Adding to backtracking (TheAlgorithms#1289)

* adding generate-parenthses algorithm

* adding generateParenthses algorithm

* adding generate parentheses algorithm

* fixing comments according to the JDoc comments, cleaning code

* fixing comments

Author: Ramzi-Abidi

Backtracking/generateParentheses.js

@@ -0,0 +1,31 @@
+/**
+ * Problem Statement: Given a number n pairs of parentheses, try to Generate all combinations of valid parentheses;
+ * @param {number} n - number of given parentheses
+ * @return {string[]} res - array that contains all valid parentheses
+ * @see https://leetcode.com/problems/generate-parentheses/
+ */
+
+const generateParentheses = (n) => {
+  const res = []
+
+  const solve = (chres, openParenthese, closedParenthese) => {
+    if (openParenthese === n && closedParenthese === n) {
+      res.push(chres)
+      return
+    }
+
+    if (openParenthese <= n) {
+      solve(chres + '(', openParenthese + 1, closedParenthese)
+    }
+
+    if (closedParenthese < openParenthese) {
+      solve(chres + ')', openParenthese, closedParenthese + 1)
+    }
+  }
+
+  solve('', 0, 0)
+
+  return res
+}
+
+export { generateParentheses }

Backtracking/tests/GenerateParentheses.test.js

@@ -0,0 +1,5 @@
+import { generateParentheses } from '../generateParentheses'
+
+test('generate all valid parentheses of input 3', () => {
+  expect(generateParentheses(3)).toStrictEqual(['((()))', '(()())', '(())()', '()(())', '()()()'])
+})