luogu 4782【模板】 2-SAT 问题

2-SAT就是给出$m$个限制表示$x==val_x || y==val_y$

求出满足的解

每个点拆成两个点，如果$x$不满足则$y$一定满足，$y$不满足同理。这样我们连边，然后$tarjan$即可

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<algorithm>
#include<queue>
#include<vector>
#include<map>
#include<set>
#define ll long long
#define db double
#define inf 2139062143
#define MAXN 2001000
#define rep(i,s,t) for(register int i=(s),i##__end=(t);i<=i##__end;++i)
#define dwn(i,s,t) for(register int i=(s),i##__end=(t);i>=i##__end;--i)
#define ren for(register int i=fst[x];i;i=nxt[i])
#define pb(i,x) vec[i].push_back(x)
#define pls(a,b) (a+b)%MOD
#define mns(a,b) (a-b+MOD)%MOD
#define mul(a,b) (1LL*(a)*(b))%MOD
using namespace std;
inline int read()
{
    int x=0,f=1;char ch=getchar();
    while(!isdigit(ch)) {if(ch=='-') f=-1;ch=getchar();}
    while(isdigit(ch)) {x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
int n,m,nxt[MAXN<<1],fst[MAXN],to[MAXN<<1],cnt;
int dfn[MAXN],low[MAXN],bl[MAXN],stp,st[MAXN],top,scc;
void add(int u,int v) {nxt[++cnt]=fst[u],fst[u]=cnt,to[cnt]=v;}
void tarjan(int x)
{
    st[++top]=x,dfn[x]=low[x]=++stp;
    ren if(!dfn[to[i]]) {tarjan(to[i]);low[x]=min(low[x],low[to[i]]);}
        else if(!bl[to[i]]) low[x]=min(low[x],dfn[to[i]]);
    if(low[x]==dfn[x])
        {scc++;int now=0;while(now!=x) now=st[top--],bl[now]=scc;}
}
int main()
{
    n=read(),m=read();int a,b,x,y;rep(i,1,m)
        a=read(),x=read(),b=read(),y=read(),
        add(a+(1^x)*n,b+y*n),add(b+(1^y)*n,a+x*n);
    rep(i,1,n<<1) if(!dfn[i]) tarjan(i);
    rep(i,1,n) if(bl[i]==bl[i+n]) return puts("IMPOSSIBLE"),0;puts("POSSIBLE");
    rep(i,1,n) printf("%d ",bl[i]>bl[i+n]);
}