Add/generate parentheses iterative approach (#10024)

* Generate parantheses iterative

* Generate parantheses iterative

* Generating parantheses code using iterative approach

* Update generate_parentheses_iterative.py

* updating DIRECTORY.md

* Update generate_parentheses_iterative.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update generate_parentheses_iterative.py

* Update generate_parentheses_iterative.py

* Update generate_parentheses_iterative.py

---------

Co-authored-by: nightmare10123 <pgadekar10123@gmail.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>
Co-authored-by: MaximSmolskiy <MaximSmolskiy@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

DIRECTORY.md

@@ -12,6 +12,7 @@
   * [Combination Sum](backtracking/combination_sum.py)
   * [Crossword Puzzle Solver](backtracking/crossword_puzzle_solver.py)
   * [Generate Parentheses](backtracking/generate_parentheses.py)
+  * [Generate Parentheses Iterative](backtracking/generate_parentheses_iterative.py)
   * [Hamiltonian Cycle](backtracking/hamiltonian_cycle.py)
   * [Knight Tour](backtracking/knight_tour.py)
   * [Match Word Pattern](backtracking/match_word_pattern.py)

backtracking/generate_parentheses_iterative.py

@@ -0,0 +1,62 @@
+def generate_parentheses_iterative(length: int) -> list:
+    """
+    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*length, add it to the result.
+        c. If open count < length, push new combination with added '(' on stack.
+        d. If close count < open count, push new combination with added ')' on stack.
+    5. Return the result containing all valid combinations.
+
+    Args:
+        length: The desired length of the parentheses combinations
+
+    Returns:
+        A list of strings representing valid combinations of parentheses
+
+    Time Complexity:
+        O(2^(2*length))
+
+    Space Complexity:
+        O(2^(2*length))
+
+    >>> generate_parentheses_iterative(3)
+    ['()()()', '()(())', '(())()', '(()())', '((()))']
+    >>> generate_parentheses_iterative(2)
+    ['()()', '(())']
+    >>> generate_parentheses_iterative(1)
+    ['()']
+    >>> generate_parentheses_iterative(0)
+    ['']
+    """
+    result = []
+    stack = []
+
+    # Each element in stack is 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)
+
+        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))