From 7a8d2c7d27b561f7245c9fbd46ea9d8841e85ae2 Mon Sep 17 00:00:00 2001
From: Federico Fiaschi <federicofiaschi277@gmail.com>
Date: Tue, 30 Jul 2024 11:13:52 +0200
Subject: [PATCH 1/2] feat: add fibonaccisearch algorithm

---
 search/fibonacci_search.ts | 56 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 56 insertions(+)
 create mode 100644 search/fibonacci_search.ts

diff --git a/search/fibonacci_search.ts b/search/fibonacci_search.ts
new file mode 100644
index 00000000..7b0a43c2
--- /dev/null
+++ b/search/fibonacci_search.ts
@@ -0,0 +1,56 @@
+/**
+ * @function fibonacciSearch
+ * @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} - index of the target number in the list, or -1 if not found
+ * @see [FibonacciSearch](https://www.geeksforgeeks.org/fibonacci-search/)
+ * @example fibonacciSearch([1,2,3], 2) => 1
+ * @example fibonacciSearch([4,5,6], 2) => -1
+ */
+
+export const fibonacciSearch = (array: number[], target: number): number => {
+    const arrayLength = array.length;
+    let fibNMinusTwo = 0;  // (n-2)'th Fibonacci No.
+    let fibNMinusOne = 1;  // (n-1)'th Fibonacci No.
+    let fibN = fibNMinusTwo + fibNMinusOne;  // n'th Fibonacci
+  
+    while (fibN < arrayLength) {
+      fibNMinusTwo = fibNMinusOne;
+      fibNMinusOne = fibN;
+      fibN = fibNMinusTwo + fibNMinusOne;
+    }
+  
+    let offset = -1;
+  
+    while (fibN > 1) {
+      let i = Math.min(offset + fibNMinusTwo, arrayLength - 1);
+  
+      if (array[i] < target) {
+        fibN = fibNMinusOne;
+        fibNMinusOne = fibNMinusTwo;
+        fibNMinusTwo = fibN - fibNMinusOne;
+        offset = i;
+      } else if (array[i] > target) {
+        fibN = fibNMinusTwo;
+        fibNMinusOne = fibNMinusOne - fibNMinusTwo;
+        fibNMinusTwo = fibN - fibNMinusOne;
+      } else {
+        // Element found then return index
+        return i;
+      }
+    }
+  
+    if (fibNMinusOne && array[offset + 1] === target) {
+      return offset + 1;
+    }
+  
+    // Element not found then return -1
+    return -1;
+  }
+  
\ No newline at end of file

From aed58baf1bcbff4902678fb93210b20fe1a5aaf7 Mon Sep 17 00:00:00 2001
From: Federico Fiaschi <federicofiaschi277@gmail.com>
Date: Tue, 30 Jul 2024 11:22:12 +0200
Subject: [PATCH 2/2] test: add test for fibonacci search algorithm

---
 search/test/fibonacci_search.test.ts | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)
 create mode 100644 search/test/fibonacci_search.test.ts

diff --git a/search/test/fibonacci_search.test.ts b/search/test/fibonacci_search.test.ts
new file mode 100644
index 00000000..6b2a689f
--- /dev/null
+++ b/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, -1],
+      [[10, 22, 35, 40, 45, 50, 80, 82, 85, 90, 100], 85, 8],
+      [[], 1, -1],
+      [[1], 1, 0],
+      [[1, 3, 5, 7, 9, 11, 13], 11, 5],
+      [[1, 3, 5, 7, 9, 11, 13], 8, -1]
+    ])(
+      'of %o, searching for %o, expected %i',
+      (array: number[], target: number, expected: number) => {
+        expect(fibonacciSearch(array, target)).toBe(expected);
+      }
+    );
+  });
\ No newline at end of file