题目链接:https://icpcarchive.ecs.baylor.edu/index.php?option=com_onlinejudge&Itemid=8&category=528&page=show_problem&problem=3916
题目大意:给定一个h*w的矩阵,每格是草地(#)或洞(.),可以花费d把一个#变成.,也可以花费f把一个.变成#,最后相邻的#和.之间要隔一个栅栏,每个花费为b.最后边界上必须全部是#,求最少花费.
分析:- - 感觉不容易想到...首先由分隔开#和.以及花费最少,联想到最小割.设置一个s,一个t,s连所有#,权重为d,若#变成.,即把这个点分到T中去,需要把这条边割断;所有.连到t,权重为f;相邻点互相连一条边,权重为b,最后如果一个在S一个在T,则需要把这条边割断.还有边界需要是草地,故把s连到边界,权值设为无穷.最后求一下从s到t的最小割即可.
1 #include<iostream> 2 #include<cstring> 3 #include<cstdio> 4 #include<vector> 5 #include<queue> 6 typedef long long ll; 7 using namespace std; 8 const int maxn=2550,maxm=25500,INF=1000000; 9 int w,h,d,f,b; 10 11 struct Edge{ 12 int from,to,cap,flow; 13 Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){} 14 }; 15 16 struct EdmondsKarp{ 17 int n,m; 18 vector<Edge> edges; 19 vector<int> G[maxn]; 20 int p[maxn],a[maxn]; 21 22 void init(int _n){ 23 this->n=n; 24 this->m=0; 25 for(int i=0;i<maxn;i++)G[i].clear(); 26 edges.clear(); 27 } 28 29 void AddEdge(int from,int to,int cap,int flow){ 30 edges.push_back(Edge(from,to,cap,flow)); 31 edges.push_back(Edge(to,from,0,flow)); 32 G[from].push_back(m++); 33 G[to].push_back(m++); 34 } 35 36 ll Maxflow(int s,int t){ 37 ll flow=0; 38 while(1){ 39 memset(a,0,sizeof(a)); 40 queue<int>Q; 41 Q.push(s); 42 a[s]=INF; 43 while(!Q.empty()){ 44 int x=Q.front();Q.pop(); 45 for(int i=0;i<G[x].size();i++){ 46 Edge &e=edges[G[x][i]]; 47 if(!a[e.to]&&e.cap>e.flow){ 48 p[e.to]=G[x][i]; 49 a[e.to]=min(a[x],e.cap-e.flow); 50 Q.push(e.to); 51 } 52 } 53 if(a[t])break; 54 } 55 if(!a[t])break; 56 for(int u=t;u!=s;u=edges[p[u]].from){ 57 edges[p[u]].flow+=a[t]; 58 edges[p[u]^1].flow-=a[t]; 59 } 60 flow+=a[t]; 61 } 62 return flow; 63 } 64 }; 65 66 int main(){ 67 int kase; 68 long long ans=0; 69 cin>>kase; 70 while(kase--){ 71 ans=0; 72 cin>>w>>h; 73 cin>>d>>f>>b; 74 EdmondsKarp ek; 75 ek.init(w*h+2); 76 char c; 77 for(int i=0;i<w*h;i++){ 78 cin>>c; 79 if(i/w==0||i/w==h-1||i%w==0||i%w==w-1){ 80 if(c!='#')ans+=f; 81 ek.AddEdge(w*h,i,INF,0); 82 } 83 else if(c=='#')ek.AddEdge(w*h,i,d,0); 84 else ek.AddEdge(i,w*h+1,f,0); 85 if(i>0&&(i-1)/w==i/w)ek.AddEdge(i,i-1,b,0); 86 if(i<w*h&&(i+1)/w==i/w)ek.AddEdge(i,i+1,b,0); 87 if(i-w>=0)ek.AddEdge(i,i-w,b,0); 88 if(i+w<w*h)ek.AddEdge(i,i+w,b,0); 89 } 90 ans+=ek.Maxflow(w*h,w*h+1); 91 cout<<ans<<endl; 92 } 93 return 0; 94 }