Brace Expansion II — C++

// Time:  O(p*l * log(p*l)), p is the production of all number of options
//                         , l is the length of a word
// Space: O(p*l)

class Solution {
public:
    vector<string> braceExpansionII(string expression) {
        int i = 0;
        return generateWords(expression, &i);
    }

private:
    vector<string> generateWords(const string& expr, int *i) {
        vector<vector<string>> options;
        while (*i != expr.length() &&
               string(",}").find(expr[*i]) == string::npos) {
            vector<string> tmp;
            if (string("{,}").find(expr[*i]) == string::npos) {
                tmp.emplace_back(string(1, expr[*i]));
                ++(*i);  // a-z
            } else if (expr[*i] == '{') {
                tmp = generateOption(expr, i);
            }
            options.emplace_back(move(tmp));
        }
        return formWords(options);
    }
      
    vector<string> generateOption(const string& expr, int *i) {
        set<string> option_set;
        while (*i != expr.length() && expr[*i] != '}') {
            ++(*i);  // { or ,
            for (const auto& option : generateWords(expr, i)) {
                option_set.emplace(option);
            }
        }
        ++(*i);  // }
        return vector<string>(option_set.cbegin(), option_set.cend());
    }
    
    vector<string> formWords(const vector<vector<string>>& options) {
        set<string> words_set;
        int total = 1;
        for (const auto& opt : options) {
            total *= opt.size();
        }
        for (int i = 0; i < total; ++i) {
            vector<string> tmp;
            int curr = i;
            for (int j = options.size() - 1; j >= 0; --j) {
                tmp.emplace_back(options[j][curr % options[j].size()]);
                curr /= options[j].size();
            }
            reverse(tmp.begin(), tmp.end());
            words_set.emplace(accumulate(tmp.cbegin(), tmp.cend(), string()));
        }
        return vector<string>(words_set.cbegin(), words_set.cend());
    }
};