feat(maths): recursive calculating of Fibonacci numbers (#107)

* feat(maths): improve fibonacci number function

* feat(maths): makes recursive fibonacci an extra function

* fix: improve tests

* test: improves tests

Author: zFlxw

maths/fibonacci.ts

@@ -1,19 +1,26 @@
 /**
- * A function to get nth Fibonacci number
- * @param number The input integer
- * @return {number} Fibonacci number of `number`
+ * A function to get nth Fibonacci number.
+ *
+ * Time Complexity: linear (O(n))
+ *
+ * @param number The index of the number in the Fibonacci sequence.
+ * @return The Fibonacci number on the nth index in the sequence.
+ *
  * @example nthFibonacci(4) => 3 | nthFibonacci(6) => 8
  * @see https://en.m.wikipedia.org/wiki/Fibonacci_number
  * @author MohdFaisalBidda <https://github.com/MohdFaisalBidda>
  */
-
 export const nthFibonacci = (number: number): number => {
-  if (number < 0)  throw "Number should be greater than 0";
-  
-  if (number === 0)  return 0;
+  if (number < 0) {
+    throw 'Number should be greater than 0';
+  }
 
-  let a = 0, b = 1;
+  if (number === 0) {
+    return 0;
+  }
 
+  let a = 0,
+    b = 1;
   for (let i = 1; i < number; ++i) {
     const c = a + b;
 
@@ -23,3 +30,29 @@ export const nthFibonacci = (number: number): number => {
 
   return b;
 };
+
+/**
+ * A function to get nth Fibonacci number recursively. **Note: This recursive approach increases the time complexity**
+ *
+ * Time Complexity: exponential (O(ϕ^n))
+ *
+ * @param number The index of the number in the Fibonacci sequence.
+ * @return The Fibonacci number on the nth index in the sequence.
+ *
+ * @example nthFibonacci(4) => 3 | nthFibonacci(6) => 8
+ * @see https://en.m.wikipedia.org/wiki/Fibonacci_number
+ * @author zFlxw <https://github.com/zFlxw>
+ */
+export const nthFibonacciRecursively = (number: number): number => {
+  if (number === 0) {
+    return 0;
+  }
+
+  if (number <= 2) {
+    return 1;
+  }
+
+  return (
+    nthFibonacciRecursively(number - 1) + nthFibonacciRecursively(number - 2)
+  );
+};

maths/test/fibonacci.test.ts

@@ -1,11 +1,13 @@
-import {nthFibonacci} from '../fibonacci';
+import { nthFibonacci, nthFibonacciRecursively } from '../fibonacci';
 
-describe('nthFibonacci', () => {
-  test('should return correct value', () => {        
-    expect(nthFibonacci(0)).toBe(0);  
-    expect(nthFibonacci(1)).toBe(1);
-    expect(nthFibonacci(5)).toBe(5);
-    expect(nthFibonacci(4)).toBe(3);
-    expect(nthFibonacci(0)).toBe(0);
-  });
-});
+const test = (func: (n: number) => number) =>
+  it.each([
+    [0, 0],
+    [1, 1],
+    [2, 1],
+    [5, 5],
+    [10, 55],
+    [15, 610],
+  ])('fib(%i) = %i', (n, expected) => expect(func(n)).toBe(expected));
+describe('Fibonacci iterative', () => test(nthFibonacci));
+describe('Fibonacci recursive', () => test(nthFibonacciRecursively));