diff --git a/DIRECTORY.md b/DIRECTORY.md index 0636ba0a7ecc..41a2d2e9af03 100644 --- a/DIRECTORY.md +++ b/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) diff --git a/backtracking/generate_parentheses_iterative.py b/backtracking/generate_parentheses_iterative.py new file mode 100644 index 000000000000..175941c7ae95 --- /dev/null +++ b/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))