leetcode No22. Generate Parentheses

Question:

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:

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

Algorthim:

此题可以用二叉树的思想：
当左括号个数小于n时，添加左括号
当左括号个数大于右括号时，添加右括号
Ex：假设n=3，先添加左括号（右括号一样），如图所示：

Accepted Code：

class Solution {
public:
vector<string> generateParenthesis(int n) {
vector<string> res;
helper(res,"",n,n);
return res;
}
void helper(vector<string> &res,string tmp,int left,int right)
{
if(left==0 && right==0)
{
res.push_back(tmp);
return;
}
if(left>0)
helper(res,tmp+'(',left-1,right);
if(left<right)  //此时左括号的个数大于右括号
helper(res,tmp+')',left,right-1);
}
};