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:

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

格式正确的原则：左括号先于右括号出现，因此用变量分别计数左括号和右括号出现的次数，一开始都是n次，出现一次就减一。当left<right时才加入右括号。backtracking方法。

class Solution {    public List<String> generateParenthesis(int n) {        List<String> res = new ArrayList<String>();        doParenthesis(res,n,n,"");        return res;    }    public void doParenthesis(List<String> res,int left,int right,String s){        if(left==0&&right==0){            res.add(s);            return;        }        if(left>0)            doParenthesis(res,left-1,right,s+"(");        if(right>0&&left<right)            doParenthesis(res,left,right-1,s+")");    }}