uva1352(排列组合)

来源：互联网发布：网络骑士小说编辑：程序博客网时间：2024/05/22 14:02

题意:

给你几个正方体,每个正方体的六个面都涂有颜色,现在你要把这些正方体重新涂色,使得所有正方体都一样(六个面颜色相同,正方体可以旋转),问最少重涂几个面;

思路:

首先,如果正方体不能旋转,那么要怎么涂.很显然,每一面都找出一样的颜色最多的那个颜色,把其他的都涂成这个颜色,那么就是最少的.

但是正方体可以旋转,通过计算我们可以知道,每一个正方体有24种旋转方式,而这个道题正方体最多4个,而且第一个不需要旋转.那么就是总共有24^3种可能性.

那么我们把每种可能性都通过上面那种方法算出最少涂的面,找出最小值:

AC:

#include<cstdio>#include<cstring>#include<algorithm>using namespace std;const int N = 30;const int INF = 0x3f3f3f3f;const int dice[24][6] = {{2, 1, 5, 0, 4, 3}, {2, 0, 1, 4, 5, 3}, {2, 4, 0, 5, 1, 3}, {2, 5, 4, 1, 0, 3},  {4, 2, 5, 0, 3, 1}, {5, 2, 1, 4, 3, 0}, {1, 2, 0, 5, 3, 4}, {0, 2, 4, 1, 3, 5},  {0, 1, 2, 3, 4, 5}, {4, 0, 2, 3, 5, 1}, {5, 4, 2, 3, 1, 0}, {1, 5, 2, 3, 0, 4},  {5, 1, 3, 2, 4, 0}, {1, 0, 3, 2, 5, 4}, {0, 4, 3, 2, 1, 5}, {4, 5, 3, 2, 0, 1},  {1, 3, 5, 0, 2, 4}, {0, 3, 1, 4, 2, 5}, {4, 3, 0, 5, 2, 1}, {5, 3, 4, 1, 2, 0},  {3, 4, 5, 0, 1, 2}, {3, 5, 1, 4, 0, 2}, {3, 1, 0, 5, 4, 2}, {3, 0, 4, 1, 5, 2},  };int n,cnt,ans,cube[N][N],turn[N];char color[N][N];int color_to_num(char* str) {for(int i = 0 ; i < cnt ; i++) {if(strcmp(color[i], str) == 0)return i;}strcpy(color[cnt] , str);return cnt++;}void judge() {int total[N];int sum = 0;int m;for(int i = 0 ; i < 6 ;i++) {memset(total , 0 ,sizeof(total));m = 0;for(int j = 0 ; j < n ; j++) {int temp = dice[turn[j]][i];total[cube[j][temp]]++;m = max(m , total[cube[j][temp]]);}sum += n - m;}ans = min(sum , ans);}void dfs(int cur) {if(cur == n) {judge();return;}for(turn[cur] = 0 ; turn[cur] < 24 ;turn[cur]++) {dfs(cur + 1);}}int main() {while(scanf("%d",&n) && n) {char str[N];cnt = 0;for(int i = 0 ; i < n ; i++) {for(int j = 0 ; j < 6 ; j++) {scanf("%s",str);int num = color_to_num(str);cube[i][j] = num;}}ans = INF;dfs(1);printf("%d\n",ans);}}

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