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# 17.Letter-Combinations-of-a-Phone-Number

## 题目描述

Given a string containing digits from 2-9 inclusive, 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. Note that 1 does not map to any letters.
Example:
Input: "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.

## 代码

### Approach 1: Backtracking

Complexity Analysis
• Time complexity : O(3^N×4^M) where `N` is the number of digits in the input that maps to 3 letters (e.g. `2, 3, 4, 5, 6, 8`) and `M` is the number of digits in the input that maps to 4 letters (e.g. `7, 9`), and `N+M` is the total number digits in the input.
• Space complexity : O(3^N×4^M) since one has to keep 3^N×4^M solutions.
class Solution {
Map<String, String> phone = new HashMap<String, String>(){{
put("2", "abc");
put("3", "def");
put("4", "ghi");
put("5", "jkl");
put("6", "mno");
put("7", "pqrs");
put("8", "tuv");
put("9", "wxyz");
}};
List<String> output = new ArrayList<String>();
public List<String> letterCombinations(String digits) {
if (digits.length() != 0) {
backtrack("", digits);
}
return output;
}
private void backtrack(String combination, String next_digits) {
if (next_digits.length() == 0) {