[DP] Update solution to Generate Parentheses

DP/GenerateParentheses.swift

@@ -1,28 +1,36 @@
 /**
  * Question Link: https://leetcode.com/problems/generate-parentheses/
- * Primary idea: Dynamic Programming, generate the current parentheses based on previous one
- * Note: Use a set to avoid duplicates
- * Time Complexity: O(n^2), Space Complexity: O(n)
+ * Primary idea: Insert left and right parentheses and ensure they are valid
+ * Time Complexity: O(2^n), Space Complexity: O(n)
  *
  */
 
 class GenerateParentheses {
     func generateParenthesis(_ n: Int) -> [String] {
-        var set = Set<String>()
+        var paths = [String](), path = [Character](repeating: " ", count: 2 * n)
 
-        guard n > 0 else {
-            return [""]
+        helper(&paths, &path, n, n, 0)
+
+        return paths
+    }
+
+    func helper(_ paths: inout [String], _ path: inout [Character], _ leftCount: Int, _ rightCount: Int, _ index: Int) {
+        if leftCount < 0 || leftCount > rightCount {
+            return
         }
 
-        for str in generateParenthesis(n - 1) {
-            for (i, char) in str.characters.enumerated() {
-                if char == "(" {
-                    set.insert(String(Array(str.characters)[0...i]) + "()" + String(Array(str.characters)[i + 1..<str.characters.count]))
-                }
-            }
-            set.insert(str + "()")
+        if leftCount == 0 && rightCount == 0 {
+            paths.append(String(path))
+            return
         }
 
-        return [String](set)
+        if leftCount > 0 {
+            path[index] = "("
+            helper(&paths, &path, leftCount - 1, rightCount, index + 1)
+        }
+        if rightCount > leftCount {
+            path[index] = ")"
+            helper(&paths, &path, leftCount, rightCount - 1, index + 1)
+        }
     }
 }

README.md

@@ -168,7 +168,7 @@
 [Unique Paths II](https://leetcode.com/problems/unique-paths-ii/)| [Swift](./DP/UniquePathsII.swift)| Medium| O(mn)| O(mn)|
 [Decode Ways](https://leetcode.com/problems/decode-ways/)| [Swift](./DP/DecodeWays.swift) | O(n)|O(n)|
 [Minimum Path Sum](https://leetcode.com/problems/minimum-path-sum/)| [Swift](./DP/MinimumPathSum.swift)| Medium| O(mn)| O(mn)|
-[Generate Parentheses](https://leetcode.com/problems/generate-parentheses/)| [Swift](./DP/GenerateParentheses.swift)| Medium| O(n^2)| O(n)|
+[Generate Parentheses](https://leetcode.com/problems/generate-parentheses/)| [Swift](./DP/GenerateParentheses.swift)| Medium| O(2^n)| O(n)|
 [Different Ways to Add Parentheses](https://leetcode.com/problems/different-ways-to-add-parentheses/)| [Swift](./DP/DifferentWaysAddParentheses.swift)| Medium| O(n^n)| O(n)|
 [Best Time to Buy and Sell Stock](https://leetcode.com/problems/best-time-to-buy-and-sell-stock/)| [Swift](./DP/BestTimeBuySellStock.swift)| Easy| O(n)| O(1)|
 [Best Time to Buy and Sell Stock II](https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/)| [Swift](./DP/BestTimeBuySellStockII.swift)| Medium| O(n)| O(1)|