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()
原文：http://www.cnblogs.com/sherylwang/p/5764756.html