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POJ-2488 A Knight’s Journey##
A Knight’s Journey
Time Limit: 1000MS Memory Limit: 65536K
Total Submissions: 43097 Accepted: 14620
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
3
1 1
2 3
4 3
Sample Output
Scenario #1:
A1
Scenario #2:
impossible
Scenario #3:
A1B3C1A2B4C2A3B1C3A4B2C4
Source
TUD Programming Contest 2005, Darmstadt, Germany
骑士如图可以走八个方向，问能否走完整个l*l的棋盘，如果能，输出走的路径，因为一定要走完，所以一定会走A1这个点，所以可以把它当成起点。
因为要存储路径并输出，所以我觉得深搜可以写。
注意题目要求路劲要按字典序，所以你走的方向也要字典序。
代码如下：
#include<stdio.h>
#include<string.h>
#include<iostream>
using namespace std;
int p,q,sx,sy,ac[30][30];//存储路径
bool vis[30][30],flag;
bool judge(int x,int y)
{if(x>=1&&x<=p&&y>=1&&y<=q&&!vis[x][y]&&!flag)return 1;return 0;
}
int dir[8][2]= {{-1,-2},{1,-2},{-2,-1},{2,-1},{-2,1},{2,1},{-1,2},{1,2}};//八个方向有讲究，建议自己画一张图看看
void dfs(int sx,int sy,int step)
{int i,nx,ny;ac[step][0]=sx;ac[step][1]=sy;if(step==p*q)//步数等于棋盘格子数，搜索结束{flag=1;//标记，可以走完return ;}for(i=0; i<8; i++){nx=sx+dir[i][0];ny=sy+dir[i][1];if(judge(nx,ny)){vis[nx][ny]=1;dfs(nx,ny,step+1);vis[nx][ny]=0;}}
}
int main()
{int t,num=1;scanf("%d",&t);while(t--){if(num!=1) printf("\n");scanf("%d %d",&p,&q);memset(vis,0,sizeof(vis));vis[1][1]=1;flag=0;dfs(1,1,1);printf("Scenario #%d:\n",num++);if(flag){for(int i=1; i<=p*q; i++)printf("%c%d",ac[i][1]-1+'A',ac[i][0]);}else printf("impossible");printf("\n");}
}
以上。
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