写一个返回指定斐波那契数的方法？

Question

The Fibonacci sequence is a set of Numbers where each number, after the first two, is the sum of the previous two numbers, resulting in the following sequence:

0 1 1 2 3 5 6 13 21 34 55 89 144 233 377 610 987 1597 2584 4181

How can I write a method, using recursion, which will return a specified fibonacci number? I want to avoid using an array

Here is what i have so far

public static int fibo(int n)
{
    if (n==1)
        return 1;
    else
        return //this is the part i am stuck on

Answer 1

As a certain fibonacci number (except 1) is on its percursor you call:

public static int fibo(int n) {
    if (n < 0) {
        throw new IndexOutOfBoundsException("Can't calculate fibonacci number for negative index");
    } else if(n == 0 || n == 1) {
        return n;
    }

    return fibo(n-1) + fibo(n-2);
}

Answer 2

public static int fibo(int n){ 
  if(n<=2)
    return (n-1);
  else 
    return fibo(n-1) + fibo(n-2);
}

Each fibonacci number is the sum of its 2 predecessors. You can't just have a base case of n=1 since when calculating n = 2 you will find it is the sum of n = 1 and n = 0? which would not be defined.

Note: This is assuming you are 1-indexing the list of fib numbers ie 0 is the first 1 the second then 1 the third etc.

Answer 3

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

    public static void main(String[] args)
    {
        System.out.println(fibonacci(11));
    }
}