POJ 3009-Curling 2.0（DFS-滑动撞击）

Bertha 。 2022-09-28 05:53 53阅读 0赞

Curling 2.0

<table> 
 <tbody> 
  <tr> 
   <td><strong>Time Limit:</strong>&nbsp;1000MS</td> 
   <td>&nbsp;</td> 
   <td><strong>Memory Limit:</strong>&nbsp;65536K</td> 
  </tr> 
  <tr> 
   <td><strong>Total Submissions:</strong>&nbsp;20305</td> 
   <td>&nbsp;</td> 
   <td><strong>Accepted:</strong>&nbsp;8282</td> 
  </tr> 
 </tbody> 
</table>

Description

On Planet MM-21, after their Olympic games this year, curling is getting popular. But the rules are somewhat different from ours. The game is played on an ice game board on which a square mesh is marked. They use only a single stone. The purpose of the game is to lead the stone from the start to the goal with the minimum number of moves.

Fig. 1 shows an example of a game board. Some squares may be occupied with blocks. There are two special squares namely the start and the goal, which are not occupied with blocks. (These two squares are distinct.) Once the stone begins to move, it will proceed until it hits a block. In order to bring the stone to the goal, you may have to stop the stone by hitting it against a block, and throw again.

![3009_1.gif][]  
Fig. 1: Example of board (S: start, G: goal)

The movement of the stone obeys the following rules:

*  At the beginning, the stone stands still at the start square.
 *  The movements of the stone are restricted to x and y directions. Diagonal moves are prohibited.
 *  When the stone stands still, you can make it moving by throwing it. You may throw it to any direction unless it is blocked immediately(Fig. 2(a)).
 *  Once thrown, the stone keeps moving to the same direction until one of the following occurs:
    
     *  The stone hits a block (Fig. 2(b), (c)).
        
         *  The stone stops at the square next to the block it hit.
         *  The block disappears.
     *  The stone gets out of the board.
        
         *  The game ends in failure.
     *  The stone reaches the goal square.
        
         *  The stone stops there and the game ends in success.
 *  You cannot throw the stone more than 10 times in a game. If the stone does not reach the goal in 10 moves, the game ends in failure.

![3009_2.gif][]  
Fig. 2: Stone movements

Under the rules, we would like to know whether the stone at the start can reach the goal and, if yes, the minimum number of moves required.

With the initial configuration shown in Fig. 1, 4 moves are required to bring the stone from the start to the goal. The route is shown in Fig. 3(a). Notice when the stone reaches the goal, the board configuration has changed as in Fig. 3(b).

![3009_3.gif][]  
Fig. 3: The solution for Fig. D-1 and the final board configuration

Input

The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. The number of datasets never exceeds 100.

Each dataset is formatted as follows.

> *the width(=w) and the height(=h) of the board  
> First row of the board*  
> ...  
> *h-th row of the board*

The width and the height of the board satisfy: 2 <= *w* <= 20, 1 <= *h* <= 20.

Each line consists of *w* decimal numbers delimited by a space. The number describes the status of the corresponding square.

> <table> 
>  <tbody> 
>   <tr> 
>    <td>0</td> 
>    <td>vacant square</td> 
>   </tr> 
>   <tr> 
>    <td>1</td> 
>    <td>block</td> 
>   </tr> 
>   <tr> 
>    <td>2</td> 
>    <td>start position</td> 
>   </tr> 
>   <tr> 
>    <td>3</td> 
>    <td>goal position</td> 
>   </tr> 
>  </tbody> 
> </table>

The dataset for Fig. D-1 is as follows:

> 6 6  
> 1 0 0 2 1 0  
> 1 1 0 0 0 0  
> 0 0 0 0 0 3  
> 0 0 0 0 0 0  
> 1 0 0 0 0 1  
> 0 1 1 1 1 1

Output

For each dataset, print a line having a decimal integer indicating the minimum number of moves along a route from the start to the goal. If there are no such routes, print -1 instead. Each line should not have any character other than this number.

