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vector<string> letterCombinations(string digits) {
        vector<string> dict = {"", "", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"};
        vector<string> res;
        DFS(dict, res, "", digits, 0);
        return res;
    }
    
    // very concise!!!
    void DFS(vector<string> &dict, vector<string> &res, string code, string digits, int kth) {
        if(kth == digits.size()) {
            res.push_back(code);
            return;
        }
        int d = digits[kth] - '0';
        string letters = dict[d];
        for(int i=0; i<letters.size(); i++) 
            DFS(dict, res, code + letters[i], digits, kth+1);
    }




//  forget about below implentations


void combine(vector<string>& result, string digits, int level,
                 vector<string> summary, string tmp) {
        if (level == digits.size()) {
            result.push_back(tmp);
            return;
        }
        string current_sum = summary[digits[level] - '2'];
        for(int i = 0; i < current_sum.size(); i++) {
            tmp.push_back(current_sum[i]);
            combine(result, digits, level + 1, summary, tmp);
            // c++ 11, used to be ==> tmp.erase(tmp.size()-1);
            tmp.pop_back();
        }
    }



// iterative solution

vector<string> append_letters(vector<string> &res, const string& letters) { // use const?
    vector<string> updated;
    if(letters == "") {
        updated = res;
        return updated;
    }
    
    if(res.empty()) {
        for(char c : letters) {
            //updated.push_back("" + c); // cannot write "" + c. those two cannot be added!
            string s = "";
            updated.push_back(s + c);
        }
    } else {
        for(string& s : res)  {
            for(char c : letters){
                updated.push_back(s + c);
            }
        }
    }
    return updated;
}

vector<string> get_all_words_on_phone_number(const string& digits) {
    vector<string> res;
    if(digits.empty()) return res;
    vector<string> vs = {"", "", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"};
    for(int i=0; i<digits.size(); i++) {
        string letters = vs[digits[i] - '0'];
        res = append_letters(res, letters);
    }
    return res;
}

int main()
{
    vector<string> res = get_all_words_on_phone_number("234");
    for(auto s : res) cout << s << "\n";
    cout << ".";
}

/*
output:
adg
adh
adi
aeg
aeh
aei
afg
afh
afi
bdg
bdh
bdi
beg
beh
bei
bfg
bfh
bfi
cdg
cdh
cdi
ceg
ceh
cei
cfg
cfh
cfi
*/