图论（网络流，二分图最小点权覆盖）：POJ 2125 Destroying The Graph

  1 #include <iostream>
  2 #include <cstring>
  3 #include <cstdio>
  4 #include <queue>
  5 using namespace std;
  6 const int maxn=1010;
  7 const int maxm=100010;
  8 const int INF=1000000000;
  9 int cnt,tot,fir[maxn],fron[maxn],dis[maxn];
 10 int to[maxm],nxt[maxm],gap[maxn],path[maxn];
 11 int cap[maxm];queue<int>q;
 12 
 13 struct Max_Flow{
 14     void Init(int tot_=0){
 15         tot=tot_;cnt=1;
 16         memset(fir,0,sizeof(fir));
 17         memset(dis,0,sizeof(dis));
 18         memset(gap,0,sizeof(gap));
 19     }
 20     
 21     void add(int a,int b,int c){
 22         nxt[++cnt]=fir[a];
 23         fir[a]=cnt;
 24         cap[cnt]=c;
 25         to[cnt]=b;
 26     }
 27     
 28     void addedge(int a,int b,int c){
 29         add(a,b,c);
 30         add(b,a,0);
 31     }
 32     
 33     bool BFS(int s,int t){
 34         dis[t]=1;q.push(t);
 35         while(!q.empty()){
 36             int x=q.front();q.pop();
 37             for(int i=fir[x];i;i=nxt[i])
 38                 if(!dis[to[i]]){
 39                     dis[to[i]]=dis[x]+1;
 40                     q.push(to[i]);
 41                 }
 42         }
 43         return dis[s];
 44     }
 45     
 46     int Aug(int s,int t,int &p){
 47         int f=INF;
 48         while(p!=s){
 49             f=min(f,cap[path[p]]);
 50             p=to[path[p]^1];
 51         }p=t;
 52         while(p!=s){
 53             cap[path[p]]-=f;
 54             cap[path[p]^1]+=f;
 55             p=to[path[p]^1];
 56         }
 57         return f;
 58     }
 59     
 60     int ISAP(int s,int t){
 61         if(!BFS(s,t))return 0;
 62         for(int i=s;i<=t;i++)fron[i]=fir[i];
 63         for(int i=s;i<=t;i++)gap[dis[i]]+=1;
 64         int p=s,ret=0;
 65         while(dis[s]<=tot){
 66             if(p==t)ret+=Aug(s,t,p);
 67             
 68             for(int &i=fron[p];i;i=nxt[i])
 69                 if(cap[i]&&dis[p]==dis[to[i]]+1){
 70                     path[p=to[i]]=i;
 71                     break;
 72                 }
 73             
 74             if(!fron[p]){
 75                 if(--gap[dis[p]]==0)
 76                     break;
 77                 int Min=tot;
 78                 for(int i=fir[p];i;i=nxt[i])
 79                     if(cap[i])Min=min(Min,dis[to[i]]);
 80                 gap[dis[p]=Min+1]+=1;fron[p]=fir[p];
 81                 if(p!=s)p=to[path[p]^1];    
 82             }    
 83         }
 84         return ret;
 85     }
 86 }isap;
 87 
 88 int n,m,top;
 89 int tag[maxn],st[maxn];
 90 void DFS(int x){
 91     tag[x]=1;
 92     for(int i=fir[x];i;i=nxt[i])
 93         if(cap[i]&&!tag[to[i]])DFS(to[i]);
 94 }
 95 
 96 int main(){
 97     scanf("%d%d",&n,&m);
 98     int s=0,t=2*n+1;
 99     isap.Init(t+1);
100     for(int i=1,v;i<=n;i++){
101         scanf("%d",&v);
102         isap.addedge(s,i,v);
103     }
104     for(int i=1,v;i<=n;i++){
105         scanf("%d",&v);
106         isap.addedge(i+n,t,v);
107     }
108     for(int i=1,a,b;i<=m;i++){
109         scanf("%d%d",&a,&b);
110         isap.addedge(b,a+n,INF);
111     }
112     
113     printf("%d\n",isap.ISAP(s,t));
114     DFS(0);
115     for(int i=1;i<=n;i++){
116         if(!tag[i])
117             st[++top]=i;
118         if(tag[i+n])
119             st[++top]=i+n;
120     }
121     printf("%d\n",top);
122     for(int i=1;i<=top;i++){
123         if(st[i]<=n)
124             printf("%d +\n",st[i]);
125         else
126             printf("%d -\n",st[i]-n);    
127     }
128     return 0;
129 }