feat: Added Double Factorial Iterative Implementation (#187)

* Update DIRECTORY.md

* 🚀feat: added double factorial (iterative)

* Update DIRECTORY.md

* removed redundant if check, fix formatting

* Update DIRECTORY.md

---------

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

Author: 3 people

DIRECTORY.md

@@ -108,6 +108,7 @@
   * [Calculate Median](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/calculate_median.ts)
   * [Degrees To Radians](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/degrees_to_radians.ts)
   * [Digit Sum](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/digit_sum.ts)
+  * [Double Factorial Iterative](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/double_factorial_iterative.ts)
   * [Euler Totient](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/euler_totient.ts)
   * [Factorial](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/factorial.ts)
   * [Factors](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/factors.ts)
@@ -128,6 +129,7 @@
   * [Number Of Digits](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/number_of_digits.ts)
   * [Pascals Triangle](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/pascals_triangle.ts)
   * [Perfect Cube](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/perfect_cube.ts)
+  * [Perfect Number](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/perfect_number.ts)
   * [Perfect Square](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/perfect_square.ts)
   * [Prime Factorization](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/prime_factorization.ts)
   * [Primes](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/primes.ts)

maths/double_factorial_iterative.ts

@@ -0,0 +1,29 @@
+/**
+ * @function DoubleFactorialIterative
+ * @description Calculate the double factorial of a number (iterative implementation)
+ * @summary In mathematics, double factorial of a number n is denoted by n!!. 
+ * It is not to be confused with (n!)!, which is the factorial function iterated twice.  
+ * The double factorial is the product of all positive integers upto n that have the same parity (odd or even)
+ * as n.  
+ * Therefore,  
+ * 9!! = 9 . 7 . 5 . 3 . 1  
+ * 10!! = 10 . 8 . 6 . 4 . 2
+ * 
+ * Please note that for factorials of even numbers, the series ends at 2.
+ * @see [Wikipedia](https://en.wikipedia.org/wiki/Double_factorial)
+ * @see [Mathworld](https://mathworld.wolfram.com/DoubleFactorial.html)
+ * @see [GeeksForGeeks](https://www.geeksforgeeks.org/double-factorial/)
+ * @example DoubleFactorialIterative(4) = 8
+ * @example DoubleFactorialIterative(5) = 15
+ */
+const DoubleFactorialIterative = (n: number) => {
+  if(n < 0) throw new RangeError("The number needs to be non-negative")
+  let doubleFactorial = 1
+
+  for(let i = n; i > 0; i -= 2)
+    doubleFactorial *= i
+
+  return doubleFactorial
+}
+
+export { DoubleFactorialIterative }

maths/test/double_factorial_iterative.test.ts

@@ -0,0 +1,7 @@
+import { DoubleFactorialIterative } from "../double_factorial_iterative";
+
+describe("Double Factorial", () => {
+	test.each([[4, 8], [5, 15], [10, 3840]])("%i!! = %i", (n, expected) => {
+		expect(DoubleFactorialIterative(n)).toBe(expected)
+	})
+})