LA 3401

彩色立方体、

【分析】

弄清楚24种状态，可以由标准姿态旋转而来。

计算24种状态：

#include <iostream>
#include <string>

int left[] = { ,,,,, };
int up[] = { ,,,,, };

//按照排列T旋转姿态p
void rot(int *T, int *p)
{
    int q[];
    memcpy(q, p, sizeof(q));
    for (int i = ; i < ; i++)
        p[i] = T[q[i]];
}

void enumerate_permutations()
{
    int p0[] = { ,,,,, };
    printf("int dice24[24][6] = {\n");
    for (int i = ; i < ; i++)
    {
        int p[];
        memcpy(p, p0, sizeof(p0));
        if (i == )rot(up, p);
        if (i == ) { rot(left, p); rot(up, p); }
        if (i == ) { rot(up, p); rot(up, p); }
        if (i == ) { rot(left, p); rot(left, p); rot(left, p); rot(up, p); }
        if (i == ) { rot(left, p); rot(left, p); rot(up, p); }
        for (int j = ; j < ; j++)
        {
            printf("{%d,%d,%d,%d,%d,%d},\n", p[], p[], p[], p[], p[], p[]);
            rot(left, p);
        }
    }
    printf("};\n");
}

int main()
{
    enumerate_permutations();
    return ;
}

得到结果

直接用到最终程序中

//2019.4.23 彩色立方体
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using namespace std;

const int maxn = ;
int n, dice[maxn][], ans;
int dice24[][] = {
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
    { ,,,,, },
};

vector<string> names;
int ID(const char* name)
{
    string s(name);
    int n = names.size();
    for (int i = ; i < n; i++)
        if (names[i] == s) return i;
    names.push_back(s);
    return n;
}

int r[maxn], color[maxn][];

void check()
{
    for (int i = ; i < n; i++)
        for (int j = ; j < ; j++)
            color[i][dice24[r[i]][j]];
    int tot = ;
    for (int j = ; j < ; j++)
    {
        int cnt[maxn * ];
        memset(cnt, , sizeof(cnt));
        int maxface = ;
        for (int i = ; i < n; i++)
            maxface = max(maxface;
            ++cnt[color[i][j]]);
            tot += n - maxface;
    }
    ans = min(ans, tot);
}

void dfs(int d)
{
    if (d == n) check();
    else for (int i = ; i < ; i++)
    {
        r[d] = i;
        dfs(d + );
    }
}

int main()
{
    while (scanf_s("%d", &n) ==  && n)
    {
        names.clear();
        for(int i=;i<n;i++)
            for (int j = ; j < ; j++)
            {
                char name[];
                scanf_s("%s", name);
                dice[i][j] = ID(name);
            }
        ans = n * ;
        r[] = ;
        dfs();
        printf("%d\n", ans);
    }
    return ;
}