注意：本文介绍的方案有误，正确答案为240种。

 

遇到一个问题如下

正六面体染色

正六面体用4种颜色染色。

共有多少种不同的染色样式？

要考虑六面体可以任意旋转、翻转。

算法如下：

1 #include 
     
       2 #pragma warning(disable: 4786) 3 #include 
      
        4  5 using namespace std; 6  7 void print(int arr[], int total_index) 8 { 9     const char *szColors[] = {
   "红", "黄", "蓝", "绿", "白", "黑", "紫", "灰", "粉"};10     const char *szSides[] = {
   "前", "右", "后", "左", "上", "下"};11     int index;12 13     printf("%d: ", total_index);14 15     for (index = 0; index < 6; index += 1)16     {17         printf("%s:%s ", szSides[index], szColors[arr[index]]);18     }19 20     printf("\n");21 }22 23 void resolve(int nColorCount)24 {25     set
       
         setHashs;26     int arr[6 * 2];27     int index, index2, index3 = 0;28 29     for (arr[0] = 0; arr[0] < nColorCount; arr[0] += 1)30         for (arr[1] = 0; arr[1] < nColorCount; arr[1] += 1)31             for (arr[2] = 0; arr[2] < nColorCount; arr[2] += 1)32                 for (arr[3] = 0; arr[3] < nColorCount; arr[3] += 1)33                     for (arr[4] = 0; arr[4] < nColorCount; arr[4] += 1)34                         for (arr[5] = 0; arr[5] < nColorCount; arr[5] += 1)35                         {36                             int hash_big = 0;37 38                             for (index = 0; index < 6; index += 1)39                             {40                                 arr[index + 6] = arr[index];41                             }42 43                             for (index = 0; index < 6; index += 1)44                             {45                                 int hash_this = 0;46 47                                 for (index2 = 0; index2 < 6; index2 += 1)48                                 {49                                     hash_this *= 10;50                                     hash_this += arr[index + index2];51                                 }52 53                                 if (hash_this > hash_big)54                                 {55                                     hash_big = hash_this;56                                 }57                             }58 59                             if (setHashs.find(hash_big) == setHashs.end())60                             {61                                 setHashs.insert(hash_big);62                                 print(arr, ++index3);63                             }64                         }65 }66 67 int main()68 {69     resolve(4);70     return 0;71 }
       
      
     

 

答案是700种方案