Sample Input

2 1
    3 2
    6 6
    1 0 0 2 1 0
    1 1 0 0 0 0
    0 0 0 0 0 3
    0 0 0 0 0 0
    1 0 0 0 0 1
    0 1 1 1 1 1
    6 1
    1 1 2 1 1 3
    6 1
    1 0 2 1 1 3
    12 1
    2 0 1 1 1 1 1 1 1 1 1 3
    13 1
    2 0 1 1 1 1 1 1 1 1 1 1 3
    0 0

Sample Output

1
    4
    -1
    4
    10
    -1

Source

[Japan 2006 Domestic][]

## 题目意思： ##

给出h\*w大小的地图，计算小球从2到3所需要的最小步数。

其中：

①最小步数不能超过10；

②在当前移动方向上，小球可以滑过所有0，直到越界或者遇到障碍1；

③小球可以撞碎当前移动方向上的一块障碍1，撞击后小球的位置是被撞击的障碍的前一个位置；

④越界视为失败；

⑤小球在移动过程中到达终点3也视为成功。

## 解题思路： ##

一个蛮特别的DFS，因为可以一直在方向上移动。

**注意**小球不能直接撞碎障碍1，必须要从非障碍的地方（相当于有助跑）才能撞击障碍，所以需要判断一下。

代码后面附有Discuss上的15组测试数据。

#include<cstdio>
    #include<cstring>
    #include<cmath>
    #include<set>
    #include<cstdlib>
    #include<iostream>
    #include<algorithm>
    using namespace std;
    #define MAXN 30
    #define INF 0x3f3f3f3f
    struct Node
    {
        int x,y;
    } s;
    
    int ma[MAXN][MAXN];
    int dir[4][2]= {
        {-1,0},{0,1},{1,0},{0,-1}};//搜索方向
    int st;//步数
    int w,h;//列行
    bool mflag;//移动是否合法
    int ans=INF;//最小步数
    void DFS(int x,int y)
    {
        if(st>=10)
            return;
        for(int i=0; i<4; ++i)//各个方向依次滑动
        {
            int tx=x;
            int ty=y;
            mflag=false;
            while(1)
            {
                tx+=dir[i][0];
                ty+=dir[i][1];
                if(ma[tx][ty]==0||ma[tx][ty]==2||ma[tx][ty]==3)//判断移动是否合法
                    mflag=true;
                if(tx<0||ty<0||tx>=h||ty>=w)//越界
                {
                    mflag=false;
                    break;
                }
                else if(ma[tx][ty]==3)//到达终点
                {
                    ++st;
                    if(st<ans) ans=st;//更新最小值
                    --st;
                    return;
                }
                else if(ma[tx][ty]==1)//撞击障碍1
                {
                    if(mflag)//合法移动
                    {
                        mflag=false;
                        ma[tx][ty]=0;
                        ++st;
                        //tx-=dir[i][0];
                        //ty-=dir[i][1];
                        DFS(tx-dir[i][0],ty-dir[i][1]);
                        mflag=false;
                        ma[tx][ty]=1;//被撞击的地方恢复原样
                        --st;
                    }
                    break;
                }
            }
        }
    
    }
    int main()
    {
    
    #ifdef ONLINE_JUDGE
    #else
        freopen("G:/cbx/read.txt","r",stdin);
        //freopen("G:/cbx/out.txt","w",stdout);
    #endif
        ios::sync_with_stdio(false);
        cin.tie(0);
        while(cin>>w>>h)
        {
            if(w==0&&h==0) break;
            st=0;
            ans=INF;
            flag=mflag=false;
            memset(ma,0,sizeof(ma));
            for(int i=0; i<h; ++i)
                for(int j=0; j<w; ++j)
                {
                    cin>>ma[i][j];
                    if(ma[i][j]==2) s.x=i,s.y=j;//起点
                }
            DFS(s.x,s.y);
            if(ans==INF) cout<<"-1"<<endl;
            else cout<<ans<<endl;
        }
        return 0;
    }

