The 2013 ACM-ICPC Asia Changsha Regional Contest - K

Pocket Cube

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Time Limit: 2 Seconds      Memory Limit: 65536 KB

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Pocket Cube is a 3-D combination puzzle. It is a 2 × 2 × 2 cube, which means it is constructed by 8 mini-cubes. For a combination of 2 × 2 mini-cubes which sharing a whole cube face, you can twist it 90 degrees in clockwise or counterclockwise direction, this twist operation is called one twist step.

Considering all faces of mini-cubes, there will be totally 24 faces painted in 6 different colors (Indexed from 0), and there will be exactly 4 faces painted in each kind of color. If 4 mini-cubes' faces of same color rely on same large cube face, we can call the large cube face as a completed face.

  

Now giving you an color arrangement of all 24 faces from a scrambled Pocket Cube, please tell us the maximum possible number of completed faces in no more than N twist steps.

Index of each face is shown as below:

Input

There will be several test cases. In each test case, there will be 2 lines. One integer N (1 ≤ N ≤ 7) in the first line, then 24 integers C_i seperated by a sinle space in the second line. For index 0 ≤ i < 24, C_i is color of the corresponding face. We guarantee that the color arrangement is a valid state which can be achieved by doing a finite number of twist steps from an initial cube whose all 6 large cube faces are completed faces.

Output

For each test case, please output the maximum number of completed faces during no more than N twist step(s).

Sample Input

1
0 0 0 0 1 1 2 2 3 3 1 1 2 2 3 3 4 4 4 4 5 5 5 5
1
0 4 0 4 1 1 2 5 3 3 1 1 2 5 3 3 4 0 4 0 5 2 5 2

Sample Output

6
2
一共是12种变化，但是有等价的，最后每一纬是2种变换，一共是6种变换。

#include <iostream>
#include <string>
#include <string.h>
#include <map>
#include <stdio.h>
#include <algorithm>
#include <queue>
#include <vector>
#include <math.h>
#include <set>
#define Max(a,b) ((a)>(b)?(a):(b))
#pragma comment(linker, "/STACK:16777216")
using namespace std ;
typedef long long LL ;
struct Cube{
    int a[] ;

    void out(){
         printf("  %d%d    \n",a[],a[]) ;
         printf("  %d%d    \n",a[],a[]) ;
         printf("%d%d%d%d%d%d\n",a[],a[],a[],a[],a[],a[]) ;
         printf("%d%d%d%d%d%d\n",a[],a[],a[],a[],a[],a[]) ;
         printf("  %d%d    \n",a[],a[]) ;
         printf("  %d%d    \n",a[],a[]) ;
         printf("  %d%d    \n",a[],a[]) ;
         printf("  %d%d    \n",a[],a[]) ;
         puts("") ;
    }

    int complete_face(){
        int sum =  ;
        if(a[]==a[]&&a[]==a[]&&a[]==a[])
           sum++ ;
        if(a[]==a[]&&a[]==a[]&&a[]==a[])
           sum++ ;
        if(a[]==a[]&&a[]==a[]&&a[]==a[])
           sum++ ;
        if(a[]==a[]&&a[]==a[]&&a[]==a[])
           sum++ ;
        if(a[]==a[]&&a[]==a[]&&a[]==a[])
           sum++ ;
        if(a[]==a[]&&a[]==a[]&&a[]==a[])
           sum++ ;
        return sum ;
    }

    Cube R_colock(){
        Cube o ;
        for(int i =  ;i <  ;i++)
            o.a[i] = a[i] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        return o ;
    }

    Cube R_count_colock(){
        Cube o ;
        for(int i =  ;i <  ;i++)
            o.a[i] = a[i] ;
        o.a[]= a[];
        o.a[]= a[];
        o.a[]= a[];
        o.a[]= a[] ;
        o.a[]= a[] ;
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        return o ;
    }

    Cube U_colock(){
        Cube o ;
        for(int i =  ;i <  ;i++)
            o.a[i] = a[i] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        return o ;
    }

    Cube U_count_colock(){
        Cube o ;
        for(int i =  ;i <  ;i++)
            o.a[i] = a[i] ;
        o.a[]= a[];
        o.a[]= a[];
        o.a[]= a[];
        o.a[]= a[] ;
        o.a[]= a[] ;
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        return o ;
    }

    Cube F_colock(){
        Cube o ;
        for(int i =  ;i <  ;i++)
            o.a[i] = a[i] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        o.a[] = a[] ;
        return o ;
    }

    Cube F_count_colock(){
        Cube o ;
        for(int i =  ;i <  ;i++)
            o.a[i] = a[i] ;
        o.a[]= a[];
        o.a[]= a[];
        o.a[]= a[];
        o.a[]= a[] ;
        o.a[]= a[] ;
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        o.a[] =a[];
        return o ;
    }

};

int N ;
int ans ;

void dfs(Cube cb ,int step){
     Cube o ;
     if(step>N)
        return  ;
     if(ans == )
        return  ;

     o = cb.F_colock() ;
     ans = Max(ans,o.complete_face()) ;
     dfs(o,step+) ;

     o = cb.F_count_colock() ;
     ans = Max(ans,o.complete_face()) ;
     dfs(o,step+) ;

     o = cb.R_colock() ;
     ans = Max(ans,o.complete_face()) ;
     dfs(o,step+) ;

     o = cb.R_count_colock() ;
     ans = Max(ans,o.complete_face()) ;
     dfs(o,step+) ;

     o = cb.U_colock();
     ans = Max(ans,o.complete_face()) ;
     dfs(o,step+) ;

     o = cb.U_count_colock() ;
     ans = Max(ans,o.complete_face()) ;
     dfs(o,step+) ;
}

int main(){
   Cube now ;
   while(scanf("%d",&N)!=EOF){
       for(int i =  ;i <  ;i++)
          scanf("%d",&now.a[i]) ;
       ans = now.complete_face() ;
       dfs(now,) ;
       printf("%d\n",ans)  ;
   }
   return  ;
}