Add Fibonacci Search (#2698)

Searches/FibonacciSearch.java

@@ -0,0 +1,72 @@
+package Searches;
+
+/*
+*  Fibonacci Search is a popular algorithm which finds the position of a target value in
+*  a sorted array
+*
+*  The time complexity for this search algorithm is O(log3(n))
+*  The space complexity for this search algorithm is O(1)
+*  @author Kanakalatha Vemuru (https://github.com/KanakalathaVemuru)
+*/
+public class FibonacciSearch implements SearchAlgorithm {
+   /**
+   * @param array is a sorted array where the element has to be searched
+   * @param key is an element whose position has to be found
+   * @param <T> is any comparable type
+   * @return index of the element
+   */
+    @Override
+    public <T extends Comparable<T>> int find(T[] array, T key) {
+        int fibMinus1 = 1;
+        int fibMinus2 = 0;
+        int fibNumber = fibMinus1 + fibMinus2;
+        int n = array.length;
+
+        while (fibNumber < n) {
+            fibMinus2 = fibMinus1;
+            fibMinus1 = fibNumber;
+            fibNumber = fibMinus2 + fibMinus1;
+        }
+
+        int offset = -1;
+
+        while (fibNumber > 1) {
+            int i = Math.min(offset + fibMinus2, n - 1);
+
+            if (array[i].compareTo(key) < 0) {
+                fibNumber = fibMinus1;
+                fibMinus1 = fibMinus2;
+                fibMinus2 = fibNumber - fibMinus1;
+                offset = i;
+            }
+            else if (array[i].compareTo(key) > 0) {
+                fibNumber = fibMinus2;
+                fibMinus1 = fibMinus1 - fibMinus2;
+                fibMinus2 = fibNumber - fibMinus1;
+            }
+            else {
+                return i;
+            } 
+        }
+
+        if (fibMinus1 == 1 && array[offset + 1] == key) {
+            return offset + 1;
+        }
+
+        return -1;
+    }
+
+    // Driver Program
+    public static void main(String[] args) {
+        Integer[] integers = {1, 2, 4, 8, 16, 32, 64, 128, 256, 512};
+
+        int size = integers.length;
+        Integer shouldBeFound = 128;
+        FibonacciSearch fsearch = new FibonacciSearch();
+        int atIndex = fsearch.find(integers, shouldBeFound);
+
+        System.out.println(
+                "Should be found: " + shouldBeFound + ". Found "+ integers[atIndex] + " at index "+ atIndex +". An array length " + size);
+    }
+
+}