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:

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

这题的核心在于如何约束保证最后的结果符合well-formed要求。本质而言如果我们用一个栈模拟，则每次添加一个‘（’，则入栈一个‘）’。栈空则无法加‘）’。否则可以加‘）’。也就是每一步都必须要保证‘（’的数目大于等于‘）’。最后‘（’和‘）’的数目都等于n。用l,r分别表示还需要添加的‘（’和‘）’的数目。代码如下：

class Solution(object):
    def generateParenthesis(self, n):
        """
        :type n: int
        :rtype: List[str]
        """
        if not n:
            return []
        cnt = 0 #the number of unadded )
        arr = [')','(']
        res = []
        self.generate([], n, n, res)
        return res
    def generate(self, cur, l, r, res):
        if l > r:  ＃非常关键
            return 
        if l == 0 and r == 0:
            res.append(''.join(cur))
            return 
        if l > 0:
            cur.append('(')
            self.generate(cur, l-1, r, res)
            cur.pop()
        if r > 0:
            cur.append(')')
            self.generate(cur, l, r-1, res)
            cur.pop()