https://www.luogu.org/problemnew/show/P4452

又一道看題解的費用流。

註意時間也影響節點，像題解那樣建邊就少很多了。

#include<bits/stdc++.h>
using namespace std;

const int MAXN=700005+1;
const int MAXM=700000;
const int INF=0x3f3f3f3f;
struct Edge{
    int to,next,cap,flow,cost;
}edge[MAXM];
int head[MAXN],tol;
int pre[MAXN],dis[MAXN];
 
bool vis[MAXN];

int n;
void init(){
    tol=0;
    memset(head,-1,sizeof(head));
}

void addedge(int u,int v,int cap,int cost){
    edge[tol].to=v;
    edge[tol].cap=cap;
    edge[tol].cost=cost;
    edge[tol].flow=0;
    edge[tol].next=head[u];
    head[u]=tol++;

    edge[tol].to=u;
    edge[tol].cap
 
=0;
    edge[tol].cost=-cost;
    edge[tol].flow=0;
    edge[tol].next=head[v];
    head[v]=tol++;
}

bool spfa(int s,int t){
    queue<int> q;
    memset(dis,INF,sizeof(dis));
    memset(vis,false,sizeof(vis));
    memset(pre,-1,sizeof(pre));

    dis[s]=0;
    vis[s]=true;
    q.push(s);
    
 
while(!q.empty()){
        int u=q.front();
        q.pop();
        vis[u]=false;
        for(int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].to;
            if(edge[i].cap>edge[i].flow&&dis[v]>dis[u]+edge[i].cost){
                dis[v]=dis[u]+edge[i].cost;
                pre[v]=i;
                if(!vis[v]){
                    vis[v]=true;
                    q.push(v);
                }
            }
        }
    }
    if(pre[t]==-1)
        return false;
    else
        return true;
}

int minCostMaxFlow(int s,int t,int &cost){
    int flow=0;
    cost=0;
    while(spfa(s,t)){
        int Min=INF;
        for(int i=pre[t];i!=-1;i=pre[edge[i^1].to]){
            if(Min>edge[i].cap-edge[i].flow)
                Min=edge[i].cap-edge[i].flow;
        }
        for(int i=pre[t];i!=-1;i=pre[edge[i^1].to]){
            edge[i].flow+=Min;
            edge[i^1].flow-=Min;
            cost+=edge[i].cost*Min;
        }
        flow+=Min;
    }
    return flow;
}
/*
int main(){
    int M,S,T;
    scanf("%d%d%d%d",&N,&M,&S,&T);
    init(N);
    while(M--){
        int u,v,cap,cost;
        scanf("%d%d%d%d",&u,&v,&cap,&cost);
        addedge(u,v,cap,cost);
    }
    int cost=0;
    int flow=minCostMaxFlow(S,T,cost);

    printf("%d %d\n",flow,cost);
}*/

int getid(int id,int T){
    return T*200+id;
}

int g[205][205]={};
int co[205][205]={};

struct Node{
    int a,b,s,t,c;
}node[2000];

int main() {
    init();
    int s=0,s1=700005,T,m,k;
    scanf("%d%d%d%d",&n,&m,&k,&T);
    int t=getid(0,T);

    addedge(s1,s,k,0);//不超過k架飛機
    for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            scanf("%d",&g[i][j]);
        }
    }
    for(int i=0;i<n;i++){
        for(int j=0;j<n;j++){
            scanf("%d",&co[i][j]);
        }
    }

    for(int i=0;i<n;i++){
        int ti=g[i][0];
        int u=getid(i,T-ti);
        addedge(u,t,k,co[i][0]);
    }

    for(int i=0;i<m;i++){
        scanf("%d%d%d%d%d",&node[i].a,&node[i].b,&node[i].s,&node[i].t,&node[i].c);
        int u=getid(node[i].a,node[i].s),v=getid(node[i].b,node[i].t);
        addedge(u,v,1,-node[i].c);
    }

    for(int i=0;i<m;i++){
        for(int j=0;j<m;j++){
            if(node[j].t+g[node[j].b][node[i].a]<=node[i].s){
                int u=getid(node[j].b,node[j].t);int v=getid(node[i].a,node[i].s);
                addedge(u,v,1,co[node[j].b][node[i].a]);
            }

        }
        if(g[0][node[i].a]<=node[i].s){
            int u=0;int v=getid(node[i].a,node[i].s);
            addedge(u,v,1,co[0][node[i].a]);
        }
        if(node[i].t+g[node[i].b][0]<=T){
            int u=getid(node[i].b,node[i].t);int v=t;
            addedge(u,v,1,co[node[i].b][0]);
        }
    }
    /*for(int ti=0;ti<T;ti++){
        for(int u=0;u<n;u++){
            addedge(getid(u,ti),getid(u,ti+1),k,0);
        }
    }*/

    /*while(m--){
        int t1,a,t2,b,cost;
        scanf("%d%d%d%d%d",&a,&b,&t1,&t2,&cost);
        int u=getid(a,t1),v=getid(b,t2);
        addedge(u,v,1,-cost);
        for(int i=0;i<n;i++){
            if(i==a)
                continue;
            int ti=g[i][a];
            if(t1-ti>=0)
                addedge(getid(i,t1-ti),u,1,co[i][a]);
        }
       // cout<<"cost="<<cost<<endl;
    }*/

    int cost;
    int flow=minCostMaxFlow(s1,t,cost);
    printf("%d\n",-cost);
}

洛谷 - P4452 - 航班安排 - 費用流