【POJ1383】Labyrinth

曾经终败给现在 2022-07-17 00:39 41阅读 0赞

Labyrinth

<table> 
 <tbody> 
  <tr> 
   <td><strong>Time Limit:</strong>&nbsp;2000MS</td> 
   <td>&nbsp;</td> 
   <td><strong>Memory Limit:</strong>&nbsp;32768K</td> 
  </tr> 
  <tr> 
   <td><strong>Total Submissions:</strong>&nbsp;4333</td> 
   <td>&nbsp;</td> 
   <td><strong>Accepted:</strong>&nbsp;1640</td> 
  </tr> 
 </tbody> 
</table>

Description

The northern part of the Pyramid contains a very large and complicated labyrinth. The labyrinth is divided into square blocks, each of them either filled by rock, or free. There is also a little hook on the floor in the center of every free block. The ACM have found that two of the hooks must be connected by a rope that runs through the hooks in every block on the path between the connected ones. When the rope is fastened, a secret door opens. The problem is that we do not know which hooks to connect. That means also that the neccessary length of the rope is unknown. Your task is to determine the maximum length of the rope we could need for a given labyrinth.

Input

The input consists of T test cases. The number of them (T) is given on the first line of the input file. Each test case begins with a line containing two integers C and R (3 <= C,R <= 1000) indicating the number of columns and rows. Then exactly R lines follow, each containing C characters. These characters specify the labyrinth. Each of them is either a hash mark (\#) or a period (.). Hash marks represent rocks, periods are free blocks. It is possible to walk between neighbouring blocks only, where neighbouring blocks are blocks sharing a common side. We cannot walk diagonally and we cannot step out of the labyrinth.  
The labyrinth is designed in such a way that there is exactly one path between any two free blocks. Consequently, if we find the proper hooks to connect, it is easy to find the right path connecting them.

Output

Your program must print exactly one line of output for each test case. The line must contain the sentence "Maximum rope length is X." where Xis the length of the longest path between any two free blocks, measured in blocks.

Sample Input

2
    3 3
    ###
    #.#
    ###
    7 6
    #######
    #.#.###
    #.#.###
    #.#.#.#
    #.....#
    #######

Sample Output

Maximum rope length is 0.
    Maximum rope length is 8.

Hint

Huge input, scanf is recommended.  
If you use recursion, maybe stack overflow. and now C++/c 's stack size is larger than G++/gcc

Source

[Central Europe 1999][]

思路：跑两次bfs，第一次求出边缘节点，因为必须从边缘节点跑bfs才能求出最长步数，好在这题权值统一都是1，所以直接记录出栈数据就行了。

#include<cstdio>
    #include<iostream>
    #include<cmath>
    #include<cstring>
    #include<queue>
    #include<algorithm>
    using namespace std;
    const int N = 1005;
    char map[N][N];
    int nx,ny,ans,n,m;
    int vis[N][N];
    int px[4]= {1,-1,0,0};
    int py[4]= {0,0,1,-1};
    struct node {
    	int x,y;
    	int step;
    } s;
    bool check(int x,int y) {
    	if(x>=0&&y>=0&&x<n&&y<m&&map[x][y]=='.'&&!vis[x][y])
    		return true;
    	return false;
    }
    void bfs(int x,int y) {
    	memset(vis,false,sizeof(vis));
    	queue<node>Q;
    	s.x=x,s.y=y,s.step=0;
    	Q.push(s);
    	vis[x][y]=true;
    	ans=0,nx=x,ny=y;
    	while(!Q.empty()) {
    		node now,end;
    		now=Q.front();
    		Q.pop();
    		ans=now.step,nx=now.x,ny=now.y;
    		for(int i=0; i<4; i++) {
    			end.x=now.x+px[i];
    			end.y=now.y+py[i];
    			end.step=now.step;
    			if(check(end.x,end.y)) {
    				vis[end.x][end.y]=true;
    				end.step=end.step+1;
    				Q.push(end);
    			}
    		}
    	}
    }
    int main() {
    	int T;
    	scanf("%d",&T);
    	while(T--) {
    		int x,y;
    		scanf("%d%d",&m,&n);
    		for(int i=0; i<n; i++) {
    			scanf("%s",map[i]);
    			for(int j=0; j<m; j++) {
    				if(map[i][j]=='.')
    					x=i,y=j;
    			}
    		}
    		bfs(x,y);
    		bfs(nx,ny);
    		printf("Maximum rope length is %d.\n",ans);
    	}
    	return 0;
    }

[题目地址：http://poj.org/problem?id=1383][http_poj.org_problem_id_1383]

[Central Europe 1999]: http://poj.org/searchproblem?field=source&key=Central+Europe+1999
[http_poj.org_problem_id_1383]: http://poj.org/problem?id=1383