A Fibonacci Sequence is a sequence of numbers in which the first and second numbers in the sequence are 0 and 1 respectively, and additional numbers in the sequence are calculated by adding the previous two.

The first few numbers in the Fibonacci Sequence look like this:

0, 1, 1, 2, 3, 5, 8, 13, 21...

Often in technical interviews a person will be asked to “create a function that returns the nth value in a Fibonacci Sequence“. A recursive algorithm can solve this problem in a few simple steps as described below.

1. The first and second numbers in the sequence will always be 0 and 1 respectively. In this example we are assuming that n=0 represents the first number in the series. If 0 or 1 is passed to our function, then no calculation is needed. Simply return the value of n.

2. If n is greater than 1, recursively call function(n-1) + function(n-2).

While this algorithm is clean and simple, it has a relatively expensive time complexity, which in the worst case is approximately exponential. There are a variety of other simple but more efficient algorithms that can be used to solve this problem as well.

package com.bigdatums.interview;

public class FibonacciRecursive {

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

    public static void main(String[] args) {
        System.out.println(fibonacciRecursive(0));
        System.out.println(fibonacciRecursive(1));
        System.out.println(fibonacciRecursive(2));
        System.out.println(fibonacciRecursive(3));
        System.out.println(fibonacciRecursive(4));
        System.out.println(fibonacciRecursive(5));
        System.out.println(fibonacciRecursive(6));
        System.out.println(fibonacciRecursive(7));
        System.out.println(fibonacciRecursive(8));
        System.out.println(fibonacciRecursive(9));
        System.out.println(fibonacciRecursive(10));
    }

}