# Letter Combinations of a Phone Number

`Backtracking`

**Medium**

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.

## Analysis

The phone digits to letters mapping:

```java
String[] KEYS = { "", "", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz" }
```

## Solution

### Recursive

利用递归，每次递归选择当前数字对应字符，然后将index+1，用下一个数字进入下一层递归；递归返回的条件是String path达到digits的长度，代表了一个组合的生成结束了，放入结果中即可。

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 times 4^M solutions.

[https://leetcode.com/problems/letter-combinations-of-a-phone-number/solution/](https://leetcode.com/problems/letter-combinations-of-a-phone-number/solution/)

```java
class Solution {
    private static final String[] KEYS = { "", "", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz" };

    public List<String> letterCombinations(String digits) {
        List<String> res = new ArrayList<>();
        if (digits.length() == 0) {
            return res;
        }

        helper(digits, 0, "", res);

        return res;
    }

    private void helper(String digits, int index, String path, List<String> res) {
        if (index == digits.length()) {
            res.add(path.toString());
            return;
        }
        String letters = KEYS[digits.charAt(index) - '0'];
        for (char c : letters.toCharArray()) {
            helper(digits, index + 1, path + c, res);
        }
    }
}
```

### Queue, BFS

```java
class Solution {
    public List<String> letterCombinations(String digits) {
        LinkedList<String> queue = new LinkedList();
        if (digits == null || digits.length() == 0) {
            return queue;
        }
        char[] digitChar = digits.toCharArray();

        String[] phone = new String[] {"", "", "abc", "def", "ghi", "jkl", "mno", "pqrs", "tuv", "wxyz"};
        queue.offer("");
        for (int i = 0; i < digitChar.length; i++) {
            char[] letters = phone[digitChar[i] - '0'].toCharArray();

            while  (queue.peek().length() == i) {
                String str = queue.poll();
                for (char c : letters) {
                    queue.offer(str + c);
                }
            }
        }
        return queue;
    }
}
```

[https://leetcode.com/problems/letter-combinations-of-a-phone-number/discuss/?currentPage=1\&orderBy=most\_votes\&query=](https://leetcode.com/problems/letter-combinations-of-a-phone-number/discuss/?currentPage=1\&orderBy=most_votes\&query=)
