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  • BZOJ 3931 网络吞吐量

    题面即题解。

    #include<iostream>
    #include<cstdio>
    #include<cstring>
    #include<algorithm>
    #include<queue>
    #define maxn 505
    #define maxv 1050
    #define maxe 300500
    #define inf 0x7f7f7f7f7f7f7f7fLL
    using namespace std;
    long long n,m,x[maxe],y[maxe],d[maxe],dis[maxv],nume=1,s,t,lim[maxv],g[maxv];
    struct edge
    {
        long long v,f,c,nxt;
    }e[maxe];
    struct sta
    {
        long long v,len;
        sta (long long v,long long len):v(v),len(len) {}
        sta () {}
        friend bool operator < (const sta & x,const sta & y)
        {
            return x.len>y.len;
        }
    };
    priority_queue <sta> q;
    queue <long long> qt;
    void addedge(long long u,long long v,long long f,long long c)
    {
        e[++nume].v=v;e[nume].f=f;e[nume].c=c;
        e[nume].nxt=g[u];g[u]=nume;
    }
    void dijkstra()
    {
        q.push(sta(1,0));dis[1]=0;
        for (long long i=2;i<=n;i++) dis[i]=inf;
        while (!q.empty())
        {
            sta head=q.top();q.pop();
            for (long long i=g[head.v];i;i=e[i].nxt)
            {
                long long v=e[i].v;
                if (dis[v]>dis[head.v]+e[i].c)
                {
                    dis[v]=dis[head.v]+e[i].c;
                    q.push(sta(v,dis[v]));
                }
            }
        }
    }
    void build()
    {
        nume=1;memset(g,0,sizeof(g));s=0;t=2*n+1;lim[1]=lim[n]=inf;
        for (long long i=1;i<=m;i++)
        {
            if (dis[x[i]]+d[i]==dis[y[i]]) {addedge(x[i]+n,y[i],inf,0);addedge(y[i],x[i]+n,0,0);}
            if (dis[y[i]]+d[i]==dis[x[i]]) {addedge(x[i],y[i]+n,0,0);addedge(y[i]+n,x[i],inf,0);}
        }
        for (long long i=1;i<=n;i++) {addedge(i,i+n,lim[i],0);addedge(i+n,i,0,0);}
        addedge(s,1,inf,0);addedge(1,s,0,0);
        addedge(2*n,t,inf,0);addedge(t,2*n,0,0);
    }
    bool bfs()
    {
        for (long long i=s;i<=t;i++) dis[i]=inf;
        dis[s]=0;while (!qt.empty()) qt.pop();qt.push(s);
        while (!qt.empty())
        {
            long long head=qt.front();qt.pop();
            for (long long i=g[head];i;i=e[i].nxt)
            {
                long long v=e[i].v;
                if ((dis[v]>dis[head]+1) && (e[i].f>0))
                {
                    dis[v]=dis[head]+1;
                    qt.push(v);
                }
            }
        }
        return dis[t]!=inf;
    }
    long long dinic(long long x,long long low)
    {
        if (x==t) return low;
        long long ret=0;
        for (long long i=g[x];i && low;i=e[i].nxt)
        {
            long long v=e[i].v;
            if ((dis[v]==dis[x]+1) && (e[i].f))
            {
                long long dd=dinic(v,min(low,e[i].f));
                ret+=dd;low-=dd;
                e[i].f-=dd;e[i^1].f+=dd;            
            }
        }
        if (!ret) dis[x]=inf;
        return ret;
    }
    int main()
    {
        scanf("%lld%lld",&n,&m);
        for (long long i=1;i<=m;i++)
        {
            scanf("%lld%lld%lld",&x[i],&y[i],&d[i]);
            addedge(x[i],y[i],0,d[i]);
            addedge(y[i],x[i],0,d[i]);
        }
        dijkstra();
        for (long long i=1;i<=n;i++) scanf("%lld",&lim[i]);
        build();
        long long mx_flow=0;
        while (bfs())
            mx_flow+=dinic(s,inf);
        printf("%lld
    ",mx_flow);
        return 0;
    }
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  • 原文地址:https://www.cnblogs.com/ziliuziliu/p/6322486.html
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