I have a code:

public class Fib {
    public static int fib(int n) {
        if (n < 2) {
           return n;
        }
        else {
   return fib(n-1)+fib(n-2);
        }
}

public static void main(String[] args) {
    for (int i=0; i<8; i++)
        System.out.print(fib(i)+", ");
}
}

After run it we will get 0, 1, 1, 2, 3, 5, 8, 13,

I have a question: How do we get 8 ? fib(6)=............

Can anyone write in detail?

Answer 1

fib(0) = 0
fib(1) = 1
fib(2) = fib(1) + fib(0) = 1
fib(3) = fib(2) + fib(1) = 2
fib(4) = fib(3) + fib(2) = 3
fib(5) = fib(4) + fib(3) = 5
fib(6) = fib(5) + fib(4) = 8

When you call fib(6) it will execute fib(5) and fib(4) etc. until it hits the base cases fib(1) and fib(0).

Answer 2

fib(6) = fib(5)+fib(4) = fib(4)+fib(3)+fib(3)+fib(2) = fib(3)+fib(2)+fib(2)+fib(1)+fib(2)+fib(1)+fib(1)+fib(0) = fib(2)+fib(1)+fib(1)+fib(0)+fib(1)+fib(0)+1+fib(1)+fib(0)+1+1+0 = fib(1)+fib(0)+1+1+0+1+0+1+1+0+1+1+0 = 1+0+1+1+0+1+0+1+1+0+1+1+0=8

Hope it helped..

Answer 3

fib(6) = fib(5) + fib(4)  //..
fib(5) = fib(4) + fib(3)  //..
fib(4) = fib(3) + fib(2)  //2 + 1 
fib(3) = fib(2) + fib(1)  //1 + 1
fib(2) = fib(1) + fib(0)  //1 + 0  Begin here (stop condition)