面试题：给定一个的电话号码，问生成的所有字母组合（容易记的电话号码）

题目： 有时候大家会很奇怪，为啥电话的键盘上会有ABC...这样的字母，尤其是在手机诞生之前就已经存在了。其实这些字母除了再发短信时有用，还有另一个作用是使电话号码容易记忆，这在美国比较的流行，比如拨打310-GINO便可向GINO订购比萨，其中GINO对应的就是4466。

哈，好玩吧。现在问题是这样的给定一个电话号码，比如123-4567或12345678，问其所有的字母组合。

比如：给定23，所有组合就是ad, ae, af, bd, be, bf, cd, ce, cf。

解答：

自己写了个递归实现。

大体思想是：

1. 建一个Mapping表，用于查找数字对应的字符。

2. 如果是一个数字，返回所有可能性的组合。

3. 如果多个数字，返回最后一个数字对应的组合跟前面已生产的字符串进行组合（笛卡尔乘积）

using System;
using System.Collections.Generic;
using System.Text;
using System.Text.RegularExpressions;

namespace NumberToWord
{
    class Program
    {
        static void Main(string[] args)
        {
            foreach (String result in NumberToWord.ConvertNumberToWord("2543693"))
            {
                Console.WriteLine(result);
            }
        }
    }
    class NumberToWord
    {
        // Mapping Table
        // PS: We may use Char[][] instead here.
                                                    //   0
                                                    //   1        2       3
                                                    //   4        5       6
                                                    //   7        8,      9
        private static String[] NumberMappingTable = {
                                                         " ",
                                                         " ",    "ABC",  "DEF",
                                                         "GHI",  "JKL",  "MNO",
                                                         "PQRS", "TUV",  "WXYZ"
                                                     };
        public static List<String> ConvertNumberToWord(String number)
        {
            List<String> resultList = new List<string>();

            // Return an empty list when input is empty.
            if (String.IsNullOrEmpty(number.Trim()))
            {
                return resultList;
            }

            // Use regular expression to test if the input number is valid.
            // Valid Characters are : 0123456789-*#
            // Valid Number is like: 342-454-3432
            //                       4564334
            // length is from 1 to 11
            Regex reg = new Regex("([0-9*#-]){1,11}", RegexOptions.Compiled);
            if (!reg.IsMatch(number))
            {
                throw new ArgumentException("Number is not well formatted!", "number", new ArgumentException());
            }

            // Replace '*', '-' and '#' with zero for looking up mapping table.
            resultList = ConvertNumberToWordInternal(number.Replace('*', '0').Replace('#', '0').Replace('-', '0'));

            return resultList;
        }
        private static List<String> ConvertNumberToWordInternal(String validNumber)
        {
            List<String> resultList = new List<string>();

            // When it's the last (from left to right) number,
            // iterate characters it mapped and write them into result List.
            if (validNumber.Length == 1)
            {
                // Get mapped characters
                String mappedChars = NumberMappingTable[Convert.ToInt32(validNumber)];
                foreach (Char ch in mappedChars)
                {
                    resultList.Add(ch.ToString());
                }
            }
            // Otherwise we combine the characters mapped by the next (right to left) number 
            // with the List we already got from resolved numbers.
            else
            {
                List<String> resolvedList = ConvertNumberToWord(validNumber.Substring(0, validNumber.Length - 1));
                foreach (String resolvedString in resolvedList)
                {
                    // The next number (from left to right) mapped characters
                    String nextNumMappedChars = NumberMappingTable[Convert.ToInt32(validNumber[validNumber.Length - 1].ToString())];
                    foreach (Char ch in nextNumMappedChars)
                    {
                        resultList.Add(resolvedString + ch.ToString());
                    }
                }
            }

            return resultList;
        }
    }
}

等有时间写个非递归实现。