leetcode: 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:

"((()))", "(()())", "(())()", "()(())", "()()()"

class Solution {
public:
void internalGenerateParenthesis(vector<string> & result,
string &s,
int n,
int left_num,
int right_num) {
if ((n == left_num) && (n == right_num)) {
result.push_back(s);
}

if (left_num < n) {
s.push_back('(');
internalGenerateParenthesis(result, s, n, left_num + 1, right_num);
s.pop_back();
}

if (right_num < left_num) {
s.push_back(')');
internalGenerateParenthesis(result, s, n, left_num, right_num + 1);
s.pop_back();
}
}

vector<string> generateParenthesis(int n) {
vector<string> result;
string s;

internalGenerateParenthesis(result, s, n, 0, 0);

return result;
}
};