bzoj:1656 [Usaco2006 Jan] The Grove 树木

Description

The pasture contains a small, contiguous grove of trees that has no 'holes' in the middle of the it. Bessie wonders: how far is it to walk around that grove and get back to my starting position? She's just sure there is a way to do it by going from her start location to successive locations by walking horizontally, vertically, or diagonally and counting each move as a single step. Just looking at it, she doesn't think you could pass 'through' the grove on a tricky diagonal. Your job is to calculate the minimum number of steps she must take. Happily, Bessie lives on a simple world where the pasture is represented by a grid with R rows and C columns (1 <= R <= 50, 1 <= C <= 50). Here's a typical example where '.' is pasture (which Bessie may traverse), 'X' is the grove of trees, '*' represents Bessie's start and end position, and '+' marks one shortest path she can walk to circumnavigate the grove (i.e., the answer): ...+... ..+X+.. .+XXX+. ..+XXX+ ..+X..+ ...+++* The path shown is not the only possible shortest path; Bessie might have taken a diagonal step from her start position and achieved a similar length solution. Bessie is happy that she's starting 'outside' the grove instead of in a sort of 'harbor' that could complicate finding the best path.

牧场里有一片树林，林子里没有坑．

    贝茜很想知道，最少需要多少步能围绕树林走一圈，最后回到起点．她能上下左右走，也能走对角线格子．牧场被分成R行C列(1≤R≤50，1≤C≤50)．下面是一张样例的地图，其中“．”表示贝茜可以走的空地，  “X”表示树林，  “*”表示起点．而贝茜走的最近的路已经特别地用“+”表示出来．

 

 

 

 

 

题目保证，最短的路径一定可以找到．

Input

* Line 1: Two space-separated integers: R and C

* Lines 2..R+1: Line i+1 describes row i with C characters (with no spaces between them).

    第1行输入R和C，接下来R行C列表示一张地图．地图中的符号如题干所述．

Output

* Line 1: The single line contains a single integer which is the smallest number of steps required to circumnavigate the grove.

    输出最少的步数．

 

Sample Input

6 7
.......
...X...
..XXX..
...XXX.
...X...
......*

Sample Output

13

 

随便找棵树然后画一条射线作为分界线，使之不能通过，然后就行BFS啦

以样例为例：

在第二行唯一一棵树那划条射线，然后BFS结果如下：（-1为树木，0为起点）

在这个数据里面并不明显，划过线的部分是不能通过的……

再看这个数据：

 

结果如下：

其他看代码咯

#include<queue>
#include<cstdio>
#include<algorithm>
using namespace std;

struct na{
    int x,y;
};
int n,m,x=-1,y;
const int fx[8]={0,0,1,-1,1,1,-1,-1},fy[8]={1,-1,0,0,1,-1,1,-1};
int map[51][51];
char c;
queue <na> q;
int main(){
    scanf("%d%d",&n,&m);
    for (int i=0;i<n;i++)
    for (int j=0;j<m;j++){
        c=getchar();
        while(c=='\n') c=getchar();
        if (c=='X') {
            map[i][j]=-1;
            if (x==-1) x=i,y=j;
        }else
        if (c=='*'){
            na tmp;tmp.x=i;tmp.y=j;q.push(tmp);
        }else map[i][j]=2500;
    }
    while(!q.empty()){
        na k=q.front();q.pop();
        for (int i=0;i<8;i++){
            na now=k;
            now.x+=fx[i];now.y+=fy[i];
            if (now.x<0||now.y<0||now.x>=n||now.y>=m) continue;
            if (k.y<=y&&k.x==x&&now.x==x-1) continue;
            if (k.y<=y&&k.x==x-1&&now.x==x) continue;
            if (map[now.x][now.y]>map[k.x][k.y]+1){
                map[now.x][now.y]=map[k.x][k.y]+1;
                q.push(now);
            }
        }
    }
    int ans=2500;
    for (int i=y-1;i>=0;i--){
        if (map[x][i]+map[x-1][i]<ans) ans=map[x][i]+map[x-1][i];
        if (map[x][i]+map[x-1][i+1]<ans) ans=map[x][i]+map[x-1][i+1];
        if (i) if (map[x][i]+map[x-1][i-1]<ans) ans=map[x][i]+map[x-1][i-1];
    }
    printf("%d\n",ans+1);
}