Implemented FibonacciSearch Using JavaScript (TheAlgorithms#348)

* Implemented FibonacciSearch Using JavaScript

* Fixed Lint/test issues

* Fixed lint/test error

* FIxed Lint issues

Author: komputarist

Search/FibonacciSearch.js

@@ -0,0 +1,77 @@
+/****************************************************************************
+ * Fibonacci Search JavaScript Implementation
+ * Author   Alhassan Atama Isiaka
+ * Version v1.0.0
+ * Copyright 2020
+ * https://github.com/komputarist
+ *
+ * This implementation is based on Generalizing the Fibonacci search we
+ * define the Fibonacci search of degree K. Like the Fibonacci search,
+ * which it reduces to for K = 2, the Fibonacci search of degree K
+ * involves only addition and subtraction.
+ *  Capocelli R.M. (1991) A Generalization of the Fibonacci Search. In:
+ * Bergum G.E., Philippou A.N., Horadam A.F. (eds) Applications of Fibonacci
+ * Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3586-3_9
+ *
+ * This snippet is free. Feel free to improve on it
+ *
+ * We define a function fibonacciSearch() that takes an array of numbers,
+ * the item (number) to be searched for and the length of the items in the array
+ ****************************************************************************/
+
+const fibonacciSearch = (arr, x, n) => {
+  let fib2 = 0 // (K-2)'th Fibonacci Number
+  let fib1 = 1 // (K-1)'th Fibonacci Number.
+  let fibK = fib2 + fib1 // Kth Fibonacci
+
+  /* We want to store the smallest fibonacci number smaller such that
+    number is greater than or equal to n, we use fibK for this */
+  while (fibK < n) {
+    fib2 = fib1
+    fib1 = fibK
+    fibK = fib2 + fib1
+  }
+  //  This marks the eliminated range from front
+  let offset = -1
+
+  /* while there are elements to be checked. We compare arr[fib2] with x.
+    When fibM becomes 1, fib2 becomes 0 */
+
+  while (fibK > 1) {
+    // Check if fibK is a valid location
+    const i = Math.min(offset + fib2, n - 1)
+
+    /*  If x is greater than the value at
+      index fib2, Partition the subarray array
+      from offset to i */
+    if (arr[i] < x) {
+      fibK = fib1
+      fib1 = fib2
+      fib2 = fibK - fib1
+      offset = i
+      /* If x is greater than the value at
+            index fib2, cut the subarray array
+            from offset to i */
+    } else if (arr[i] > x) {
+      fibK = fib2
+      fib1 = fib1 - fib2
+      fib2 = fibK - fib1
+    } else {
+    //  return index for found element
+      return i
+    }
+  }
+
+  //    comparing the last element with x */
+  if (fib1 && arr[offset + 1] === x) {
+    return offset + 1
+  }
+  //    element not found. return -1
+  return -1
+}
+// Example
+const myArray = [10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100]
+const n = myArray.length
+const x = 90
+const fibFinder = fibonacciSearch(myArray, x, n)
+console.log('Element found at index:', fibFinder)