2024 Jiangsu Collegiate Programming Contest H

记录一下为数不多的网络流

#pragma GCC optimize(3,"Ofast","inline")
#include<bits/stdc++.h>
#include <execution>
using namespace std;
using i64 = long long;
using i128 = __int128;

template <typename T>struct MCFgraph{
    struct edge{
        int v;T c,f;
        edge(int v,T c,T f):v(v),c(c),f(f){}
    };  
    const int n;
    vector<edge> e;
    vector<vector<int>> g;
    vector<i64> h,dis;
    vector<int> pre;
    bool dij(int s,int t){
        dis.assign(n,numeric_limits<i64>::max());pre.assign(n,-1);
        priority_queue<pair<i64,int>,vector<pair<i64,int>>,greater<pair<i64,int>>> q;
        dis[s]=0;q.emplace(0,s);
        while(!q.empty()){
            i64 d = q.top().first;int u = q.top().second;q.pop();
            for(int i:g[u]){
                int v = e[i].v;
                T c = e[i].c;
                T f = e[i].f;
                if(c>0&&dis[v]>d+h[u]-h[v]+f){
                    dis[v] = d+h[u]-h[v]+f;
                    pre[v]=i;
                    q.emplace(dis[v],v);
                }
            }
        }
        return dis[t]!=numeric_limits<i64>::max();
    }
    MCFgraph(int n):n(n),g(n){}
    void addedge(int u,int v,T c,T f){
        g[u].push_back(e.size());
        e.emplace_back(v,c,f);
        g[v].push_back(e.size());
        e.emplace_back(u,0,-f);
    }
    pair<T,i64> flow(int s,int t){
        T flow = 0;i64 cost = 0;h.assign(n,0);
        while(dij(s,t)){
            for(int i = 0;i<n;++i) h[i]+=dis[i];
            T aug = numeric_limits<i64> ::max();
            for(int i = t;i!=s;i = e[pre[i]^1].v) aug= min(aug,e[pre[i]].c);
            for(int i = t;i!=s;i = e[pre[i]^1].v){e[pre[i]].c-=aug;e[pre[i]^1].c+=aug;}
            flow+=aug;cost+=i64(aug*h[t]);
        }
        return make_pair(flow,cost);
    }
};
using mcf = MCFgraph<i64>;

void solve(){
    int n;
    cin>>n;
    mcf g(4*n+10);//0,4*n+1 (i-1)*3+1+2+3
    int id=3*n+1;
    constexpr i64 inf = 1e18;
    vector<int> a(n+1);
    for(int i = 1;i<=n;++i){
        int op;
        cin>>op;
        if(i+1<=n){
            g.addedge((i-1)*3+1,i*3+1,inf,0);
            g.addedge((i-1)*3+2,i*3+2,inf,0);
            g.addedge((i-1)*3+3,i*3+3,inf,0);
        }
        if(op==1){
            cin>>a[i];
            g.addedge(0,id,1,0);
            g.addedge(id,(i-1)*3+1,1,1);
            g.addedge(id,(i-1)*3+2,1,(a[i]+9)/10);
            g.addedge(id,(i-1)*3+3,1,0);
            g.addedge(id,4*n+1,1,a[i]);
            id++;//更新id
        }else{
            g.addedge((i-1)*3+1,4*n+1,1,0);
            g.addedge((i-1)*3+2,4*n+1,1,0);
            g.addedge((i-1)*3+3,4*n+1,1,0);
        }
    }
    i64 sum = reduce(std::execution::par,a.begin()+1,a.end(),0);
    cout<<sum-g.flow(0,4*n+1).second<<"\n";
}

signed main(){
    ios::sync_with_stdio(0);cin.tie(0);
    int t=1;
    cin>>t;
    while(t--) solve();
    return 0;
}