feat: add fibonaccisearch algorithm (#244)

* feat: add fibonaccisearch algorithm

* test: add test for fibonacci search algorithm

* fix: changed variable names and function return

* remove redundant @function

* fix tests

* fix type

* fix formatting

---------

Co-authored-by: Lars Müller <[email protected]>
Co-authored-by: Lars Mueller <[email protected]>

Author: Fechuli

search/fibonacci_search.ts

@@ -0,0 +1,57 @@
+/**
+ * @description Fibonacci search algorithm for a sorted array.
+ *
+ * The algorithm searches for a specific value in a sorted array using Fibonacci numbers
+ * to divide the array into smaller subarrays. This algorithm is useful for large arrays where
+ * the cost of accessing elements is high.
+ *
+ * @param {number[]} array - sorted list of numbers
+ * @param {number} target - target number to search for
+ * @return {number | null} - index of the target number in the list, or null if not found
+ * @see [FibonacciSearch](https://www.geeksforgeeks.org/fibonacci-search/)
+ * @example fibonacciSearch([1,2,3], 2) => 1
+ * @example fibonacciSearch([4,5,6], 2) => null
+ */
+
+export const fibonacciSearch = (
+  array: number[],
+  target: number
+): number | null => {
+  const arrayLength = array.length
+  let a = 0 // (n-2)'th Fibonacci No.
+  let b = 1 // (n-1)'th Fibonacci No.
+  let c = a + b // n'th Fibonacci
+
+  while (c < arrayLength) {
+    a = b
+    b = c
+    c = a + b
+  }
+
+  let offset = -1
+
+  while (c > 1) {
+    let i = Math.min(offset + a, arrayLength - 1)
+
+    if (array[i] < target) {
+      c = b
+      b = a
+      a = c - b
+      offset = i
+    } else if (array[i] > target) {
+      c = a
+      b = b - a
+      a = c - b
+    } else {
+      // Element found then return index
+      return i
+    }
+  }
+
+  if (b && array[offset + 1] === target) {
+    return offset + 1
+  }
+
+  // Element not found then return null
+  return null
+}

search/test/fibonacci_search.test.ts

@@ -0,0 +1,18 @@
+import { fibonacciSearch } from '../fibonacci_search'
+
+describe('Fibonacci search', () => {
+  test.each([
+    [[1, 2, 3], 2, 1],
+    [[4, 5, 6], 2, null],
+    [[10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100], 85, 8],
+    [[], 1, null],
+    [[1], 1, 0],
+    [[1, 3, 5, 7, 9, 11, 13], 11, 5],
+    [[1, 3, 5, 7, 9, 11, 13], 8, null]
+  ])(
+    'of %o, searching for %o, expected %i',
+    (array: number[], target: number, expected: number | null) => {
+      expect(fibonacciSearch(array, target)).toBe(expected)
+    }
+  )
+})