17. Letter Combinations of a Phone Number

Given a digit string, return all possible letter combinations that the number could represent.

A mapping of digit to letters (just like on the telephone buttons) is given below.

Input:
Digit string "23"

Output:
 ["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"].

Note:
Although the above answer is in lexicographical order, your answer could be in any order you want.

S: recursion O(4^n)

class Solution {
public:
    vector<string> letterCombinations(string digits) {
        vector<string> result;
        if (digits.size() == 0) return result;
        letter = vector<string>(10, "");
        letter[2] = "abc";
        letter[3] = "def";
        letter[4] = "ghi";
        letter[5] = "jkl";
        letter[6] = "mno";
        letter[7] = "pqrs";
        letter[8] = "tuv";
        letter[9] = "wxyz";     
        dfs(digits, 0, "", result);
        return result;
    }
private:
    vector<string> letter;
    void dfs(string digit, int start, string s, vector<string>& result) {
        if (start == digit.size()) result.push_back(s);
        int idx = digit[start] - '0';
        for (char c : letter[idx]) {
            dfs(digit, start + 1, s + c, result);
        }
    }
};