diff --git a/backtracking/generate_parentheses_iterative.py b/backtracking/generate_parentheses_iterative.py new file mode 100644 index 000000000000..4fdbb80ed117 --- /dev/null +++ b/backtracking/generate_parentheses_iterative.py @@ -0,0 +1,73 @@ +""" + 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(n: int) -> list: + """ + >>> generate_parentheses(3) + ['()()()', '()(())', '(())()', '(()())', '((()))'] + + >>> generate_parentheses(2) + ['()()', '(())'] + + >>> generate_parentheses(1) + ['()'] + + >>> generate_parentheses(0) + [''] + + """ + 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 * n: + result.append(current_combination) + else: + if open_count < n: + 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 + + +def main() -> None: + print(generate_parentheses(4)) + + +if __name__ == "__main__": + import doctest + + doctest.testmod() + main()