Solution found with recursion

Top150Interview/22_Generate_Parenthesis.py

@@ -1,25 +1,57 @@
-def generateParenthesis(n: int) -> List[str]:
+def generateParenthesis(n: int) -> list[str]:
     """
     :type n: int
     :rtype: List[str]
     """
-    stack = []
-    pairs = ""
-    opening_brackets = {'('}
-    closing_brackets = {')'}
-    bracket_pairs = {')': '('}
+    # Attempted solution
+    # stack = []
+    # pairs = ""
+    # opening_brackets = {'('}
+    # closing_brackets = {')'}
+    # bracket_pairs = {')': '('}
 
-    # Create n pairs
-    for i in range(n):
-        pairs += "()"
-    # print(pairs)
+    # # Create n pairs
+    # for i in range(n):
+    #     pairs += "()"
+    # # print(pairs)
     
-    # Create and filter permutations
-    for pair in permutations(pairs):
-        parenthesis = "".join(pair)
-        # print(pair)
-        # print(parenthesis)
-        if parenthesis in bracket_pairs.keys():
-            if not stack or stack[-1] != bracket_pairs[parenthesis]:
-                print('bad')    
+    # # Create and filter permutations
+    # for pair in permutations(pairs):
+    #     parenthesis = "".join(pair)
+    #     # print(pair)
+    #     # print(parenthesis)
+    #     if parenthesis in bracket_pairs.keys():
+    #         if not stack or stack[-1] != bracket_pairs[parenthesis]:
+    #             print('bad')    
+
+    # Solution
+    def dfs(left, right, s):
+        print(f'left: {left}')
+        print(f'right: {right}')
+        print(f's:   {s}')
+
+
+        # Check if the length of the string is double the size of n
+        # Example n=2, s= "(())"
+        # Returns the string once 6 characters have been filled out
+        if len(s) == n * 2:
+            res.append(s)
+            return 
+        
+        # Continuously fills left parenthesis until n
+        # Example: n = 2, s = "(", then stops at s="(("
+        if left < n:
+            # Recursive call to add more to the left
+            dfs(left + 1, right, s + '(')
+
+        # Continuously fills right parenthesis until it matches with the left
+        # Example: n = 2, s = "(()", then stops at s="(())"
+        if right < left:
+            # Recursive call to add more to the right
+            dfs(left, right + 1, s + ')')
+
+    res = []
+    dfs(0, 0, '')
+    # print(res)
+    return res
 generateParenthesis(3)