P2517 [HAOI2010]订货

思路

费用流水题

对每月拆点，入点向出点连cap=ui的边，s向入点连cost=di的边，i的入点向i+1的入点连cap=S的边即可

代码

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <queue>
#include <vector>
using namespace std;
struct Edge{
    int u,v,cap,flow,cost;
};
const int MAXN = 5001;
const int INF = 0x3f3f3f3f;
vector <Edge> edges;
vector <int> G[MAXN];
int n,m,s,t,S;
int a[MAXN],p[MAXN],d[MAXN];
bool vis[MAXN];
void addedge(int u,int v,int cap,int cost){
    edges.push_back((Edge){u,v,cap,0,cost});
    edges.push_back((Edge){v,u,0,0,-cost});
    int cnt=edges.size();
    G[u].push_back(cnt-2);
    G[v].push_back(cnt-1);
}
bool spfa(int s,int t,int &cost,int &flow){
    memset(d,0x3f,sizeof(d));
    memset(vis,0,sizeof(vis));
    d[s]=0;p[s]=0;a[s]=0x3f3f3f3f;
    queue<int> q;
    q.push(s);
    vis[s]=true;
    while(!q.empty()){
        int x=q.front();q.pop();
        vis[x]=false;
        for(int i=0;i<G[x].size();i++){
            Edge &e=edges[G[x][i]];
            if(e.cap>e.flow&&d[e.v]>d[x]+e.cost){
                d[e.v]=d[x]+e.cost;
                p[e.v]=G[x][i];
                a[e.v]=min(a[x],e.cap-e.flow);
                if(!vis[e.v]){
                    q.push(e.v);
                    vis[e.v]=true;
                }
            }
        }
    }
    if(d[t]==0x3f3f3f3f)
        return false;
    flow+=a[t];
    cost+=d[t]*a[t];
    for(int u=t;u!=s;u=edges[p[u]].u){
        edges[p[u]].flow+=a[t];
        edges[p[u]^1].flow-=a[t];
    }
    return true;
}
void MFMC(int s,int t,int &flow,int &cost){
    flow=0;
    cost = 0;
    while(spfa(s,t,cost,flow));
    return;
}
int main(){
    s=MAXN-2;
    t=MAXN-3;
    scanf("%d %d %d",&n,&m,&S);
    for(int i=1;i<=n;i++){
        int mid;
        scanf("%d",&mid);
        addedge(i,i+n,mid,0);
        addedge(i+n,t,INF,0);
    }
    for(int i=1;i<=n;i++){
        int mid;
        scanf("%d",&mid);
        addedge(s,i,INF,mid);
        if(i!=n)
            addedge(i,i+1,S,m);
    }
    int flow,cost;
    MFMC(s,t,flow,cost);
    printf("%d\n",cost);
    return 0;
}