leetcode22 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:
[
  "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"
]
"""
"""
每次增加括号时需要判断之前字符串中左右括号的个数
判断增加‘(’或‘)’依据为，
#若当前字符串的长度等于2n则字符串存入列表中
若之前字符串中左括号个数小于n，则应增加左括号，
若之前字符串中右括号个数小于左括号，则应增加右括号
"""
class Solution:
    def generateParenthesis(self, n):
        result = []
        # 函数嵌套
        def trackback(S="", left=0, right=0):
            if len(S) == 2 * n:
                result.append(S)
            if left < n:
                trackback(S + '(', left + 1, right)
            if right < left:
                trackback(S + ')', left, right + 1)
        trackback()
        return result