Added second approach to parentheses

Author: ignacio-chiazzo

GenerateParentheses.js

@@ -14,7 +14,8 @@ For example, given n = 3, a solution set is:
 ]
 */
 
-var generateParentheses = function(n) {
+// ************************************************  Approach1  ************************************************
+var generateParenthesesApproach1 = function(n) {
   if(n == 0) { return [""] };
 
   var str = "(".repeat(n);
@@ -40,15 +41,58 @@ var genParAux = function(str, position, leftParentheses, sol) {
   } 
 }
 
+// ************************************************  Approach2  ************************************************
+var generateParenthesesApproach2 = function(n) {
+  if(n == 0) { return [""] };
+
+  var sol = [];
+  genParAuxApproach2("", 0, 0, 0, n * 2, sol)
+  return sol;
+}
+
+var genParAuxApproach2 = function(str, leftPar, rightPar, index, totalCharCount, sol) {
+  if(index == totalCharCount) {
+    if(rightPar == leftPar) {
+      sol.push(str);
+    }
+    return;
+  }
+
+  var strLeft = insertAt(str, index, "(");
+  genParAuxApproach2(strLeft, leftPar + 1, rightPar, index + 1, totalCharCount, sol);
+
+  if(rightPar == leftPar) { return; }
+  
+  var strRight = insertAt(str, index, ")");
+  genParAuxApproach2(strRight, leftPar, rightPar + 1, index + 1, totalCharCount, sol);
+}
+
+var insertAt = function(str, position, value) {
+  return str.slice(0, position) + value + str.slice(position);
+}
+
 function main() {
+  console.log("Approach 1")
   console.log("0:");
-  console.log(generateParentheses(0));
+  console.log(generateParenthesesApproach1(0));
   console.log("1:");
-  console.log(generateParentheses(1));
+  console.log(generateParenthesesApproach1(1));
   console.log("2:");
-  console.log(generateParentheses(2));
+  console.log(generateParenthesesApproach1(2));
   console.log("3:");
-  console.log(generateParentheses(3));
-}
+  console.log(generateParenthesesApproach1(3));
+
+  console.log("-------------");
 
+  console.log("Approach 1")
+  console.log("0:");
+  console.log(generateParenthesesApproach2(0));
+  console.log("1:");
+  console.log(generateParenthesesApproach2(1));
+  console.log("2:");
+  console.log(generateParenthesesApproach2(2));
+  console.log("3:");
+  console.log(generateParenthesesApproach2(3));
+}
+main();
 module.exports.main = main