Description
BackgroundThe 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, . . .
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.
#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 直接DFS就好，只是要记住路径：
#include <iostream>
#include <string.h>
#include <stdio.h> using namespace std;
int dx[]={-1, 1, -2, 2, -2, 2, -1, 1}, dy[] = {-2, -2, -1, -1, 1, 1, 2, 2};
int path[30][30], vis[30][30], p, q, cnt;
bool flag; void DFS(int r, int c, int sp)
{
path[sp][0] = r ;
path[sp][1] = c ;
if(sp == p*q )
{
flag = 1 ;
return ;
}
for(int i=0; i<8; i++)
{
int x = r + dx[i] ;
int y = c + dy[i] ;
if(x>=1 && x<=p && y>=1 && y<=q && !vis[x][y] && !flag)
{
vis[x][y] = 1 ;
DFS(x,y,sp+1);
vis[x][y] = 0 ;
}
}
} int main()
{
int n, k;
cin >> n ;
for(k=1; k<=n; k++)
{
flag = 0 ;
cin >> p >> q ;
memset(vis,0,sizeof(vis));
vis[1][1] = 1;
DFS(1,1,1);
cout << "Scenario #" << k << ":" << endl ;
if(flag)
{
for(int i=1; i<=p*q; i++)
printf("%c%d",path[i][1]-1+'A',path[i][0]);
}
else cout << "impossible" ;
cout << endl ;
if(k!=n) cout << endl ;
} return 0;
}