正题

题目链接:https://www.luogu.org/problem/U94222?contestId=23574

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题目大意

$n$个点若条有向边,求一条路径要求

1. 经过一个酒店
2. 经过权值最大
3. 消费最小
4. 起点编号最小

按照顺序满足。

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解题思路

将强连通分量缩成一个点，然后用$g_{i,0/1}$到达第$i$个点，是否经过酒店的最大权值，$f_{i,0/1}$最小消费，$n{u}_{i,0/1}$最小编号即可。然后跑$DAGdp$即可

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$code$

#include<cstdio>
#include<stack>
#include<queue>
#include<cstring>
#define ll long long
using namespace std;
const ll N=110000;
stack<ll> Stack;
queue<ll> q;
struct line{ll to,from,next;
}a[N];
ll n,m,x,y,tot,maxs,top,num;
ll in[N],ls[N],fl[N],cost[N],f[N][2],g[N][2];
ll J[N],low[N],dfn[N],anc[N],anv[N],val[N],nu[N][2];
bool ins[N],v[N],hotel[N];
void addl(ll x,ll y,ll tot)
{a[tot].to=y;a[tot].from=x;a[tot].next=ls[x];ls[x]=tot;
}
void tarjan(ll x)
{ins[x]=true;dfn[x]=low[x]=++top;Stack.push(x);for (ll i=ls[x];i;i=a[i].next)if (!dfn[a[i].to]){tarjan(a[i].to);low[x]=min(low[x],low[a[i].to]);}else if (ins[a[i].to])low[x]=min(low[x],dfn[a[i].to]);if (low[x]==dfn[x]){while (Stack.top()!=x){ll y=Stack.top();fl[y]=x;anc[x]+=cost[y];anv[x]+=val[y];hotel[x]|=hotel[y];Stack.pop();ins[y]=0;nu[x][0]=min(nu[x][0],y);}fl[x]=x;anc[x]+=cost[x];anv[x]+=val[x];ins[x]=0;nu[x][0]=min(nu[x][0],x);nu[x][1]=nu[x][0];Stack.pop();}
}
void bfs()
{while (!q.empty()){ll x=q.front();q.pop();for (ll i=ls[x];i;i=a[i].next){ll y=a[i].to;if(g[x][0]+anv[y]>g[y][hotel[y]])g[y][hotel[y]]=g[x][0]+anv[y],f[y][hotel[y]]=f[x][0]+anc[y],nu[y][hotel[y]]=nu[x][0];else if(g[x][0]+anv[y]==g[y][hotel[y]]&&f[y][hotel[y]]>f[x][0]+anc[y])f[y][hotel[y]]=f[x][0]+anc[y],nu[y][hotel[y]]=nu[x][0];else if(g[x][0]+anv[y]==g[y][hotel[y]]&&f[y][hotel[y]]==f[x][0]+anc[y])nu[y][hotel[y]]=min(nu[y][hotel[y]],nu[x][0]);if(g[x][1]+anv[y]>g[y][1])g[y][1]=g[x][1]+anv[y],f[y][1]=f[x][1]+anc[y],nu[y][1]=nu[x][1];else if(g[x][1]+anv[y]==g[y][1]&&f[y][1]>f[x][1]+anc[y])f[y][1]=f[x][1]+anc[y],nu[y][1]=nu[x][1];else if(g[x][1]+anv[y]==g[y][1]&&f[y][1]==f[x][1]+anc[y])nu[y][1]=min(nu[y][1],nu[x][1]);if(g[x][0]+anv[y]>g[y][0])g[y][0]=g[x][0]+anv[y],f[y][0]=f[x][0]+anc[y],nu[y][0]=nu[x][0];else if(g[x][0]+anv[y]==g[y][0]&&f[y][0]>f[x][0]+anc[y])f[y][0]=f[x][0]+anc[y],nu[y][0]=nu[x][0];else if(g[x][0]+anv[y]==g[y][0]&&f[y][0]==f[x][0]+anc[y])nu[y][0]=min(nu[y][0],nu[x][0]);in[y]--;if (!in[y]&&!v[y]){q.push(y);v[y]=1;}}}
}
int main()
{memset(nu,0x3f,sizeof(nu));scanf("%lld",&n);for(ll i=1;i<=n;i++)scanf("%lld",&cost[i]);for(ll i=1;i<=n;i++)scanf("%lld",&val[i]);scanf("%lld",&m);for(ll i=1;i<=m;i++)scanf("%lld",&J[i]);for(ll i=1;i<=m;i++)while(1){ll x;scanf("%lld",&x);if(!x) break;addl(x,(x+J[i]-1)%n+1,++tot);}for(ll i=1;i<=n;i++)scanf("%lld",&hotel[i]);for(ll i=1;i<=n;i++)if (!dfn[i])tarjan(i);ll Tot=tot;tot=0;memset(ls,0,sizeof(ls));for (ll i=1;i<=Tot;i++){x=a[i].from;y=a[i].to;if (fl[x]!=fl[y]){tot++;addl(fl[x],fl[y],tot);in[fl[y]]++;}}memset(g,-127,sizeof(g));for (ll i=1;i<=n;i++)if (fl[i]==i&&!in[i]){q.push(i);v[i]=true;g[i][0]=g[i][hotel[i]]=anv[i];f[i][0]=f[i][hotel[i]]=anc[i];}bfs();maxs=0;g[0][0]=g[0][1]=0;ll mark=0,Mark=0;for(ll i=1;i<=n;i++)if(fl[i]==i){if(g[i][0]>g[mark][0]) mark=i;else if(g[i][0]==g[mark][0]&&f[i][0]<f[mark][0])mark=i;else if(g[i][0]==g[mark][0]&&f[i][0]==f[mark][0]&&nu[i][0]<nu[mark][0])mark=i;if(g[i][1]>g[Mark][1]) Mark=i;else if(g[i][1]==g[Mark][1]&&f[i][1]<f[Mark][1])Mark=i;else if(g[i][1]==g[Mark][1]&&f[i][1]==f[Mark][1]&&nu[i][1]<nu[Mark][1])Mark=i;}if(!Mark)printf("%lld %lld %lld",-nu[mark][0],-g[mark][0],-f[mark][0]);else printf("%lld %lld %lld",nu[Mark][1],g[Mark][1],f[Mark][1]);
}