POJ2226 Muddy Fields 二分匹配 最小顶点覆盖 好题

  1 #include<cstdio>
  2 #include<cstring>
  3 #include<vector>
  4 #include<queue>
  5 
  6 using namespace std;
  7 
  8 const int maxn=2510;
  9 const int inf=0x3f3f3f3f;
 10 const int s=0;
 11 int t;
 12 int tota;
 13 int totb;
 14 
 15 inline int min(int x,int y)
 16 {
 17     return x<y?x:y;
 18 }
 19 
 20 struct Edge
 21 {
 22     int to,cap,rev;
 23 };
 24 vector<Edge>edge[maxn];
 25 int iter[maxn];
 26 int level[maxn];
 27 char str[55][55];
 28 int hash[55][55];
 29 
 30 void addedge(int from,int to,int cap)
 31 {
 32     edge[from].push_back((Edge){to,cap,edge[to].size()});
 33     edge[to].push_back((Edge){from,0,edge[from].size()-1});
 34 }
 35 
 36 void build_graph(int n,int m)
 37 {
 38     for(int i=0;i<n*m;i++)
 39         edge[i].clear();
 40     tota=0;
 41     for(int i=1;i<=n;i++)
 42     {
 43         int j=1;
 44         while(j<=m)
 45         {
 46             if(str[i][j]==‘*‘)
 47             {
 48                 tota++;
 49                 hash[i][j]=tota;
 50                 while(j<=m&&str[i][j+1]==‘*‘)
 51                 {
 52                     j++;
 53                     hash[i][j]=tota;
 54                 }
 55             }
 56             j++;
 57         }
 58     }
 59     totb=tota;
 60     for(int j=1;j<=m;j++)
 61     {
 62         int i=1;
 63         while(i<=n)
 64         {
 65             if(str[i][j]==‘*‘)
 66             {
 67                 totb++;
 68                 addedge(hash[i][j],totb,1);
 69                 while(i<=n&&str[i+1][j]==‘*‘)
 70                 {
 71                     i++;
 72                     addedge(hash[i][j],totb,1);
 73                 }
 74             }
 75             i++;
 76         }
 77     }
 78     t=tota+totb+1;
 79     for(int i=1;i<=tota;i++)
 80         addedge(s,i,1);
 81     for(int i=tota+1;i<=totb;i++)
 82         addedge(i,t,1);
 83 }
 84 
 85 void bfs()
 86 {
 87     memset(level,-1,sizeof level);
 88     queue<int>que;
 89     while(!que.empty())
 90         que.pop();
 91     que.push(s);
 92     level[s]=1;
 93     while(!que.empty())
 94     {
 95         int u=que.front();
 96         que.pop();
 97         for(int i=0;i<edge[u].size();i++)
 98         {
 99             Edge &e=edge[u][i];
100             if(e.cap>0&&level[e.to]<0)
101             {
102                 level[e.to]=level[u]+1;
103                 que.push(e.to);
104             }
105         }
106     }
107 }
108 
109 int dfs(int u,int f)
110 {
111     if(u==t)
112         return f;
113     for(int &i=iter[u];i<edge[u].size();i++)
114     {
115         Edge &e=edge[u][i];
116         if(e.cap>0&&level[e.to]>level[u])
117         {
118             int d=dfs(e.to,min(f,e.cap));
119             if(d>0)
120             {
121                 e.cap-=d;
122                 edge[e.to][e.rev].cap+=d;
123                 return d;
124             }
125 
126         }
127     }
128     return 0;
129 }
130 
131 int solve()
132 {
133     int flow=0;
134     while(true)
135     {
136         bfs();
137         if(level[t]<0)
138             return flow;
139         memset(iter,0,sizeof iter);
140         int f;
141         while(f=dfs(s,inf))
142         {
143             flow+=f;
144         }
145     }
146 }
147 
148 int main()
149 {
150     int n,m;
151     while(~scanf("%d%d",&n,&m))
152     {
153         for(int i=1;i<=n;i++)
154         {
155             scanf("%s",str[i]+1);
156         }
157         build_graph(n,m);
158         printf("%d\n",solve());
159     }
160     return 0;
161 }