Borg Maze（BFS+MST）

Posted 2021-01-21 fighting-sh

Borg Maze

http://poj.org/problem?id=3026

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 18230		Accepted: 5870

Description

The Borg is an immensely powerful race of enhanced humanoids from the delta quadrant of the galaxy. The Borg collective is the term used to describe the group consciousness of the Borg civilization. Each Borg individual is linked to the collective by a sophisticated subspace network that insures each member is given constant supervision and guidance. 

Your task is to help the Borg (yes, really) by developing a program which helps the Borg to estimate the minimal cost of scanning a maze for the assimilation of aliens hiding in the maze, by moving in north, west, east, and south steps. The tricky thing is that the beginning of the search is conducted by a large group of over 100 individuals. Whenever an alien is assimilated, or at the beginning of the search, the group may split in two or more groups (but their consciousness is still collective.). The cost of searching a maze is definied as the total distance covered by all the groups involved in the search together. That is, if the original group walks five steps, then splits into two groups each walking three steps, the total distance is 11=5+3+3.

Input

On the first line of input there is one integer, N <= 50, giving the number of test cases in the input. Each test case starts with a line containg two integers x, y such that 1 <= x,y <= 50. After this, y lines follow, each which x characters. For each character, a space `` ‘‘ stands for an open space, a hash mark ``#‘‘ stands for an obstructing wall, the capital letter ``A‘‘ stand for an alien, and the capital letter ``S‘‘ stands for the start of the search. The perimeter of the maze is always closed, i.e., there is no way to get out from the coordinate of the ``S‘‘. At most 100 aliens are present in the maze, and everyone is reachable.

Output

For every test case, output one line containing the minimal cost of a succesful search of the maze leaving no aliens alive.

Sample Input

2
6 5
##### 
#A#A##
# # A#
#S  ##
##### 
7 7
#####  
#AAA###
#    A#
# S ###
#     #
#AAA###
#####  

Sample Output

8
11

Source

Svenskt M?sterskap i Programmering/Norgesmesterskapet 2001

 

 

 

很坑，数据n,m后面有很长的空格，要用gets读掉

  1 #include<iostream>
  2 #include<algorithm>
  3 #include<queue>
  4 #include<cstring>
  5 #include<cmath>
  6 #include<cstdio>
  7 using namespace std;
  8 
  9 struct sair{
 10     int x,y,step;
 11 }p[100005];
 12 int fa[100005];
 13 int n,m;
 14 
 15 int Find(int x){
 16     int r=x,y;
 17     while(x!=fa[x]){
 18         x=fa[x];
 19     }
 20     while(r!=x){
 21         y=fa[r];
 22         fa[r]=x;
 23         r=y;
 24     }
 25     return x;
 26 }
 27 
 28 int join(int x,int y){
 29     int xx=Find(x);
 30     int yy=Find(y);
 31     if(xx!=yy){
 32         fa[xx]=yy;
 33         return true;
 34     }
 35     return false;
 36 }
 37 
 38 struct DIST{
 39     int x,y,dis;
 40 }dis[1000005];
 41 
 42 bool cmp(DIST a,DIST b){
 43     return a.dis<b.dis;
 44 }
 45 
 46 int dir[4][2]={0,1,1,0,0,-1,-1,0};
 47 int co;
 48 
 49 char mp[505][505];
 50 int book[505][505];
 51 
 52 void BFS(int x,int y){
 53     queue<sair>Q;
 54     memset(book,0,sizeof(book));
 55     sair s,e;
 56     s.x=x,s.y=y,s.step=0;;
 57     Q.push(s);
 58     while(!Q.empty()){
 59         s=Q.front();
 60         Q.pop();
 61         for(int i=0;i<4;i++){
 62             e.x=s.x+dir[i][0];
 63             e.y=s.y+dir[i][1];
 64             if(e.x>=0&&e.x<n&&e.y>=0&&e.y<m&&!book[e.x][e.y]&&mp[e.x][e.y]!=‘#‘){
 65                 e.step=s.step+1;
 66                 Q.push(e);
 67                 book[e.x][e.y]=1;
 68                 if(mp[e.x][e.y]==‘A‘||mp[e.x][e.y]==‘S‘){
 69                     dis[co].x=x*m+y+1,dis[co].y=e.x*m+e.y+1,dis[co++].dis=e.step;
 70                 }
 71             }
 72         }
 73     }
 74 }
 75 
 76 int main(){
 77     int T;
 78     scanf("%d",&T);
 79     while(T--){
 80         co=0;
 81         char dd[105];
 82         scanf("%d %d",&m,&n);
 83         gets(dd);
 84         for(int i=0;i<=m*n;i++) fa[i]=i;
 85         for(int i=0;i<n;i++) gets(mp[i]);
 86         for(int i=0;i<n;i++){
 87             for(int j=0;j<m;j++){
 88                 if(mp[i][j]==‘S‘||mp[i][j]==‘A‘){
 89                     BFS(i,j);
 90                 }
 91             }
 92         }
 93         sort(dis,dis+co,cmp);
 94         int ans=0;
 95         for(int i=0;i<co;i++){
 96             if(join(dis[i].x,dis[i].y)){
 97                 ans+=dis[i].dis;
 98             }
 99         }
100         printf("%d
",ans);
101     }
102 }
103 /*
104 1
105 50 7
106 ##################################################
107 #            AAAAAAA#AAAAAA AAA            S     #
108 #   AAAAAAAAAA       AAAAAAAAAAAAAA#####AAAAA### #
109 #    A##A#A#A#A###A#A#A#A#A#A#A#A#A#A#A##A#A#    #
110 #    A                                 ###########
111 #             AAAAAAAAAAAA##########             #
112 ##################################################
113 */

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