[ 前后缀优化建图 2-SAT ] Codeforces587D Duff in Mafia

题解

#include<bits/stdc++.h>using namespace std;#define ll long longinline char nc(){    static char buf[100000],*p1=buf,*p2=buf;    return p1==p2&&(p2=(p1=buf)+fread(buf,1,100000,stdin),p1==p2)?EOF:*p1++;}inline void Read(int& x){    char c=nc();    for(;c<'0'||c>'9';c=nc());    for(x=0;c>='0'&&c<='9';x=(x<<3)+(x<<1)+c-48,c=nc());}inline void Read(ll& x){    char c=nc();    for(;c<'0'||c>'9';c=nc());    for(x=0;c>='0'&&c<='9';x=(x<<3)+(x<<1)+c-48,c=nc());}#define N 50010#define M 2000000struct Edge{    int x,y,c,f;}e[N<<1];vector<int>g[M];int i,j,k,n,m,p,T,cnt,c[N];int num,pr[M],sf[M];int dfn[M],low[M],f[M],st[M],top;int l,r,t[N];inline bool Cmp(Edge a,Edge b){    if(a.x==b.x)return a.c<b.c;    return a.x<b.x;}inline void Dfs(int x){    dfn[x]=low[x]=++T;st[++top]=x;    for(int i=0;i<g[x].size();i++){        int v=g[x][i];        if(!dfn[v])Dfs(v),low[x]=min(low[x],low[v]);else        if(!f[v])low[x]=min(low[x],dfn[v]);    }    if(low[x]==dfn[x]){        cnt++;        while(st[top]!=x)f[st[top--]]=cnt;        f[st[top--]]=cnt;    }}inline bool Check(int x){    for(int i=1;i<=m/2;i++)    if(t[i]>x)g[i*2-1].push_back(i*2);    bool F=1;    memset(dfn,0,sizeof(dfn));    memset(f,0,sizeof(f));    T=cnt=0;    for(int i=1;i<=num;i++)if(!dfn[i])Dfs(i);    for(int i=1;i<=m/2;i++)    if(f[i*2]==f[i*2-1]){        F=0;        break;    }    for(int i=1;i<=m/2;i++)    if(t[i]>x)g[i*2-1].pop_back();    return F;}int main(){    Read(n);Read(m);    for(i=1;i<=m;i++)Read(e[i].x),Read(e[i].y),Read(e[i].c),Read(t[i]),e[i].f=i,e[i+m]=e[i],swap(e[i+m].x,e[i+m].y),r=max(r,t[i]);    m<<=1;    sort(e+1,e+m+1,Cmp);    num=m;    for(i=1;i<=m;i=j+1){        pr[i]=++num;sf[i]=++num;        for(j=i;j<=m&&e[j+1].x==e[j].x&&e[j+1].c==e[j].c;)pr[++j]=++num,sf[j]=++num;        for(p=i;p<=j;p++){            if(p>i)g[e[p].f*2].push_back(pr[p-1]),g[pr[p]].push_back(pr[p-1]);            if(p<j)g[e[p].f*2].push_back(sf[p+1]),g[sf[p]].push_back(sf[p+1]);            g[pr[p]].push_back(e[p].f*2-1);g[sf[p]].push_back(e[p].f*2-1);        }    }    for(i=1;i<=m;i=j+1){        pr[i]=++num;sf[i]=++num;        for(j=i;j<=m&&e[j+1].x==e[j].x;)pr[++j]=++num,sf[j]=++num;        for(p=i;p<=j;p++){            if(p>i)g[e[p].f*2-1].push_back(pr[p-1]),g[pr[p]].push_back(pr[p-1]);            if(p<j)g[e[p].f*2-1].push_back(sf[p+1]),g[sf[p]].push_back(sf[p+1]);            g[pr[p]].push_back(e[p].f*2);g[sf[p]].push_back(e[p].f*2);        }    }    if(!Check(r)){        puts("No");        return 0;    }    while(l<=r){        int Mid=l+r>>1;        if(Check(Mid))r=Mid-1;else l=Mid+1;    }    puts("Yes");    Check(l);    k=0;    for(i=1;i<=m/2;i++)    if(f[i*2-1]<f[i*2])c[++k]=i;    printf("%d %d\n",l,k);    for(i=1;i<=k;i++)printf("%d ",c[i]);    return 0;}