The Fibonacci search uses the divide and conquer algorithm to sort the array, the Fibonacci search is an addition to the binary search in simple words it is an extension to the binary search.

Fibonacci_Search.JAVA

//This is a java program to search an element using Fibonacci search
import java.util.Scanner;
 
public class Fibonacci_Search 
{
    static int kk = -1, nn = -1;
    static int fib[] = { 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,
            377, 610, 98, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368,
            75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309,
            3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986,
            102334155, 165580141 };
 
    static int fibsearch(int a[], int n, long x) 
    {
        int inf = 0, pos, k;
        if (nn != n) 
        {
            k = 0;
            while (fib[k] < n) k++; kk = k; nn = n; } else k = kk; while (k > 0) 
        {
            pos = inf + fib[--k];
            if ((pos >= n) || (x < a[pos])) ; else if (x > a[pos]) 
            {
                inf = pos + 1;
                k--;
            }
            else 
                return pos;
        }
        return -1;
    }
 
    public static void main(String args[]) 
    {
        int arr[] = { 2, 3, 45, 56, 67, 78, 89, 99, 100, 101 };
        int num, pos;
        Scanner scan = new Scanner(System.in);
        System.out.println("Enter an element to search: ");
        num = scan.nextInt();
        pos = fibsearch(arr, 10, num);
        if (pos >= 0)
            System.out.println("\nElement is at index : "
                    + fibsearch(arr, 10, num));
        else
            System.out.println("\nElement NOT found!! ");
        scan.close();
    }
}

Source: http://codingsec.net/2016/03/the-faster-way-to-search-the-array-fibonacci-search/