正六面体用若干种颜色染色的问题解法

注意：本文介绍的方案有误，正确答案为240种。http://books.google.com.hk/books?id=On5QwCvEA9kC&pg=PA105&lpg=PA105&dq=%E5%85%AD%E9%9D%A2%E4%BD%93+%E5%9B%9B%E7%A7%8D%E9%A2%9C%E8%89%B2&source=bl&ots=Lc7xqJW4IC&sig=uG7Llh_kDgZSN3BGhLWaBU0nANg&hl=en&sa=X&ei=NYtXUYHFIY-UiQfhnYDQCQ&ved=0CEsQ6AEwAw#v=onepage&q&f=false

 

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：

#include <stdio.h>
#pragma warning(disable: 4786)
#include <set>

using namespace std;

void print(int arr[], int total_index)
{
    const char *szColors[] = {"红", "黄", "蓝", "绿", "白", "黑", "紫", "灰", "粉"};
    const char *szSides[] = {"前", "右", "后", "左", "上", "下"};
    int index;

    printf("%d: ", total_index);

    for (index = 0; index < 6; index += 1)
    {
        printf("%s:%s ", szSides[index], szColors[arr[index]]);
    }

    printf("\n");
}

void resolve(int nColorCount)
{
    set<int> setHashs;
    int arr[6 * 2];
    int index, index2, index3 = 0;

    for (arr[0] = 0; arr[0] < nColorCount; arr[0] += 1)
        for (arr[1] = 0; arr[1] < nColorCount; arr[1] += 1)
            for (arr[2] = 0; arr[2] < nColorCount; arr[2] += 1)
                for (arr[3] = 0; arr[3] < nColorCount; arr[3] += 1)
                    for (arr[4] = 0; arr[4] < nColorCount; arr[4] += 1)
                        for (arr[5] = 0; arr[5] < nColorCount; arr[5] += 1)
                        {
                            int hash_big = 0;

                            for (index = 0; index < 6; index += 1)
                            {
                                arr[index + 6] = arr[index];
                            }

                            for (index = 0; index < 6; index += 1)
                            {
                                int hash_this = 0;

                                for (index2 = 0; index2 < 6; index2 += 1)
                                {
                                    hash_this *= 10;
                                    hash_this += arr[index + index2];
                                }

                                if (hash_this > hash_big)
                                {
                                    hash_big = hash_this;
                                }
                            }

                            if (setHashs.find(hash_big) == setHashs.end())
                            {
                                setHashs.insert(hash_big);
                                print(arr, ++index3);
                            }
                        }
}

int main()
{
    resolve(4);
    return 0;
}

 

答案是700种方案