22. Generate Parentheses 生成括号

 Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

For example, given n = 3, a solution set is:

[
  "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"
]

class Solution:
    def generateParenthesis(self, n):
        """
        :type n: int
        :rtype: List[str]
        """
        res = []
        def gen(s="", open=0, close=0):
            if len(s) is 2 * n:
                res.append(s)
            else:
                if open < n:
                    gen(s + "(", open + 1, close)
                if close < open:
                    gen(s + ")", open, close + 1)
        gen()
        return res

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