[BZOJ3931][CQOI2015]网络吞吐量（spfa+最大流）

题目描述

传送门

题解

求出最短路径图之后拆点跑最大流。

判断一条边在最短路图上：dis[edge[i].x]+redis[edge[i].y]+edge[i].w==dis[n]或dis[edge[i].y]+redis[edge[i].x]+edge[i].w==dis[n]，其中dis和redis都是单源最短路，源分别为1和n

代码

#include<algorithm>
#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>
using namespace std;
#define LL long long
const int max_n=505;
const int max_N=max_n*2;
const int max_m=1e5+5;
const int max_e=max_m*4;
const LL INF=1e18;

int n,m,N;LL val[max_n],dis[max_n],redis[max_n]; bool vis[max_n];
int tot,point[max_N],nxt[max_e],v[max_e];LL remain[max_e],c[max_e];
int deep[max_N],cur[max_N],last[max_N],num[max_N];
struct hp{int x,y;LL w;}edge[max_m];
queue <int> q;
LL maxflow;

inline void add(int x,int y,LL z)
{
    ++tot; nxt[tot]=point[x]; point[x]=tot; v[tot]=y; c[tot]=z;
    ++tot; nxt[tot]=point[y]; point[y]=tot; v[tot]=x; c[tot]=z;
}
inline void spfa_1(int s,int t)
{
    for (int i=1;i<=n;++i) dis[i]=INF; dis[s]=0;
    memset(vis,0,sizeof(vis)); vis[s]=true;
    while (!q.empty()) q.pop(); q.push(s);

    while (!q.empty())
    {
        int now=q.front(); q.pop();
        vis[now]=false;
        for (int i=point[now];i;i=nxt[i])
            if (dis[v[i]]>dis[now]+c[i])
            {
                dis[v[i]]=dis[now]+c[i];
                if (!vis[v[i]])
                {
                    vis[v[i]]=true;
                    q.push(v[i]);
                }
            }
    }
}
inline void spfa_2(int s,int t)
{
    for (int i=1;i<=n;++i) redis[i]=INF; redis[s]=0;
    memset(vis,0,sizeof(vis)); vis[s]=true;
    while (!q.empty()) q.pop(); q.push(s);

    while (!q.empty())
    {
        int now=q.front(); q.pop();
        vis[now]=false;
        for (int i=point[now];i;i=nxt[i])
            if (redis[v[i]]>redis[now]+c[i])
            {
                redis[v[i]]=redis[now]+c[i];
                if (!vis[v[i]])
                {
                    vis[v[i]]=true;
                    q.push(v[i]);
                }
            }
    }
}
inline void addedge(int x,int y,LL cap)
{
    ++tot; nxt[tot]=point[x]; point[x]=tot; v[tot]=y; remain[tot]=cap;
    ++tot; nxt[tot]=point[y]; point[y]=tot; v[tot]=x; remain[tot]=0;
}

inline void bfs(int t)
{
    for (int i=1;i<=N;++i) deep[i]=N; deep[t]=0;
    while (!q.empty()) q.pop(); q.push(t);

    while (!q.empty())
    {
        int now=q.front(); q.pop();
        for (int i=point[now];i!=-1;i=nxt[i])
            if (deep[v[i]]==N&&remain[i^1])
            {
                deep[v[i]]=deep[now]+1;
                q.push(v[i]);
            }
    }
}
inline LL addflow(int s,int t)
{
    int now=t; LL ans=INF;
    while (now!=s)
    {
        ans=min(ans,remain[last[now]]);
        now=v[last[now]^1];
    }
    now=t;
    while (now!=s)
    {
        remain[last[now]]-=ans;
        remain[last[now]^1]+=ans;
        now=v[last[now]^1];
    }
    return ans;
}
inline void isap(int s,int t)
{
    bfs(t);
    for (int i=1;i<=N;++i) ++num[deep[i]];
    for (int i=1;i<=N;++i) cur[i]=point[i];

    int now=s;
    while (deep[s]<N)
    {
        if (now==t)
        {
            maxflow+=addflow(s,t);
            now=s;
        }
        bool has_find=false;
        for (int i=cur[now];i!=-1;i=nxt[i])
        {
            if (deep[v[i]]+1==deep[now]&&remain[i])
            {
                has_find=true;
                cur[now]=i;
                last[v[i]]=i;
                now=v[i];
                break;
            }
        }
        if (!has_find)
        {
            int minn=N-1;
            for (int i=point[now];i!=-1;i=nxt[i])
                if (remain[i])
                    minn=min(minn,deep[v[i]]);
            if (!(--num[deep[now]])) break;
            num[deep[now]=minn+1]++;
            cur[now]=point[now];
            if (now!=s)
                now=v[last[now]^1];
        }
    }
}
int main()
{
    scanf("%d%d",&n,&m);
    for (int i=1;i<=m;++i)
    {
        scanf("%d%d%lld",&edge[i].x,&edge[i].y,&edge[i].w);
        add(edge[i].x,edge[i].y,edge[i].w);
    }
    for (int i=1;i<=n;++i) scanf("%lld",&val[i]);
    spfa_1(1,n);
    spfa_2(n,1);

    tot=-1;
    memset(point,-1,sizeof(point));
    memset(nxt,-1,sizeof(nxt));
    for (int i=1;i<=m;++i)
    {
        if (dis[edge[i].x]+redis[edge[i].y]+edge[i].w==dis[n])
            addedge(edge[i].x+n,edge[i].y,INF);
        else if (dis[edge[i].y]+redis[edge[i].x]+edge[i].w==dis[n])
            addedge(edge[i].y+n,edge[i].x,INF);
    }
    addedge(1,1+n,INF);
    addedge(n,n+n,INF);
    for (int i=2;i<n;++i)
        addedge(i,i+n,val[i]);
    N=n*2;
    isap(1,N);
    printf("%lld\n",maxflow);
}