Added second approach to parentheses

Author: ignacio-chiazzo

GenerateParentheses.js

@@ -14,15 +14,24 @@ For example, given n = 3, a solution set is:
 ]
 */
 
-var generateParentheses = function(n) {
-  if(n == 0) { return [""] };
+// ************************************************  Approach1  ************************************************
+var generateParenthesesApproach1 = function(n) {
+  if(n === 0) { return [] };
 
   var str = "(".repeat(n);
-  var sol = [];
+    sol = [];
+  
   genParAux(str, 0, 0, sol)
   return sol;
 };
 
+/* 
+@param {string} str contains the string generated.
+@param {number} position Current position of the string where new parenthesis would be added.
+@param {string} leftParenthesis Amount for parenthesis left to be added.
+@param {[string]} sol array that contains the solution found so far.
+*/
+
 var genParAux = function(str, position, leftParentheses, sol) {
   if(position === str.length) {
     var ret = str + ")".repeat(leftParentheses);
@@ -31,7 +40,7 @@ var genParAux = function(str, position, leftParentheses, sol) {
   }
 
   genParAux(str, position + 1, leftParentheses + 1, sol); // Don't insert anything
-  if(leftParentheses == 0) { return; }
+  if(leftParentheses === 0) { return; }
 
   for(var i = 1; i <= leftParentheses; i++) {
     var parString = ")".repeat(i);
@@ -40,15 +49,48 @@ var genParAux = function(str, position, leftParentheses, sol) {
   } 
 }
 
-function main() {
-  console.log("0:");
-  console.log(generateParentheses(0));
-  console.log("1:");
-  console.log(generateParentheses(1));
-  console.log("2:");
-  console.log(generateParentheses(2));
-  console.log("3:");
-  console.log(generateParentheses(3));
+// ************************************************  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");
+  [0, 1, 2, 3].forEach(function(elem) {
+    console.log(`${elem}: ${generateParenthesesApproach2(elem)}`);
+  })
+
+  console.log("-------------");
+
+  console.log("Approach 2");
+  [0, 1, 2, 3].forEach(function(elem) {
+    console.log(`${elem}: ${generateParenthesesApproach2(elem)}`);
+  })
+}
+main();
 module.exports.main = main