此文首发于我的个人博客：LeetCode 22. Generate Parentheses–Python 解法–广度优先、深度优先解法 — zhang0peter的个人博客

LeetCode题解文章分类：LeetCode题解文章集合
LeetCode 所有题目总结：LeetCode 所有题目总结

题目地址：Generate Parentheses - LeetCode

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:

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

这道题目看起来不难，只要把所有的可能性都输出即可。

可以深度优先，或者广度优先解决。

广度优先的Python解法如下，先输出 ()()()...

class Solution:
    def generateParenthesis(self, n: int) -> List[str]:
        def helper(s='', left=0, n=0):
            if n == 0:
                self.res.append(s+')'*left)
                return
            if left > 0:
                helper(s+')', left-1, n)
            helper(s+'(', left+1, n-1)
        self.res = []
        helper('', 0, n)
        return self.res

深度优先解法如下，先 ((()))

class Solution:
    def generateParenthesis(self, n: int) -> List[str]:
        def helper(s='', left=0, n=0):
            if n == 0:
                self.res.append(s+')'*left)
                return
            helper(s+'(', left+1, n-1)
            if left > 0:
                helper(s+')', left-1, n)
        self.res = []
        helper('', 0, n)
        return self.res