1 //2017-09-23
  2 #include <iostream>
  3 #include <cstdio>
  4 #include <algorithm>
  5 #include <cmath>
  6 #include <map>
  7 
  8 using namespace std;
  9 
 10 const int INF = 0x3f3f3f3f;
 11 int a[10][10], target, postion[10], b[10], d[10000], sx, sy, deep;
 12 bool ok;
 13 map<int, bool> vis;
 14 char dir[4] = {‘d‘, ‘l‘, ‘r‘, ‘u‘};
 15 int dx[4] = {1, 0, 0, -1};//分别对应上下左右四个方向
 16 int dy[4] = {0, -1, 1, 0};
 17 int kase;
 18 
 19 int Astar()
 20 {
 21     int h = 0;
 22     for(int i = 1; i <= 3; i++)
 23       for(int j = 1; j <= 3; j++)
 24         if(a[i][j]!=0)
 25         {
 26             int num = a[i][j];
 27             int nx = (postion[num]-1)/3;
 28             int ny = (postion[num]-1)%3;
 29             h += (abs(i-nx-1)+abs(j-ny-1));
 30         }
 31     return h;
 32 }
 33 
 34 int toInt()//把矩阵转换为int型数字
 35 {
 36     int res = 0;
 37     for(int i = 1; i <= 3; i++)
 38       for(int j = 1; j <= 3; j++)
 39         res = res*10+a[i][j];
 40     return res;
 41 }
 42 
 43 void IDAstar(int x, int y, int pre, int step)
 44 {
 45     if(ok)return ;
 46     int h = Astar();
 47     if(!h && toInt()==target)//找到答案
 48     {
 49         printf("Case %d: %d\n", ++kase, step);
 50         for(int i = 0; i < step; i++)
 51           printf("%c", dir[d[i]]);
 52         printf("\n");
 53         ok = 1;
 54         return ;
 55     }
 56     if(step+h>deep)return ;//现实＋理想<现状，则返回，IDA*最重要的剪枝
 57     int now = toInt();
 58     //if(vis[now])return ;//如果状态已经搜过了，剪枝，避免重复搜索
 59     //vis[now] = true;
 60     for(int i = 0; i < 4; i++)
 61     {
 62         if(i+pre == 3)continue;
 63         int nx = x+dx[i];
 64         int ny = y+dy[i];
 65         if(nx>=1&&nx<=3&&ny>=1&&ny<=3)
 66         {
 67             d[step] = i;
 68             swap(a[x][y], a[nx][ny]);
 69             IDAstar(nx, ny, i, step+1);
 70             swap(a[x][y], a[nx][ny]);
 71             d[step] = 0;
 72         }
 73     }
 74     return;
 75 }
 76 
 77 char str1[20], str2[20];
 78 
 79 int main()
 80 {
 81     int T;
 82     scanf("%d", &T);
 83     char ch;
 84     kase = 0;
 85     while(T--)
 86     {
 87         ok = false;
 88         deep = 0;
 89         int cnt = 0;
 90         scanf("%s%s", str1, str2);
 91         for(int i = 1; i <= 3; i++)
 92         {
 93             for(int j = 1; j <= 3; j++)
 94             {
 95                 ch = str1[(i-1)*3+j-1];
 96                 if(ch == ‘X‘)
 97                 {
 98                     a[i][j] = 0;
 99                     sx = i;
100                     sy = j;
101                 }else
102                   a[i][j] = ch - ‘0‘;
103                 b[cnt++] = a[i][j];
104             }
105         }
106         target = 0;
107         getchar();
108         for(int i = 1; i <= 9; i++){
109             target *= 10;
110             ch = str2[i-1];
111             if(ch == ‘X‘)
112               target += 0;
113             else{
114                 target += ch-‘0‘;
115                 postion[ch-‘0‘] = i;
116             }        
117         }
118         while(!ok)
119         {
120             vis.clear();
121             IDAstar(sx, sy, INF, 0);
122             deep++;//一层一层增加搜索的深度
123         }
124     }
125 
126     return 0;
127 }