23 leetcode - Generate Parentheses

#!/usr/bin/python
# -*- coding: utf-8 -*-
'''
英文:Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.
举例:
given n = 3, a solution set is:
[ "((()))",
  "(()())",
  "(())()",
  "()(())",
  "()()()"]
'''
class Solution(object):
    def generateParenthesis(self, n):
        """
        :type n: int
        :rtype: List[str]
        """
        if n < 1:
          return []
        result = []
        tmp = ['('] * n * 2
        left = n - 1
        right = n
        #第一个一定要为(
        self.fun(tmp,result,left,right,1)
        return result

    def fun(self,tmp,result,left,right,index):
        if left == 0 and right == 0:
            result.append(''.join(tmp))

        if left > 0:  #只要有(,就能放
            tmp[index] = '('
            self.fun(tmp,result,left - 1,right,index + 1)

        if right > 0 and left < right:#(放了,)才能放,保证有一个(与之配对
            if left == 0:  #小优化....
                for i in range(right):
                    tmp[index + i] = ')'
                result.append(''.join(tmp))
                return 0
            tmp[index] = ')'
            self.fun(tmp,result,left,right - 1,index + 1)

if __name__ == "__main__":
    s = Solution()
    print s.generateParenthesis(3)