solved 'Generate Parentheses' on LeetCode https://leetcode.com/problems/generate-parentheses/

paren_gen.py

class Solution(object):
    def generateParenthesis(self, n):
        """
        :type n: int
        :rtype: List[str]
        """
        self.valid_parens = []
        self.n = n
        # 0 open, 0 closed, recursively build valid strings.
        self.buildParenString(0, 0, '')
        return self.valid_parens
    
    def buildParenString(self, opened, closed, curr_str):
        if closed == self.n:
            self.valid_parens.append(curr_str)
        else:
            # Open another parenthesis if possible.
            if opened < self.n:
                self.buildParenString(opened + 1, closed, curr_str + '(')
            # Can only close them if there is more opened brackets.
            if opened > closed:
                self.buildParenString(opened, closed + 1, curr_str + ')')