uva 10733 The Colored Cubes

链接:http://uva.onlinejudge.org/external/107/10733.pdf

题意: N 种颜色可以涂成多少种立方体~

思路: 使正六面体保持不变的运动群总共有:

1.不变置换(1)(2)(3)(4)(5)(6), 共1个;

2.沿对面中心轴旋转 90度, 270度 (1)(2345)(6), (1)(5432)(6) 同类共 6个;

3.沿对面中心轴旋转 180度 (1)(24)(35)(6), 同类共 3个;

4.沿对角线轴旋转 120度, 240度 (152)(346), (251)(643) 同类共 8个;

5.沿对边中点轴旋转 180度 (16)(25)(43) 同类共 6个;

 1 #include <cstdio>

 2 #include <iostream>

 3 using namespace std;

 4 int N, M;

 5 typedef long long LL;

 6 LL P_M(int a, int b )

 7 {

 8     LL res=1,t=a;

 9     while(b){

10         if(b&1)res*=t;

11         t*=t;

12         b>>=1;

13     }

14     return res;

15 }

16 

17 int main()

18 {

19     int n;

20     while(scanf("%d",&n)!=EOF&&n)

21     {

22         LL ans=0;

23         ans += P_M(n,6);

24         ans += 3*P_M(n,4);

25         ans += 12*P_M(n,3);

26         ans += 8*P_M(n,2);

27         ans /= 24;

28         printf("%lld\n",ans);

29 

30     }

31 }

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