1737: 太空飞行计划问题 最大权闭合子图

1、建立两个超级点S,T。

2、对每个实验跟S链接一条容量为收入的边。

3、对每个一起跟T链接一条容量为花费的边。

4、对每个实验要用到的一起链接一条容量为无穷大的边。

链表

#include <iostream>
#include <queue>
#include <vector>
#include <cstdio>
#include <cstring>
using namespace std;
 
const int MAXN = 101,MAXM = MAXN*MAXN*2,INF = ~0U >> 1;
struct Edge{
   Edge *next,*op;
   int t,c;
}*V[MAXN],*P[MAXN],ES[MAXM],*Stae[MAXN];
int N,M,S,T,EC,Ans,Maxflow;
int Lv[MAXN],Stap[MAXN];
void Clear()
{
    for(int i = 0;i < MAXN;++i)
        V[i] = NULL,ES[i].next = NULL,ES[i].op = NULL;
    EC = 0; Ans = 0; Maxflow = 0;
}
inline void addedge(int a,int b,int c)
{
    ES[++EC].next = V[a];V[a] = ES+EC;V[a]->t = b;V[a]->c = c;
    ES[++EC].next = V[b];V[b] = ES+EC;V[b]->t = a;V[b]->c = 0;
    V[a]->op = V[b]; V[b]->op = V[a];
}
bool Dinic_Lable()               //构造层次图
{
    int head,tail,i,j;
    Stap[head=tail=0] = S;
    memset(Lv,-1,sizeof(Lv));
    Lv[S] = 0;
    while(head<=tail){
        i = Stap[head++];
        for(Edge *e = V[i];e;e = e->next){
            j = e->t;
            if(e->c&&Lv[j]==-1){
                Lv[j] = Lv[i] + 1;
                if(j==T)
                    return true;
                Stap[++tail] = j;
            }
        }
    }
    return false;
}
void Dinic_Augment()            //增广
{
    int i,j,delta,Stop;
    for(i = S;i <= T;++i)
        P[i] = V[i];
    Stap[Stop=1] = S;
    while(Stop){
        i = Stap[Stop];
        if(i != T){
            for(;P[i];P[i] = P[i]->next)
                if(P[i]->c&&Lv[i]+1==Lv[j=P[i]->t])
                   break;
            if(P[i]){
                Stap[++Stop] = j;
                Stae[Stop] = P[i];
            }
            else
                Stop--,Lv[i] = -1;
        }
        else
        {
            delta = INF;
            for(i = Stop;i >= 2;--i)
                if(Stae[i]->c < delta)
                    delta = Stae[i]->c;
            Maxflow += delta;
            for(i = Stop;i >= 2;--i){
                Stae[i]->c -= delta;
                Stae[i]->op->c += delta;
                if(Stae[i]->c == 0)
                    Stop = i-1;
            }
        }
 
    }
}
void Dinic()
{
    while(Dinic_Lable())
        Dinic_Augment();
}
void init()
{
    int i,a,c;
    S = 0; T = M+N+1;
    for(i = 1;i <= M;++i){
        scanf("%d",&c);
        addedge(S,i,c);
        Ans += c;
//        for(;;){
//            int sum = 0;
//            c = getchar();
//            while(c == ' ')c = getchar();
//            if(c=='\n') break;
//            while(c!=' '&&c!='\n'){
//                sum *= 10;
//                sum += c - '0';
//                c = getchar();
//            }              printf("sum ==  %d\n",sum);
//            addedge(i,sum+M,INF);
//            if(c=='\n') break;
//        }
        for (;;){
            while((c=getchar())==' '); ungetc(c,stdin);
            if (c==10 || c==13) break;
            scanf("%d",&a);
            addedge(i,a+M,INF);
        }
    }
 
    for(i = 1;i <= N;++i){
        scanf("%d",&c);
        addedge(i+M,T,c);
    }
}
void print()
{
    for(int i = 1;i <= M;++i)
        if(Lv[i]!=-1)
           printf("%d ",i);
    putchar('\n');
    for(int i = M+1;i <= M+N;++i)
        if(Lv[i]!=-1)
           printf("%d ",i-M);
    Ans -= Maxflow;
    printf("\n%d\n",Ans);
}
int main()
{
//    freopen("Input.txt","r",stdin);
    while(~scanf("%d%d",&M,&N)){
        Clear();
        init();
        Dinic();
        print();
    }
    return 0;
}
 
  

容器实现

#include <iostream>
#include <algorithm>
#include <sstream>
#include <vector>
#include <queue>
#include <cstdio>
#include <cstring>
using namespace std;
 
const int MAXN = 1e3 + 5,INF = ~0U >> 2;
struct Edge{
   int from,to,cap,flow;
   Edge(int f,int t,int c,int _f)
       :from(f),to(t),cap(c),flow(_f){};
};
vector<Edge> edges;
vector<int> G[MAXN];
int N,M,S,T;
int d[MAXN],cur[MAXN];
bool vst[MAXN];
void Init()
{
    for(int i = 0;i < MAXN;++i)
        G[i].clear();
    edges.clear();
}
inline void AddEdge(int from,int to,int cap)
{
    edges.push_back(Edge(from,to,cap,0));
    edges.push_back(Edge(to,from,0,0));
    int sz = edges.size();
    G[from].push_back(sz-2);
    G[to].push_back(sz-1);
}
bool BFS()
{
    memset(vst,false,sizeof(vst));
    queue<int> Q;
    Q.push(S);
    d[S] = 0;
    vst[S] = true;
    while(!Q.empty()){
        int x = Q.front();
        Q.pop();
        for(int i = 0;i < (int)G[x].size();++i){
            Edge& e = edges[G[x][i]];
            if(!vst[e.to]&&e.cap>e.flow){
                vst[e.to] = true;
                d[e.to] = d[x] + 1;
                Q.push(e.to);
            }
        }
    }
    return vst[T];
}
int DFS(int u,int a)
{
    if(u==T||a==0)
        return a;
    int f,flow = 0;
    for(int& i = cur[u];i < (int)G[u].size();++i){
         Edge& e = edges[G[u][i]];
         if(d[u]+1==d[e.to]&&(f=DFS(e.to,min(a,e.cap-e.flow)))>0){
             e.flow += f;
             edges[G[u][i]^1].flow -= f;
             flow += f;
             a -= f;
             if(a==0)break;
         }
    }
    return flow;
}
int Maxflow()
{
    int flow = 0;
    while(BFS()){
        memset(cur,0,sizeof(cur));
        flow += DFS(S,INF);
    }
    return flow;
}
void Solve()
{
    int i,c,ans = 0;
    S = 0; T = M+N+1;
    for(i = 1;i <= M;++i){
        scanf("%d",&c);
        AddEdge(S,i,c);
        ans += c;
        string str;
        getline(cin,str);
        istringstream ssin(str);
        while(ssin>>c)
            AddEdge(i,c+M,INF);
    }
    for(i = 1;i <= N;++i){
        scanf("%d",&c);
        AddEdge(i+M,T,c);
    }
    int maxflow = Maxflow();
    for(i = 1;i <= M;++i)
       if(vst[i])
         printf("%d ",i);
    putchar('\n');
    for(i = M+1;i <= M+N;++i)
       if(vst[i])
          printf("%d ",i-M);
    printf("\n%d\n",ans-maxflow);
}
int main()
{
//    freopen("Input.txt","r",stdin);
    while(~scanf("%d%d",&M,&N)){
        Init();
        Solve();
    }
    return 0;
}