HihoCoder1398 Network flow 5. Maximum weight closed subgraph (network flow)

topic analysis

Note that the number of edges is a constraint, not the number of vertices.

Code overview

#include<bits/stdc++.h>
using namespace std;
const int nmax = 10000;
const int INF = 0x3f3f3f3f;
typedef long long ll;
typedef struct{
    int to,nxt;
    ll w;
}Edge;
Edge e[nmax<<1];
int cur[nmax], dep[nmax], head[nmax] ,S, T, tot,n,m;
ll w,ans = 0;
void add(int u, int v, ll w){
    e[tot].to = v;
    e[tot].nxt = head[u];
    e[tot].w = w;
    head[u] = tot ++;
}
bool bfs(){
    memset(dep,-1,sizeof dep); dep[S] = 0;
    queue<int> q; q.push(S);
    while(!q.empty()){
        int now = q.front(); q.pop();
        for(int i = head[now]; i!= -1; i = e[i].nxt){
            int v = e[i].to;
            if(dep[v] == -1 && e[i].w){
                dep[v] = dep[now] + 1;
                q.push(v);
            }
        }
    }
    return dep[T] !=-1;
}
ll dfs(int now, ll flow){
    if(now == T || !flow) return flow;
    ll f = 0;
    for(int & i = cur[now]; i!=-1; i = e[i].nxt){
        int v = e[i].to;
        if(dep[v] == dep[now] + 1 && e[i].w){
            ll tt = dfs(v,min(flow,e[i].w));
            if(tt){
                e[i].w -= tt; e[i^1].w += tt;
                flow -= tt;
                f += tt;
                if(flow == 0) break;
            }
        }
    }
    return f;
}
void dinic(){
    while(bfs()){
        for(int i = 0;i<=T;++i) cur[i] = head[i];
        while(ll tt = dfs(S,INF)) ans -= tt;
    }
}
int main(){
    scanf("%d %d",&n,&m);
    memset(head,-1,sizeof head); tot = 0;
    S = 0; T = n+m+1;
    for(int i = 1;i<=m;++i){
        scanf("%lld",&w);
        add(i+n,T,w); add(T,i+n,0);
    }
    int nn,num;
    for(int i = 1;i<=n;++i){
        scanf("%lld %d",&w,&nn);
        ans += w;
        add(S,i,w);
        add(i,S,0);
        for(int j = 1;j<=nn;++j){
            scanf("%d",&num);
            add(i,num+n,INF);
            add(num+n,i,0);
        }
    }
    dinic();
    printf("%lld\n",ans);
    return 0;
}