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:

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

#include <vector>
#include <string>
using namespace std;
class Solution {
public:
    vector<string> generateParenthesis(int n) {
        vector<string> result;
        vector<bool> path;
        dfs(0,0,0,path,result,n);
        return result;   
    }

private:
    void dfs(int curr,int r,int l,vector<bool>& path,
        vector<string>& result,int n){
        if(curr == 2*n){
            string s;
            for(int i=0;i<2*n;i++){
                if(path[i]==true){
                    s.push_back('(');
                }else s.push_back(')');
            }
            result.push_back(s);
            return;
        }
        
        if(r==l){
            path.push_back(true);
            dfs(curr+1,r+1,l,path,result,n);
            path.pop_back();
        }else if(r>l && r<n){
            path.push_back(true);
            dfs(curr+1, r+1, l, path, result, n);
            path.pop_back();
            path.push_back(false);
            dfs(curr+1, r, l+1, path, result, n);
            path.pop_back();
        }else{
            path.push_back(false);
            dfs(curr+1,r,l+1,path,result,n);
            path.pop_back();
        }
        
    }
};

int main()
{
    Solution s;
    vector<string> result;
    result = s.generateParenthesis(3);
    return 0;
}