【模板】2—SAT问题

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参考题目：洛谷P4782

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解析：

联赛完后统一更模板题题解。

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代码：

#include<bits/stdc++.h>
using namespace std;
#define ll long long
#define re register
#define gc getchar
#define pc putchar
#define cs const

inline int getint(){
	re int num;
	re char c;
	while(!isdigit(c=gc()));num=c^48;
	while(isdigit(c=gc()))num=(num<<1)+(num<<3)+(c^48);
	return num;
}

cs int N=2000006;
vector<int> edge[N];

int dfn[N],low[N],dfs_clock;
int scc[N],scc_clock;
int sta[N],top;
bool insta[N];

inline void tarjan(int u){
	dfn[u]=low[u]=++dfs_clock;
	sta[++top]=u;
	insta[u]=true;
	for(int re e=0;e<edge[u].size();++e){
		int re v=edge[u][e];
		if(dfn[v]){
			if(insta[v])low[u]=min(low[u],dfn[v]);
		}
		else tarjan(v),low[u]=min(low[u],low[v]);
	}
	if(dfn[u]==low[u]){
		++scc_clock;
		do{
        	scc[u]=scc_clock;
            u=sta[top--];
			insta[u]=false;
        }while(low[u]!=dfn[u]);
	}
}

int n,m;
inline bool _2_SAT(){
	for(int re i=1;i<=n*2;++i){
		if(!dfn[i])tarjan(i);
	}
	for(int re i=1;i<=n;++i)if(scc[i]==scc[i+n])return false;
	return true;
}


signed main(){
	n=getint();
	m=getint();
	for(int re i=1;i<=m;++i){
		int a=getint(),va=getint(),b=getint(),vb=getint();
		edge[a+n*va].push_back(b+n*(1-vb));
		edge[b+n*vb].push_back(a+n*(1-va));
	}
	if(_2_SAT()){
		puts("POSSIBLE");
		for(int re i=1;i<=n;++i){
			printf("%d ",scc[i]<scc[i+n]);
		}
	}
	else puts("IMPOSSIBLE");
	return 0;
}