Generate Parentheses

def generateParenthesis(n):
    result = []
    path = []

    def is_balanced(text):
        balance = 0
        for ch in text:
            balance += 1 if ch == "(" else -1
            if balance < 0:
                return False  # a ")" with nothing open to close
        return balance == 0

    def fill():
        if len(path) == 2 * n:
            text = "".join(path)
            if is_balanced(text):
                result.append(text)
            return
        for ch in "()":  # "(" first keeps the output sorted
            path.append(ch)
            fill()
            path.pop()

    fill()
    return result

def generateParenthesis(n):
    result = []
    path = []

    def backtrack(opened, closed):
        if len(path) == 2 * n:
            result.append("".join(path))
            return
        # "(" sorts before ")", so trying it first keeps the output sorted
        if opened < n:
            path.append("(")
            backtrack(opened + 1, closed)
            path.pop()
        if closed < opened:  # only close a pair that is open
            path.append(")")
            backtrack(opened, closed + 1)
            path.pop()

    backtrack(0, 0)
    return result