给定一个仅包含数字 2-9 的字符串，返回所有它能表示的字母组合。
给出数字到字母的映射如下（与电话按键相同）。注意 1 不对应任何字母。

示例:

输入："23"
输出：["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"].
说明:
尽管上面的答案是按字典序排列的，但是你可以任意选择答案输出的顺序。

代码

class Solution {
public:
    vector<string> letterCombinations(string digits) {
        vector<string> res;
        if (digits.empty()) return res;
        string dict[] = {"abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"};//建立一个字典，用来保存每个数字所代表的字符串
        letterCombinationsDFS(digits, dict, 0, "", res);
        return res;
    }
    void letterCombinationsDFS(string digits, string dict[], int level, string out, vector<string> &res) {
        if (level == digits.size()) res.push_back(out);
        else {
            string str = dict[digits[level] - '2'];
            for (int i = 0; i < str.size(); ++i) {
                out.push_back(str[i]);
                letterCombinationsDFS(digits, dict, level + 1, out, res);
                out.pop_back();
            }
        }
    }
};