From 877fcd33d4c0856c63447ab47554a761cce8d2c8 Mon Sep 17 00:00:00 2001
From: zain-cs <mzainulabidin.cs@gmail.com>
Date: Wed, 11 Feb 2026 23:27:13 +0500
Subject: [PATCH 1/2] Improve generate_parentheses_iterative: Add input
 validation, type hints, and documentation

- Added input validation for negative and non-integer inputs
- Improved type hints (list[str] and tuple types)
- Updated complexity analysis to Catalan number growth
- Added doctests for error cases
- Added explicit edge case handling for length=0
- Improved inline comments for clarity
---
 .../generate_parentheses_iterative.py         | 44 +++++++++++++++----
 1 file changed, 35 insertions(+), 9 deletions(-)

diff --git a/backtracking/generate_parentheses_iterative.py b/backtracking/generate_parentheses_iterative.py
index 175941c7ae95..53984a4fdd35 100644
--- a/backtracking/generate_parentheses_iterative.py
+++ b/backtracking/generate_parentheses_iterative.py
@@ -1,4 +1,4 @@
-def generate_parentheses_iterative(length: int) -> list:
+def generate_parentheses_iterative(length: int) -> list[str]:
     """
     Generate all valid combinations of parentheses (Iterative Approach).
 
@@ -18,13 +18,18 @@ def generate_parentheses_iterative(length: int) -> list:
 
     Returns:
         A list of strings representing valid combinations of parentheses
+    
+    Raises:
+        ValueError: If length is negative
+        TypeError: If length is not an integer
 
     Time Complexity:
-        O(2^(2*length))
+         O(4^n / sqrt(n)) - Catalan number growth
 
     Space Complexity:
-        O(2^(2*length))
+        O(4^n / sqrt(n)) - Storage for all valid combinations
 
+    
     >>> generate_parentheses_iterative(3)
     ['()()()', '()(())', '(())()', '(()())', '((()))']
     >>> generate_parentheses_iterative(2)
@@ -33,22 +38,43 @@ def generate_parentheses_iterative(length: int) -> list:
     ['()']
     >>> generate_parentheses_iterative(0)
     ['']
+    >>> generate_parentheses_iterative(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: length must be non-negative
+    >>> generate_parentheses_iterative(2.5)
+    Traceback (most recent call last):
+        ...
+    TypeError: length must be an integer
     """
-    result = []
-    stack = []
-
+    # Input validation
+    if not isinstance(length, int):
+        raise TypeError("length must be an integer")
+    if length < 0:
+        raise ValueError("length must be non-negative")
+    
+    # Handle edge case
+    if length == 0:
+        return [""]
+    
+    result: list[str] = []
+    
     # Each element in stack is a tuple (current_combination, open_count, close_count)
-    stack.append(("", 0, 0))
+    stack: list[tuple[str, int, int]] = [("", 0, 0)]
 
     while stack:
         current_combination, open_count, close_count = stack.pop()
 
+        # If we've used all pairs, add to result
         if len(current_combination) == 2 * length:
             result.append(current_combination)
-
+            continue
+        
+        # Add '(' if we haven't used all open parentheses
         if open_count < length:
             stack.append((current_combination + "(", open_count + 1, close_count))
-
+            
+        # Add ')' if it maintains validity
         if close_count < open_count:
             stack.append((current_combination + ")", open_count, close_count + 1))
 

From 93bb327a23acc1cdf7666591c2e77f1bec29313c Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Wed, 11 Feb 2026 18:29:54 +0000
Subject: [PATCH 2/2] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 backtracking/generate_parentheses_iterative.py | 14 +++++++-------
 1 file changed, 7 insertions(+), 7 deletions(-)

diff --git a/backtracking/generate_parentheses_iterative.py b/backtracking/generate_parentheses_iterative.py
index 53984a4fdd35..918d809e92f0 100644
--- a/backtracking/generate_parentheses_iterative.py
+++ b/backtracking/generate_parentheses_iterative.py
@@ -18,7 +18,7 @@ def generate_parentheses_iterative(length: int) -> list[str]:
 
     Returns:
         A list of strings representing valid combinations of parentheses
-    
+
     Raises:
         ValueError: If length is negative
         TypeError: If length is not an integer
@@ -29,7 +29,7 @@ def generate_parentheses_iterative(length: int) -> list[str]:
     Space Complexity:
         O(4^n / sqrt(n)) - Storage for all valid combinations
 
-    
+
     >>> generate_parentheses_iterative(3)
     ['()()()', '()(())', '(())()', '(()())', '((()))']
     >>> generate_parentheses_iterative(2)
@@ -52,13 +52,13 @@ def generate_parentheses_iterative(length: int) -> list[str]:
         raise TypeError("length must be an integer")
     if length < 0:
         raise ValueError("length must be non-negative")
-    
+
     # Handle edge case
     if length == 0:
         return [""]
-    
+
     result: list[str] = []
-    
+
     # Each element in stack is a tuple (current_combination, open_count, close_count)
     stack: list[tuple[str, int, int]] = [("", 0, 0)]
 
@@ -69,11 +69,11 @@ def generate_parentheses_iterative(length: int) -> list[str]:
         if len(current_combination) == 2 * length:
             result.append(current_combination)
             continue
-        
+
         # Add '(' if we haven't used all open parentheses
         if open_count < length:
             stack.append((current_combination + "(", open_count + 1, close_count))
-            
+
         # Add ')' if it maintains validity
         if close_count < open_count:
             stack.append((current_combination + ")", open_count, close_count + 1))