feat: Added implementation for ugly numbers (#146)

* Update DIRECTORY.md

* Added ugly numbers 🧟

* Update DIRECTORY.md

* 🚀 feat: use generator for ugly nums

* Formatting filenames ad9848e

* Update DIRECTORY.md

* Test first 11 ugly numbers

* fix oopsie

---------

Co-authored-by: autoprettier <actions@github.com>
Co-authored-by: Lars Müller <34514239+appgurueu@users.noreply.github.com>

Author: 3 people

DIRECTORY.md

@@ -124,6 +124,7 @@
       * [Hexagonal Numbers.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/series/test/hexagonal_numbers.test.ts)
   * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/sieve_of_eratosthenes.ts)
   * [Signum](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/signum.ts)
+  * [Ugly Numbers](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/ugly_numbers.ts)
   * [Zellers Congruence](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/zellers_congruence.ts)
 
 ## Other

maths/test/ugly_numbers.test.ts

@@ -0,0 +1,6 @@
+import { UglyNumbers } from '../ugly_numbers';
+
+test('Ugly Numbers', () => {
+  const uglyNumbers = UglyNumbers();
+  expect(Array(11).fill(undefined).map(() => uglyNumbers.next())).toEqual([1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15]);
+})

maths/ugly_numbers.ts

@@ -0,0 +1,36 @@
+/**
+ * @generator
+ * @description Generates ugly numbers
+ * @summary Ugly numbers are natural numbers whose only prime factors are 2, 3 and 5.
+ * They can be represented in the form 2^a * 3^b * 5*c. By convention, 1 is also considered to be
+ * an ugly number.
+ * The first few terms of the sequence are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20...
+ * 
+ * For the provided n, the nth ugly number shall be computed.
+ * @see [GeeksForGeeks](https://www.geeksforgeeks.org/ugly-numbers/)
+ */
+function* UglyNumbers() {
+  yield 1
+
+  let idx2 = 0, idx3 = 0, idx5 = 0
+  const uglyNumbers = [1]
+
+  let nextx2: number, nextx3: number, nextx5: number, nextUglyNum: number
+
+  while(true) {
+    nextx2 = uglyNumbers[idx2] * 2
+    nextx3 = uglyNumbers[idx3] * 3
+    nextx5 = uglyNumbers[idx5] * 5
+
+    nextUglyNum = Math.min(nextx2, nextx3, nextx5)
+    yield nextUglyNum
+
+    if(nextx2 === nextUglyNum) idx2++
+    if(nextx3 === nextUglyNum) idx3++
+    if(nextx5 === nextUglyNum) idx5++
+    
+    uglyNumbers.push(nextUglyNum)
+  }
+}
+
+export { UglyNumbers }