POJ 2488 A Knight's Journey DFS（深度优先搜索）

雨点打透心脏的1/2处 2024-02-19 19:14 22阅读 0赞

A Knight's Journey

<table> 
 <tbody> 
  <tr> 
   <td><strong>Time Limit:</strong> 1000MS</td> 
   <td>&nbsp;</td> 
   <td><strong>Memory Limit:</strong> 65536K</td> 
  </tr> 
  <tr> 
   <td><strong>Total Submissions:</strong> 53688</td> 
   <td>&nbsp;</td> 
   <td><strong>Accepted:</strong> 18228</td> 
  </tr> 
 </tbody> 
</table>

Description

![2488_1.jpg][]**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

题意解读：

国际象棋，从（1，1）开始走，看能否走完这个棋盘（大小为他给出的p和q），要求按字典序输出走的顺序。

分析：是求是否有解，DFS

难点：按字典序输出走的顺序

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMzI1Njk4_size_16_color_FFFFFF_t_70][]

按上图顺序，就可以安字典序输出了，看好坐标轴的方向啊

#include<iostream>
    #include<cstdio>
    #include<cstring>
    using namespace std;
    int dir[8][2]={
       {-1,-2},{1,-2},{-2,-1},{2,-1},{-2,1},{2,1},{-1,2},{1,2}};
    int map[26][26];
    int a,b,d=1;
    struct node{
    	int x,y;
    }s[60];
    int DFS(int dx,int dy,int f)
    {
    	map[dx][dy]=1;
    	if(f==a*b)
    	{
    		printf("Scenario #%d:\n",d);
    		for(int i=0;i<f;i++)
    		{
    			printf("%c%d",(s[i].y+65),s[i].x+1);
    		}
    		printf("\n");
    	}
    	for(int i=0;i<8;i++)
    	{
    		int x1=dx+dir[i][0];
    		int y1=dy+dir[i][1];
    		if(f==a*b)
    		return 1;
    		if(x1<0||y1<0||x1>a-1||y1>b-1)
    		continue;
    		if(map[x1][y1]==0)
    		{
    			
    			map[x1][y1]=1;
    			s[f].x=x1;
    			s[f].y=y1;
    			if(DFS(x1,y1,f+1))
    			{
    				
    				return 1;
    			}
    			map[x1][y1]=0;
    		}
    		
    	}
    	
    	return 0;
    }
    int main()
    {
    	int n,i,j;
    	scanf("%d",&n);
    	while(n--)
    	{
    		scanf("%d %d",&a,&b);
    		memset(map,0,sizeof(map));
    		
    		if(DFS(0,0,1)==0)
    		{
    			printf("Scenario #%d:\nimpossible\n",d);
    		}
    		
    		printf("\n");
    		d++;
    	}
    	
    	
    	return 0;
    }

[2488_1.jpg]: https://image.dandelioncloud.cn/pgy_files/images/2024/01/29/72034c157ece41b7a626ff4d543d4824.png
[TUD Programming Contest 2005]: http://poj.org/searchproblem?field=source&key=TUD+Programming+Contest+2005
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMzI1Njk4_size_16_color_FFFFFF_t_70]: https://image.dandelioncloud.cn/pgy_files/images/2024/01/29/898a079f383744fb9b120efc2f053057.png