2013
12-21

# The Rotation Game

The rotation game uses a # shaped board, which can hold 24 pieces of square blocks (see Fig.1). The blocks are marked with symbols 1, 2 and 3, with exactly 8 pieces of each kind.

Initially, the blocks are placed on the board randomly. Your task is to move the blocks so that the eight blocks placed in the center square have the same symbol marked. There is only one type of valid move, which is to rotate one of the four lines, each consisting of seven blocks. That is, six blocks in the line are moved towards the head by one block and the head block is moved to the end of the line. The eight possible moves are marked with capital letters A to H. Figure 1 illustrates two consecutive moves, move A and move C from some initial configuration.

The input consists of no more than 30 test cases. Each test case has only one line that contains 24 numbers, which are the symbols of the blocks in the initial configuration. The rows of blocks are listed from top to bottom. For each row the blocks are listed from left to right. The numbers are separated by spaces. For example, the first test case in the sample input corresponds to the initial configuration in Fig.1. There are no blank lines between cases. There is a line containing a single 0′ after the last test case that ends the input.

For each test case, you must output two lines. The first line contains all the moves needed to reach the final configuration. Each move is a letter, ranging from A’ to H’, and there should not be any spaces between the letters in the line. If no moves are needed, output No moves needed’ instead. In the second line, you must output the symbol of the blocks in the center square after these moves. If there are several possible solutions, you must output the one that uses the least number of moves. If there is still more than one possible solution, you must output the solution that is smallest in dictionary order for the letters of the moves. There is no need to output blank lines between cases.

1 1 1 1 3 2 3 2 3 1 3 2 2 3 1 2 2 2 3 1 2 1 3 3
1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3
0

AC
2
DDHH
2

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
#include<vector>
#include<cmath>
#include<map>
#include<string>
#define inf 1<<30
#define eps 1e-7
#define LD long double
#define LL long long
#define maxn 1005
using namespace std;
int central[8]={6,7,8,11,12,15,16,17};  //中间8个方格的位置
int rotation[4][7]={{0,2,6,11,15,20,22},{1,3,8,12,17,21,23},{10,9,8,7,6,5,4},{19,18,17,16,15,14,13}};//分别是每7个按顺序列好
int to[8]={0,1,2,3,1,0,3,2};    //8种转换分别对应于哪7个方块
int rev[8]={5,4,7,6,1,0,3,2};   //每一种转换的相反转换是哪个
int ope[maxn];    //存储转换操作
int a[24];    //原始序列
bool flag;  //是否有解
int depth;    //当前搜索深度
int get_h(int *m){   //得到估价函数h
int a=0,b=0,c=0;
for(int i=0;i<8;i++)
if(m[central[i]]==1)
a++;
else if(m[central[i]]==2)
b++;
else if(m[central[i]]==3)
c++;
return 8-max(a,max(b,c));
}
void change(int *b,int kind){
if(kind<4){
int tmp=b[rotation[to[kind]][0]];
for(int i=0;i<6;i++)
b[rotation[to[kind]][i]]=b[rotation[to[kind]][i+1]];
b[rotation[to[kind]][6]]=tmp;
}
else{
int tmp=b[rotation[to[kind]][6]];
for(int i=6;i>0;i--)
b[rotation[to[kind]][i]]=b[rotation[to[kind]][i-1]];
b[rotation[to[kind]][0]]=tmp;
}
}
void IDAstar(int *b,int tmp_depth,int father){   //当前序列，当前深度，父节点
if(get_h(b)>tmp_depth)    //这就是利用估价函数的剪枝，h的值表示至少还需要多少步，如果在当前深度完成不了就剪掉
return;
if(flag)    //如果已经有解就退出
return;
if(tmp_depth==0&&get_h(b)==0){   //深度为0，且为目标状态
flag=true;
for(int j=depth;j>0;j--)
printf("%c",ope[j]+'A');
printf("\n%d\n",b[6]);
return;
}
for(int i=0;i<8;i++){
int tmp[24];
if(rev[i]==father)   //避免死循环，相反操作两次则抵消
continue;
for(int i=0;i<24;i++)
tmp[i]=b[i];
change(tmp,i);
ope[tmp_depth]=i;
dfs(tmp,tmp_depth-1,i);
}
}
int main(){
while(scanf("%d",&a[0])!=EOF&&a[0]){
for(int i=1;i<24;i++)
scanf("%d",&a[i]);
if(get_h(a)==0){
printf("No moves needed\n%d\n",a[6]);  //wa两次，不需要操作也需要输出中心数字
continue;
}
flag=false;
for(depth=get_h(a);;depth++){   //迭代加深，至少需要h(a)步，很好理解
dfs(a,depth,-1);
if(flag)   //有解则退出
break;
}
}
return 0;
}

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