## 测试数据： ##

Input

1 17
    1 
    0 
    0 
    0 
    0 
    1 
    0 
    1 
    0 
    1 
    1 
    1 
    0 
    0 
    3 
    2 
    0 
    3 6
    0 0 1 
    1 1 1 
    2 3 1 
    1 1 0 
    0 1 0 
    0 0 1 
    18 14
    1 0 1 0 1 1 1 0 0 0 0 1 1 1 0 1 0 3 
    0 1 0 1 0 1 1 0 0 0 0 1 1 0 1 1 1 0 
    0 0 0 0 0 1 0 0 1 1 0 0 0 0 1 0 1 0 
    1 1 0 1 1 1 1 1 1 0 1 1 1 1 0 1 1 0 
    1 1 1 0 0 1 1 0 0 2 1 1 1 1 1 1 0 1 
    0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 1 1 0 
    1 0 0 1 1 1 0 1 0 1 0 0 0 0 1 0 1 0 
    0 1 1 1 0 1 1 1 0 0 1 0 1 0 0 0 0 0 
    0 1 1 1 0 1 0 1 1 1 0 1 1 1 1 1 0 0 
    1 0 0 1 1 1 0 0 1 0 1 0 1 1 1 0 0 0 
    0 1 0 0 1 0 1 0 1 0 1 1 1 1 0 1 0 1 
    1 1 1 1 0 1 1 1 0 1 0 0 0 0 1 1 1 0 
    1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 
    0 0 1 1 0 1 0 0 0 0 1 1 1 1 0 0 1 0 
    14 12
    0 1 0 0 1 1 0 1 0 1 0 1 2 1 
    0 0 0 0 0 0 0 0 0 1 0 0 1 1 
    1 0 0 1 1 1 1 0 0 0 0 0 1 0 
    1 0 1 1 1 0 1 0 3 1 1 0 0 0 
    0 1 0 0 1 0 1 0 1 0 0 0 1 0 
    0 0 0 1 0 1 1 1 0 1 1 0 0 0 
    1 0 1 0 0 1 0 0 0 1 0 0 0 0 
    1 0 0 1 1 1 1 1 1 0 0 0 0 0 
    0 1 0 1 0 1 0 1 1 0 0 0 0 0 
    1 1 1 1 1 0 0 1 0 0 0 1 1 1 
    0 0 1 1 1 0 1 1 1 1 1 0 0 0 
    0 0 0 1 0 0 1 1 1 0 1 0 1 0 
    9 13
    1 0 1 1 0 0 1 0 0 
    0 0 1 1 1 1 1 0 1 
    1 1 0 1 0 0 0 0 1 
    1 1 1 0 0 0 0 1 0 
    1 1 0 1 1 1 1 1 1 
    0 1 0 1 0 1 1 0 0 
    0 1 0 3 1 1 0 0 1 
    0 1 0 1 1 0 0 0 1 
    2 1 1 0 0 1 0 0 1 
    0 1 0 1 0 0 1 1 0 
    1 0 1 1 1 0 0 1 1 
    0 0 1 0 0 1 0 0 0 
    1 1 1 0 0 1 1 1 0 
    2 7
    3 0 
    1 1 
    0 0 
    1 0 
    1 0 
    0 1 
    2 0 
    4 13
    1 0 1 0 
    1 0 0 1 
    1 0 1 1 
    3 1 0 0 
    1 0 1 1 
    0 1 1 0 
    0 0 0 0 
    2 1 0 1 
    1 1 0 0 
    1 1 1 1 
    1 0 0 0 
    0 0 1 0 
    1 0 0 1 
    14 19
    0 1 0 1 1 0 0 1 1 1 1 1 0 0 
    1 0 0 0 3 0 0 1 1 1 2 0 1 1 
    0 1 1 1 0 1 0 0 0 0 1 0 0 0 
    0 1 1 0 0 0 0 1 0 0 1 0 0 0 
    0 0 1 1 0 1 1 0 1 0 0 1 0 1 
    1 0 0 1 1 1 1 1 0 1 1 0 1 0 
    1 0 0 0 1 0 0 0 1 0 1 0 0 0 
    1 0 1 0 0 1 0 0 1 0 1 0 1 0 
    0 1 0 0 0 1 0 0 0 0 1 1 0 0 
    0 1 0 0 1 1 0 1 1 1 0 1 0 1 
    1 1 0 1 1 0 0 1 0 0 0 0 1 1 
    1 0 1 1 0 1 1 1 1 1 1 1 1 0 
    0 1 1 0 0 1 0 1 1 1 1 0 0 1 
    1 1 0 1 0 1 1 0 1 1 0 0 0 0 
    1 0 1 1 0 0 0 0 0 0 0 1 0 1 
    0 1 0 0 1 0 1 0 0 1 1 0 1 0 
    1 0 1 0 0 0 1 1 0 0 1 1 1 1 
    0 1 1 0 1 1 0 0 0 1 0 1 0 1 
    1 1 0 0 1 0 1 1 0 0 0 1 0 0 
    5 4
