feat: add fibonaccisearch algorithm

search/fibonacci_search.ts

@@ -0,0 +1,58 @@
+/**
+ * @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 | 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

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+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);
+      }
+    );
+  });