Fix/generate parentheses iterative approach

backtracking/generate_parentheses_iterative.py

@@ -0,0 +1,72 @@
+"""
+    >>> generate_parentheses_iterative(1)
+    ['()']
+
+    >>> generate_parentheses_iterative(0)
+    ['']
+
+Generate all valid combinations of parentheses (Iterative Approach).
+
+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 ')'.
+
+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*n, add it to the result.
+    c. If open count is < n, push new combination with added '(' onto the stack.
+    d. If close count < open count, push new combination with added ')' on stack.
+5. Return the result containing all valid combinations.
+
+Args:
+    n (int): The desired length of the parentheses combinations
+
+Returns:
+    list: A list of strings representing valid combinations of parentheses
+
+Time Complexity:
+    O(2^(2n))
+
+Space Complexity:
+    O(2^(2n))
+"""
+
+
+def generate_parentheses_iterative(length: int = 0) -> list:
+    """
+    >>> generate_parentheses_iterative(3)
+    ['()()()', '()(())', '(())()', '(()())', '((()))']
+
+    >>> generate_parentheses_iterative(2)
+    ['()()', '(())']
+
+    >>> generate_parentheses_iterative()
+    ['']
+
+    """
+    result = []
+    stack = []
+
+    # Each element in stack has a tuple (current_combination, open_count, close_count).
+    stack.append(("", 0, 0))
+
+    while stack:
+        current_combination, open_count, close_count = stack.pop()
+
+        if len(current_combination) == 2 * length:
+            result.append(current_combination)
+        else:
+            if open_count < length:
+                stack.append((current_combination + "(", open_count + 1, close_count))
+            if close_count < open_count:
+                stack.append((current_combination + ")", open_count, close_count + 1))
+
+    return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print(generate_parentheses_iterative(3))