    1 0 0 1 0 
    3 1 1 1 2 
    1 0 0 1 1 
    1 1 0 0 0 
    18 6
    0 1 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 0 
    1 0 1 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 
    0 1 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1 1 
    1 1 0 0 0 1 0 0 0 1 1 0 1 0 1 2 0 0 
    1 0 3 1 1 1 0 0 0 0 1 1 0 0 0 0 1 1 
    1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 1 1 0 
    19 17
    1 1 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 
    0 0 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 
    0 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 0 
    1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 0 0 0 
    1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 0 0 0 0 
    1 0 0 0 1 1 1 0 1 1 1 1 1 0 1 1 1 0 0 
    1 0 0 0 0 1 1 3 1 1 0 0 0 0 1 0 0 0 0 
    0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 1 1 0 
    0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 2 1 
    1 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 
    0 0 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 
    0 1 0 0 0 0 0 0 1 1 1 0 0 1 1 0 1 0 1 
    1 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 1 1 
    0 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 
    1 0 0 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 0 
    0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 1 0 1 1 
    1 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 0 0 0 
    18 2
    1 1 0 1 0 1 1 0 1 0 0 3 0 0 1 0 1 0 
    0 0 0 1 0 1 0 1 1 2 1 1 0 1 0 0 1 0 
    7 10
    1 0 0 0 1 1 0 
    1 0 1 1 1 0 1 
    0 1 1 0 1 1 1 
    0 1 1 1 0 1 1 
    1 1 0 0 0 1 0 
    1 1 0 1 2 1 0 
    0 3 0 0 1 0 0 
    0 1 1 1 0 0 0 
    1 0 1 0 1 0 0 
    1 1 1 1 1 1 0 
    14 6
    0 0 1 0 0 0 0 1 1 0 1 1 1 0 
    0 0 1 0 1 0 1 1 1 1 1 1 1 1 
    1 1 0 2 1 1 0 0 1 0 0 0 0 1 
    1 0 1 1 1 1 1 1 1 1 1 1 1 0 
    1 0 1 1 1 0 1 1 0 1 1 0 0 0 
    1 0 1 0 0 1 0 0 1 0 0 0 0 3 
    4 8
    0 1 0 0 
    0 0 0 0 
    1 0 0 1 
    0 0 0 0 
    0 0 0 0 
    3 0 1 0 
    1 0 1 0 
    1 0 0 2

Output

1
    1
    -1
    -1
    9
    4
    2
    5
    -1
    7
    6
    -1
    10
    -1
    -1

[3009_1.gif]: /images/20220708/3ec9205a19a742868ff50f60dc27ae16.png
[3009_2.gif]: /images/20220708/68c736860fae44a2b8d56c63db92ead2.png
[3009_3.gif]: /images/20220708/51899929d3904e578be59f844ddc6976.png
[Japan 2006 Domestic]: http://poj.org/searchproblem?field=source&key=Japan+2006+Domestic