【bzoj2893】征服王

比较明显的缩点，变成dag上最小路径覆盖，指定了起点终点所以建模有一些变化。

跑费用流，增广的次数即为答案。

#include<bits/stdc++.h>
#define maxn 5005
#define maxm 100005
#define INF 0x7f7f7f7f
using namespace std;

inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)f=-1;ch=getchar();}
    while(ch>=‘0‘&&ch<=‘9‘){x=x*10+ch-‘0‘;ch=getchar();}
    return x*f;
}

struct scsc{
    int next,from,to,w,c;
}edge[maxm<<1];

struct _scsc{
    int next,to;
}_edge[maxm<<1];

int n,m,_Len,Len,scc,top,Time,_head[maxn],head[maxn],dfn[maxn],low[maxn],s[maxn],vis[maxn],hav[maxn],belong[maxn],p[maxn][2];
int sss,ttt,ss[maxn],tt[maxn],d[maxn],pre[maxn];

void addedge(int u,int v,int w,int c){
    edge[++Len].to=v;edge[Len].from=u;edge[Len].next=head[u];edge[Len].w=w;edge[Len].c=c;head[u]=Len;
    edge[++Len].to=u;edge[Len].from=v;edge[Len].next=head[v];edge[Len].w=0;edge[Len].c=-c;head[v]=Len;
}

void _addedge(int u,int v){
    _edge[++_Len].to=v;_edge[_Len].next=_head[u];_head[u]=_Len;
}

void tarjan(int u){
    dfn[u]=low[u]=++Time;
    s[++top]=u;vis[u]=1;
    for(int i=_head[u];i;i=_edge[i].next){
        int v=_edge[i].to;
        if(!dfn[v]){
            tarjan(v);
            low[u]=min(low[u],low[v]);
        }else
        if(vis[v])low[u]=min(low[u],dfn[v]);
    }
    int now=0;
    if(dfn[u]==low[u]){
        ++scc;
        while(now!=u){
            now=s[top--];
            vis[now]=0;
            ++hav[scc];
            belong[now]=scc;
        }
    }
}

int id=0;

void rebuild(int s,int t){
    for(int i=1;i<=scc;++i)p[i][0]=++id,p[i][1]=++id;
    for(int i=1;i<=sss;++i)addedge(s,p[belong[ss[i]]][0],INF,0);
    for(int i=1;i<=ttt;++i)addedge(p[belong[tt[i]]][1],t,INF,0);
    for(int i=1;i<=scc;++i)addedge(p[i][0],p[i][1],1,1),addedge(p[i][0],p[i][1],INF,0);
    for(int u=1;u<=n;++u){
        for(int i=_head[u];i;i=_edge[i].next){
            int v=_edge[i].to;
            if(belong[u]!=belong[v])
                addedge(p[belong[u]][1],p[belong[v]][0],INF,0);
        }
    }
}

int spfa(int s,int t){
    queue<int>Q;
    memset(d,-1,sizeof(d));
    Q.push(s);vis[s]=1;d[s]=0;
    while(!Q.empty()){
        int u=Q.front();Q.pop();
        for(int i=head[u];i;i=edge[i].next){
            int v=edge[i].to;
            if(edge[i].w&&d[v]<d[u]+edge[i].c){
                d[v]=d[u]+edge[i].c;pre[v]=i;
                if(!vis[v]){
                    vis[v]=1;
                    Q.push(v);
                }
            }
        }
        vis[u]=0;
    }
    return d[t]!=-1;
}

int mcmf(int s,int t){
    int ret=0,now=0,last=0;
    while(spfa(s,t)){
        int w=INF;last=now;
        for(int i=pre[t];i;i=pre[edge[i].from])w=min(w,edge[i].w);
        for(int i=pre[t];i;i=pre[edge[i].from]){
            edge[i].w-=w;
            edge[i^1].w+=w;
            now+=w*edge[i].c;
        }
        if(now==last)break;
        ++ret;
    }
    if(now!=scc)return -1;
    return ret;
}

void Init(){
    Len=1;memset(head,0,sizeof(head));id=scc=0;
    _Len=0;memset(_head,0,sizeof(_head));
    memset(pre,0,sizeof(pre));
    memset(dfn,0,sizeof(dfn));
    memset(low,0,sizeof(low));
    int f1,f2;
    n=read();m=read();sss=read();ttt=read();
    for(int i=1;i<=sss;++i)ss[i]=read();
    for(int i=1;i<=ttt;++i)tt[i]=read();
    for(int i=1;i<=m;++i){
        f1=read();f2=read();
        _addedge(f1,f2);
    }
}

void WoRk(){
    for(int i=1;i<=n;++i)if(!dfn[i])tarjan(i);
    int s=0,t=2*n+1;
    rebuild(s,t);
    int ans=mcmf(s,t);
    if(ans==-1)printf("no solution\n");else printf("%d\n",ans);
}

int main(){
    int t=read();
    while(t--){
        Init();
        WoRk();
    }
    return 0;
}