BZOJ1266 AHOI2006上学路线（最短路+最小割）

　　求出最短路后找出可能在最短路上的边，显然割完边后我们需要让图中这样的边无法构成1到n的路径，最小割即可，非常板子。

#include<iostream> 
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<cstring>
#include<algorithm>
using namespace std;
int read()
{
    int x=0,f=1;char c=getchar();
    while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();}
    while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar();
    return x*f;
}
#define N 510
#define M 250000
#define inf 2000000000
int n,m,p[N],d[N],t=0;
bool flag[N];
struct data{int to,nxt,len,cost;
}edge[M];
void addedge(int x,int y,int z,int c){t++;edge[t].to=y,edge[t].nxt=p[x],edge[t].len=z,edge[t].cost=c,p[x]=t;}
namespace flow
{
    int cur[N],q[N],d[N],ans=0;
    struct data{int to,nxt,cap,flow;
    }edge[M];
    void addedge(int x,int y,int z)
    {
        t++;edge[t].to=y,edge[t].nxt=p[x],edge[t].cap=z,edge[t].flow=0,p[x]=t;
        t++;edge[t].to=x,edge[t].nxt=p[y],edge[t].cap=0,edge[t].flow=0,p[y]=t;
    }
    bool bfs()
    {
        memset(d,255,sizeof(d));d[1]=0;
        int head=0,tail=1;q[1]=1;
        do
        {
            int x=q[++head];
            for (int i=p[x];~i;i=edge[i].nxt)
            if (d[edge[i].to]==-1&&edge[i].flow<edge[i].cap)
            {
                d[edge[i].to]=d[x]+1;
                q[++tail]=edge[i].to;
            }
        }while (head<tail);
        return ~d[n];
    }
    int work(int k,int f)
    {
        if (k==n) return f;
        int used=0;
        for (int i=cur[k];~i;i=edge[i].nxt)
        if (d[k]+1==d[edge[i].to])
        {
            int w=work(edge[i].to,min(f-used,edge[i].cap-edge[i].flow));
            edge[i].flow+=w,edge[i^1].flow-=w;
            if (edge[i].flow<edge[i].cap) cur[k]=i;
            used+=w;if (used==f) return f;
        }
        if (used==0) d[k]=-1;
        return used;
    }
    void dinic()
    {
        while (bfs())
        {
            memcpy(cur,p,sizeof(p));
            ans+=work(1,inf);
        }
        cout<<ans;
    }
}
int main()
{
#ifndef ONLINE_JUDGE
    freopen("bzoj1266.in","r",stdin);
    freopen("bzoj1266.out","w",stdout);
    const char LL[]="%I64d
";
#else
    const char LL[]="%lld
";
#endif
    n=read(),m=read();
    for (int i=1;i<=m;i++)
    {
        int x=read(),y=read(),z=read(),c=read();
        addedge(x,y,z,c);addedge(y,x,z,c);
    }
    memset(d,42,sizeof(d));d[1]=0;
    for (int i=1;i<=n;i++)
    {
        int mn=0;
        for (int j=1;j<=n;j++)
        if (!flag[j]&&d[j]<d[mn]) mn=j;
        flag[mn]=1;
        for (int j=p[mn];j;j=edge[j].nxt)
        if (d[mn]+edge[j].len<d[edge[j].to]) d[edge[j].to]=d[mn]+edge[j].len;
    }
    cout<<d[n]<<endl;
    t=-1;memset(p,255,sizeof(p));
    for (int i=1;i<=m;i++)
    {
        if (d[edge[i<<1].to]+edge[i<<1].len==d[edge[i*2-1].to]) 
        flow::addedge(edge[i<<1].to,edge[i*2-1].to,edge[i<<1].cost);
        if (d[edge[i*2-1].to]+edge[i*2-1].len==d[edge[i<<1].to]) 
        flow::addedge(edge[i*2-1].to,edge[i<<1].to,edge[i<<1].cost);
    }
    flow::dinic();
    return 0;
}