[USACO]Magic Squares

题意：给定你一个2*2的魔方，问你根据它所给的三种变换使得初始的状态，得到目标状况的最少步数。

解题思路：bfs + 状态压缩，因为8面筛子只有8！，只需要把一个组合数映射到hs数判重即可

解题代码：

// File Name: msquare.c
// Author: darkdream
// Created Time: 2014年03月10日 星期一 21时01分14秒
/*
ID: dream.y1
PROG: msquare
LANG: C++
*/
#include<stdio.h>
#include<string.h>
#include<stdlib.h>
#include<time.h>
#include<math.h>
struct node{
  int a[9];
  char N;
  int step;
  int last;
}list[50000];
int hs[50000];
int A[10];
int hehe(int *a)
{
    int ths[10] ;
    memset(ths,0,sizeof(ths));
    int vhs = 0 ;
    for(int i = 1;i <= 8 ;i ++)
    {
        int tsum =0 ; 
        for(int j = 1;j < a[i] ;j ++)
            if(!ths[j])
                tsum ++ ; 
        vhs += (tsum * A[ 8-i ]);
        ths[a[i]] = 1; 
    }
    return vhs;
}
void printans(int p)
{
   if(p == 1 )
       return;
   printans(list[p].last);
   printf("%C",list[p].N);
}
int main(){
   freopen("msquare.in","r",stdin);
   freopen("msquare.out","w",stdout);
   memset(hs,0,sizeof(hs));
   memset(list,0,sizeof(list));
   A[0] = 0; 
   A[1] = 1; 
   for(int i = 2; i <= 8 ;i ++)
   {
     A[i] = i* A[i-1];
   }
   //freopen("/home/plac/problem/input.txt","r",stdin);
   int temp[10];

   for(int i = 1;i <= 8 ;i  ++)
   {
      scanf("%d",&temp[i]) ; 
      list[1].a[i] = i ; 
   }
   int ans = hehe(temp);
   //printf("%d\n",ans);
   
   if(ans == 0 )
   {
       printf("0\n\n");
       return 0 ;
   }
   hs[hehe(list[1].a)] = 1;
   list[1].step = 0; 
   int low = 1, high = 1; 
   while(low <= high )
   {
      
      for(int i = 1;i <= 8;i ++)
          temp[i] = list[low].a[9-i];

      int vhs =  hehe(temp);
      if(!hs[vhs])
      {
         hs[vhs] = 1; 
         high ++ ; 
         list[high].step = list[low].step + 1;  
         for(int i = 1;i <= 8;i ++)
         {
          list[high].a[i] = temp[i];
         }
         list[high].N = 'A'; 
         list[high].last = low;
         if(vhs == ans)
         {
           printf("%d\n",list[high].step);
           printans(high);
           break;
         }
      }  // first
      
      temp[1] = list[low].a[4];
      temp[8] = list[low].a[5];
      for(int i= 2;i <= 4;i ++)
      {
        temp[i] = list[low].a[i-1];
      }
      for(int i= 5;i <= 7;i ++)
      {
        temp[i] = list[low].a[i+1];
      }
      vhs =  hehe(temp);
      if(!hs[vhs])
      {
         hs[vhs] = 1; 
         high ++ ; 
         list[high].step = list[low].step + 1;  
         for(int i = 1;i <= 8;i ++)
         {
          list[high].a[i] = temp[i];
         }
         list[high].N = 'B'; 
         list[high].last = low;
         if(vhs == ans)
         {
           printf("%d\n",list[high].step);
           printans(high);
           break;
         }
        
      }  // 2 change
     

      temp[1] = list[low].a[1];
      temp[2] = list[low].a[7];
      temp[3] = list[low].a[2];
      temp[4] = list[low].a[4];
      temp[5] = list[low].a[5];
      temp[6] = list[low].a[3];
      temp[7] = list[low].a[6];
      temp[8] = list[low].a[8];
      vhs =  hehe(temp);
      if(!hs[vhs])
      {
         hs[vhs] = 1; 
         high ++ ; 
         list[high].step = list[low].step + 1;  
         for(int i = 1;i <= 8;i ++)
         {
          list[high].a[i] = temp[i];
         }
         list[high].N = 'C'; 
         list[high].last = low;
         if(vhs == ans)
         {
           printf("%d\n",list[high].step);
           printans(high);
           break;
         }
      }
   
     low ++ ; 
   }
 printf("\n");   
return 0 ;
}