22. 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:

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

本题开始做的时候以为用栈比较好，但是做错了，后来看了discussion 发现答案解法很好。用了两个open，close来做为假想的栈，代码如下：

public class Solution {
    public List<String> generateParenthesis(int n) {
        List<String> res = new ArrayList<String>();
        backtracking(res,"",0,0,n);
        return res;
    }
    public void backtracking(List<String> res,String word,int open,int close,int max){
        if(word.length()==max*2){
            res.add(word);
            return ;
        }else{
            if(open<max){
                backtracking(res,word+"(",open+1,close,max);
            }
            if(close<open){
                backtracking(res,word+")",open,close+1,max);
            }
        }
    }
}