leetcode: 22. Generate Parentheses

# 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:
#
# [
#   "((()))",
#   "(()())",
#   "(())()",
#   "()(())",
#   "()()()"
# ]

l_num = 剩余的 左括号数
r_num = 剩余的 右括号数

只需要保证 l_num <= r_num ，当前的组合就一定是有效的。

class Solution():
    def generateParenthesis(self, n):
        res = []
        self.generate(res, '', n, n)
        return res
    def generate(self, res, cur, l_num, r_num):
        if l_num <= r_num:
            if r_num == 0:
                res.append(cur)
                return
            if l_num > 0:
                self.generate(res, cur+'(', l_num-1, r_num)
            if r_num > 0:
                self.generate(res, cur+')', l_num, r_num-1)


if __name__ == "__main__":
    assert Solution().generateParenthesis(3) == ['((()))', '(()())', '(())()', '()(())', '()()()']