Added a backtracking solution for the generate paranthesis.

anxious-coder-lhs · anxious-coder-lhs · commit d2b2623b151d · 2020-10-14T23:53:42.000+05:30
diff --git a/level_medium/LeetCode_22_Generate_Paranthesis_3.ts b/level_medium/LeetCode_22_Generate_Paranthesis_3.ts
@@ -0,0 +1,36 @@
+/**
+ * Solution is based on the backtracking paradigm. The solution explores the entire solution
+ * space for all the permutations that are possible. While making the permutations, it also
+ * checks for the boundary conditions to see if the solution can be found in this path. If the
+ * solution cannot be found, the solution space is backtracked and it is not explored further.
+ * 
+ * Complexity: Time and Space O((4^n)/(n^(1/2)).
+ * Refer https://leetcode.com/problems/generate-parentheses/solution/ for more details.
+ * 
+ * @param n 
+ */
+function generateParenthesis(n: number): string[] {
+    const result: string[] = [];
+    genHelper(n * 2, result);
+    return result;
+};
+
+function genHelper(n: number, result: string[], open: number = 0, close: number = 0, str: string = "") {
+    
+    // Base Condition to terminate the recursion
+    if (str.length >= n) {
+        result.push(str);
+        return;
+    }
+    
+    // Boundary conditions to validate if the backtracking is required, or we can proceed.
+    if (open < n/2) {
+        genHelper(n, result, open + 1, close, str + "(");
+    }
+    
+    // Boundary condition to validate the backtracking again if required, or we can proceed.
+    if (open > close) {
+        // 2nd condition validates if we have not added closing braces before the opening braces.
+        genHelper(n, result, open, close + 1, str + ")");
+    }
+}
