algorithm: catalan numbers (#1149)

Dynamic-Programming/CatalanNumbers.js

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+/*
+ * Author: IcarusTheFly (https://github.com/IcarusTheFly)
+ * Catalan Numbers explanation can be found in the following links:
+ * Wikipedia: https://en.wikipedia.org/wiki/Catalan_number
+ * Brilliant: https://brilliant.org/wiki/catalan-numbers
+ */
+
+/**
+ * @function catalanNumbers
+ * @description Returns all catalan numbers from index 0 to n
+ * @param {number} n
+ * @returns {number[]} Array with the catalan numbers from 0 to n
+ */
+
+export const catalanNumbers = (n) => {
+  if (n === 0) {
+    return [1]
+  }
+  const catList = [1, 1]
+
+  for (let i = 2; i <= n; i++) {
+    let newNumber = 0
+    for (let j = 0; j < i; j++) {
+      newNumber += catList[j] * catList[i - j - 1]
+    }
+    catList.push(newNumber)
+  }
+
+  return catList
+}

Dynamic-Programming/tests/CatalanNumbers.test.js

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+import { catalanNumbers } from '../CatalanNumbers'
+
+describe('Testing catalanNumbers function', () => {
+  test('should return the expected array for inputs from 0 to 20', () => {
+    const expectedOutput = [
+      1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900,
+      2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, 6564120420
+    ]
+
+    for (let i = 0; i <= 20; i++) {
+      expect(catalanNumbers(i)).toStrictEqual(expectedOutput.slice(0, i + 1))
+    }
+  })
+})