22. Generate Parentheses leetcode Python 2016 new Season

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:

"((()))", "(()())", "(())()", "()(())", "()()()"




bfs takes  n! time.. to get all the solutions.

class Solution(object):
    def bfs(self, left, right, depth, n, string, result):
        if depth == 2 * n:
            result.append(string)
            return
        if left < n:
            string += '('
            self.bfs(left + 1, right, depth + 1, n, string, result)
            string = string[:len(string) - 1]
        if left > right:
            string += ')'
            self.bfs(left, right + 1, depth + 1, n, string, result)
            string = string[:len(string) - 1]
    def generateParenthesis(self, n):
        """
        :type n: int
        :rtype: List[str]
        """
        result = []
        self.bfs(0, 0, 0, n, '', result)
        return result