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A Knight's Journey

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 27258 Accepted: 9295

Description

Background 
The knight is getting bored of seeing the same black and white squares again and again and has decided to make a journey 
around the world. Whenever a knight moves, it is two squares in one direction and one square perpendicular to this. The world of a knight is the chessboard he is living on. Our knight lives on a chessboard that has a smaller area than a regular 8 * 8 board, but it is still rectangular. Can you help this adventurous knight to make travel plans? 

Problem 
Find a path such that the knight visits every square once. The knight can start and end on any square of the board.

Input

The input begins with a positive integer n in the first line. The following lines contain n test cases. Each test case consists of a single line with two positive integers p and q, such that 1 <= p * q <= 26. This represents a p * q chessboard, where p describes how many different square numbers 1, . . . , p exist, q describes how many different square letters exist. These are the first q letters of the Latin alphabet: A, . . .

Output

The output for every scenario begins with a line containing "Scenario #i:", where i is the number of the scenario starting at 1. Then print a single line containing the lexicographically first path that visits all squares of the chessboard with knight moves followed by an empty line. The path should be given on a single line by concatenating the names of the visited squares. Each square name consists of a capital letter followed by a number. 
If no such path exist, you should output impossible on a single line.

Sample Input

31 12 34 3

Sample Output

Scenario #1:A1Scenario #2:impossibleScenario #3:A1B3C1A2B4C2A3B1C3A4B2C4

大致题意：给出一个p行q列的国际棋盘，马可以从任意一个格子开始走，问马能否不重复的走完所有的棋盘。如果可以，输出按字典序排列最小的路径。打印路径时，列用大写字母表示（A表示第一列），行用阿拉伯数字表示（从1开始），先输出列，再输出行。

分析：如果马可以不重复的走完所有的棋盘，那么它一定可以走到A1这个格子。所以我们只需从A1这个格子开始搜索，就能保证字典序是小的；除了这个条件，我们还要控制好马每次移动的方向，控制方向时保证字典序最小（即按照下图中格子的序号搜索）。控制好这两个条件，直接从A1开始深搜就行了。

#include<cstdio>  #include<cstring>  #include<algorithm>  using namespace std;    int path[88][88], vis[88][88], p, q, cnt;  bool flag;    int dx[8] = {-1, 1, -2, 2, -2, 2, -1, 1};  int dy[8] = {-2, -2, -1, -1, 1, 1, 2, 2};    bool judge(int x, int y)  {      if(x >= 1 && x <= p && y >= 1 && y <= q && !vis[x][y] && !flag)          return true;      return false;  }    void DFS(int r, int c, int step)  {      path[step][0] = r;      path[step][1] = c;      if(step == p * q)      {          flag = true;          return ;      }      for(int i = 0; i < 8; i++)      {          int nx = r + dx[i];          int ny = c + dy[i];          if(judge(nx,ny))          {                vis[nx][ny] = 1;              DFS(nx,ny,step+1);              vis[nx][ny] = 0;          }      }  }    int main()  {      int i, j, n, cas = 0;      scanf("%d",&n);      while(n--)      {          flag = 0;          scanf("%d%d",&p,&q);          memset(vis,0,sizeof(vis));          vis[1][1] = 1;          DFS(1,1,1);          printf("Scenario #%d:\n",++cas);          if(flag)          {              for(i = 1; i <= p * q; i++)                  printf("%c%d",path[i][1] - 1 + 'A',path[i][0]);          }          else              printf("impossible");          printf("\n");          if(n != 0)              printf("\n");      }      return 0;  }