poj_2488A Knight's Journey

A Knight's Journey

Time Limit:1000MS		Memory Limit:65536K
Total Submissions:22481		Accepted:7598

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

#include <iostream>
#include <cstring>
using namespace std;

const int MAXN = 30;
int m,n;
const int moves[8][2] = {-1, -2, 1, -2, -2, -1, 2, -1, -2, 1, 2, 1, -1, 2, 1, 2};
bool visited[MAXN][MAXN];
char path[MAXN][2];
bool flag;

bool DFS(int x, int y,int setp)
{
	if(m * n == setp)
	{
		flag = true;
		return true;
	}
	for(int i=0;i<8;i++)
	{
		int p = x + moves[i][0];
		int q = y + moves[i][1];
		if(p>=1&&p<=m&&q>=1&&q<=n&&!visited[p][q])
		{
			path[setp][0] = p + 'A' - 1;
			path[setp][1] = q + '0';
			visited[p][q] = true;
			DFS(p,q,setp+1);
			if(flag) return true;
			visited[p][q] = false;
		}
	}
	return false;
}


int main()
{
	freopen("in.txt","r",stdin);
	int t,i,j;
	cin>>t;
	for(i=1;i<=t;i++)
	{
		cin>>n>>m;
		memset(visited,false,sizeof(visited));
		memset(path,0,sizeof(path));

		flag = false;
		path[0][0] = 'A';
		path[0][1] = '1';
		visited[1][1] = true;

		printf("Scenario #%d:\n",i);
		if(DFS(1,1,1))
		{
			for(j=0;j<n*m;j++)
				printf("%c%c",path[j][0],path[j][1]);
		}
		else 
			printf("impossible");
		printf("\n\n");
		
	}
	return 0;
}