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.
思路：
经典的backtracking（回溯算法）的题目。当一个题目，存在各种满足条件的组合，并且需要把它们全部列出来时，就可以考虑backtracking了。当然，backtracking在一定程度上属于穷举，所以当数据特别大的时候，不合适。而对于那些题目，可能就需要通过动态规划来完成。
　　这道题假设输入的是”23”，2对应的是”abc”，3对应的是”edf”，那么我们在递归时，先确定2对应的其中一个字母（假设是a），然后进入下一层，穷举3对应的所有字母，并组合起来（”ae”，”ad”，”af”），当”edf”穷举完后，返回上一层，更新字母b，再重新进入下一层。这个就是backtracing的基本思想。

public class Solution {    public List<String> letterCombinations(String digits) {                String[] table = new String[]{"","","abc","def","ghi","jkl","mno","pqrs","tuv","wxyz"};        List<String> list = new ArrayList<String>();                letterCombinations(list,digits,"",0,table);        return list;    }    private void letterCombinations (List<String> list, String digits, String curr, int index,String[] table) {                if (index == digits.length()) {            if(curr.length() != 0) list.add(curr);            return;        }        String temp = table[digits.charAt(index) - '0'];        for (int i = 0; i < temp.length(); i++) {                       String next = curr + temp.charAt(i);                       letterCombinations(list,digits,next,index+1,table);        }    }}