1877: [SDOI2009]晨跑费用流-优快云博客

本文介绍了一种解决拆点费用流问题的算法实现过程，包括数据结构设计、SPFA算法应用以及最大流量最小费用计算。

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拆点费用流。。

#include<iostream>
#include<cstdio>
#include<cstring>
#define M 405
#define inf 1000000007
using namespace std;
int n,m,T,cnt=1,ans1,ans2;
int head[405],dis[405],q[405],path[405];
bool vis[405];
int list[50005],next[50005],from[50005],flow[50005],cost[50005];
inline int read()
{
    int a=0,f=1; char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1; c=getchar();}
    while (c>='0'&&c<='9') {a=a*10+c-'0'; c=getchar();}
    return a*f;
}
inline void insert(int x,int y,int z,int w)
{
    next[++cnt]=head[x];
    head[x]=cnt;
    from[cnt]=x;
    list[cnt]=y;
    flow[cnt]=z;
    cost[cnt]=w;
}
inline bool spfa()
{
    for (int i=1;i<=T;i++) dis[i]=inf;
    dis[1]=0; q[1]=1; vis[1]=1;
    int t=0,w=1,x;
    while (t!=w)
    {
        t=(t+1)%M;
        x=q[t];
        for (int i=head[x];i;i=next[i])
            if (flow[i]&&dis[list[i]]>dis[x]+cost[i])
            {
                dis[list[i]]=dis[x]+cost[i];
                path[list[i]]=i;
                if (!vis[list[i]])
                {
                    vis[list[i]]=1;
                    w=(w+1)%M;
                    q[w]=list[i];
                }
            }
        vis[x]=0;
    }
    return dis[T]!=inf;
}
inline void mcf()
{
    int x=inf;
    for (int i=path[T];i;i=path[from[i]]) x=min(x,flow[i]);
    for (int i=path[T];i;i=path[from[i]])
        ans2+=x*cost[i],flow[i]-=x,flow[i^1]+=x;
    ans1+=x;
}
int main()
{
    n=read(); m=read(); T=2*n;
    for (int i=1;i<=m;i++)
    {
        int u=read(),v=read(),w=read();
        insert(u+n,v,1,w); insert(v,u+n,0,-w);
    }
    insert(1,n+1,inf,0); insert(n+1,1,0,0);
    insert(n,n+n,inf,0); insert(n+n,n,0,0);
    for (int i=2;i<n;i++)
        insert(i,i+n,1,0),insert(i+n,i,0,0);
    while (spfa()) mcf();
    cout << ans1 << " " << ans2 << endl;
    return 0;
}