17. Letter Combinations of a Phone Number（电话号码的字母组合）

Medium

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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.

方法一：递归

import java.util.ArrayList;
import java.util.List;

class Solution {
    public List<String> letterCombinations(String digits) {
        List<String> result=new ArrayList<String>();  //存结果
        String[] map={"","","abc","def","ghi","jkl","mno","pqrs","tuv","wxyz"};
        char[]tmp=new char[digits.length()];
        if(digits.length()<1)
            return result;
        rec(digits,0,tmp,map,result);
        return result;
    }

    private void rec(String digits, int index, char[] tmp, String[] map, List<String> result) {
        if(index==digits.length()){
            result.add(new String(tmp));
            return;
        }
        char tmpChar=digits.charAt(index);
        for(int i=0;i< map[tmpChar - '0'].length();i++){
            tmp[index]=map[tmpChar-'0'].charAt(i);
            rec(digits,index+1,tmp,map,result);
        }
    }

}

方法二：回溯

import java.util.ArrayList;
import java.util.List;

class Solution {
    public List<String> letterCombinations(String digits) {
        List<String> result=new ArrayList<String>();  //存结果
        String[] map={"","","abc","def","ghi","jkl","mno","pqrs","tuv","wxyz"};
        StringBuilder tmp=new StringBuilder();
        if(digits.length()<1)
            return result;
        backtrack(digits, 0,tmp,map,result);
        return result;
    }

    private void backtrack(String digits, int index, StringBuilder tmp, String[] map, List<String> result) {
        if(index==digits.length()){
            result.add(new String(tmp));
            return;
        }
        char tmpChar=digits.charAt(index);
        for(int i=0;i< map[tmpChar - '0'].length();i++){
            tmp.append(map[tmpChar-'0'].charAt(i));
            backtrack(digits,index+1,tmp,map,result);
            tmp.deleteCharAt(tmp.length()-1);
        }
    }

}

总结：

递归是一种数据结构，是函数中调用本身来解决问题。

回溯就是通过不同的尝试来生成问题的解，有点类似于穷举，但是和穷举不同的是回溯会“剪枝”，意思就是对已经知道错误的结果没必要再枚举接下来的答案了。

回溯搜索是深度优先搜索（DFS）的一种。对于某一个搜索树来说（搜索树是起记录路径和状态判断的作用），回溯和DFS，其主要的区别是，回溯法在求解过程中不保留完整的树结构，而深度优先搜索则记下完整的搜索树。