Add type hints and improve code quality for generate_parentheses_iterative

Author: zain-cs

backtracking/generate_parentheses_iterative.py

@@ -5,7 +5,7 @@ def generate_parentheses_iterative(length: int) -> list[str]:
     The algorithm works as follows:
     1. Initialize an empty list to store the combinations.
     2. Initialize a stack to keep track of partial combinations.
-    3. Start with empty string and push it onstack along with the counts of '(' and ')'.
+    3. Start with empty string and push it on stack along with the counts of '(' and ')'.
     4. While the stack is not empty:
         a. Pop a partial combination and its open and close counts from the stack.
         b. If the combination length is equal to 2*length, add it to the result.
@@ -17,19 +17,13 @@ def generate_parentheses_iterative(length: int) -> list[str]:
         length: The desired length of the parentheses combinations
 
     Returns:
-        A list of strings representing valid combinations of parentheses
-
-    Raises:
-        ValueError: If length is negative
-        TypeError: If length is not an integer
-
+        A list of strings representing valid combinations of parentheses.
+        
     Time Complexity:
-         O(4^n / sqrt(n)) - Catalan number growth
-
+        O(2^(2*length))
     Space Complexity:
-        O(4^n / sqrt(n)) - Storage for all valid combinations
-
-
+        O(2^(2*length))
+        
     >>> generate_parentheses_iterative(3)
     ['()()()', '()(())', '(())()', '(()())', '((()))']
     >>> generate_parentheses_iterative(2)
@@ -38,22 +32,7 @@ def generate_parentheses_iterative(length: int) -> list[str]:
     ['()']
     >>> 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
     """
-    # 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 [""]
 
@@ -65,22 +44,20 @@ def generate_parentheses_iterative(length: int) -> list[str]:
     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))
 
     return result
 
 
+
 if __name__ == "__main__":
     import doctest