vector<string> generateParenthesis(int n) {

vector<string> result;

generate(n, 0, 0, "", result);

return result;

}

void generate(int n, int open, int close, string str, vector<string>& result) {

if (open == n && close == n) {

result.push_back(str);

return;

}

if (open < n) {

generate(n, open + 1, close, str + '(', result);

}

if (open > close) {

generate(n, open, close + 1, str + ')', result);

}

}

vector<string> generateParenthesis(int n) {

stack<vector<string>> stk;

vector<string> result;

stk.push({"(", "1", "0"}); // {string, left_count, right_count}

while (!stk.empty()) {

for (int i = 0; i < stk.size(); i++) {

vector<string> item = stk.top();

stk.pop();

int left = stoi(item[1]), right = stoi(item[2]);

if (left == n && right == n) {

result.push_back(item[0]);

continue;

}

if (left < n) {

stk.push({item[0] + "(", to_string(++left), to_string(right)});

left--; // reverse left count

}

if (left > right) {

stk.push({item[0] + ")", to_string(left), to_string(++right)});

}

}

}

return result;

}