2-sat模板

Posted 2021-11-26 bxd123

　　2-sat有很多写法

可以用tarjan  

#include<bits/stdc++.h>
#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
//input by bxd
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define repp(i,a,b) for(int i=(a);i>=(b);--i)
#define RI(n) scanf("%d",&(n))
#define RII(n,m) scanf("%d%d",&n,&m)
#define RIII(n,m,k) scanf("%d%d%d",&n,&m,&k)
#define RS(s) scanf("%s",s);
#define ll long long
#define pb push_back
#define REP(i,N)  for(int i=0;i<(N);i++)
#define CLR(A,v)  memset(A,v,sizeof A)
//////////////////////////////////
#define inf 0x3f3f3f3f
const int N=16000;
const int M=5*N;
 int n,m;
int pos,head[N],pos2,head2[N];
struct Edge
{
    int to,nex;
}edge[M],edge2[M];
void add(int a,int b)
{
    edge[++pos].nex=head[a];
    head[a]=pos;
    edge[pos].to=b;
}
void add2(int a,int b)
{
    edge2[++pos2].nex=head2[a];
    head2[a]=pos2;
    edge2[pos2].to=b;
}

int tot,ind,cnt,Stack[N],dfn[N],low[N],belong[N],in[N],vis[N];
int f[N];
void tarjan(int x)
{
    dfn[x]=low[x]=++tot;
    Stack[++ind]=x;
    vis[x]=1;
    for(int i=head[x];i;i=edge[i].nex)
    {
        int v=edge[i].to;
        if(!dfn[v])
        {
            tarjan(v);
            low[x]=min(low[x],low[v]);
        }
        else if(vis[v])
            low[x]=min(low[x],low[v]);
    }
    if(dfn[x]==low[x])
    {
        cnt++;int v;
        do
        {
            v=Stack[ind--];
            vis[v]=0;
            belong[v]=cnt;
        }
        while(v!=x);
    }
}
int ans[N];
void init()
{
    cnt=pos=ind=tot=pos2=0;
    CLR(head2,0);
    CLR(head,0);
    CLR(vis,0);
    CLR(in,0);
    CLR(Stack,0);
    CLR(dfn,0);
    CLR(low,0);
    CLR(ans,0);
}

void builddag()
{
    rep(i,0,2*n-1)
    {
        int u=belong[i];
        for(int j=head[i];j;j=edge[j].nex)
        {
            int v=belong[edge[j].to];
            if(v!=u)
                add2(v,u),in[u]++;
        }
    }
}

void solve()
{
    for(int i=0;i<2*n;i+=2)
        if(belong[i]==belong[i^1])
        {
            printf("NIE\n");
            return ;
        }
        else
            f[ belong[i] ]=belong[i+1],f[belong[i+1]]=belong[i];

     builddag();
    queue<int>q;
    rep(i,1,cnt)
    if(!in[i])
        q.push(i);
    while(!q.empty())
    {
        int u=q.front();q.pop();
        if(!ans[u])
            ans[u]=1,ans[f[u]]=2;
        for(int i=head2[u];i;i=edge2[i].nex)
        {
            int v=edge2[i].to;
            if(--in[v]==0)q.push(v);
        }
    }
    for(int i=0;i<2*n;i+=2)
    if(ans[belong[i]]==1)
        printf("%d\n",i+1);
    else printf("%d\n",i+2);
}

int main()
{
    while(RII(n,m)==2)
    {
        init();
        rep(i,1,m)
        {
            int a,b;RII(a,b);
            b--;a--;add(a,b^1);add(b,a^1);
        }
        rep(i,0,2*n-1)
        if(!dfn[i])
            tarjan(i);
        solve();

    }
    return 0;
}

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lrj白书提供的dfs

#include<bits/stdc++.h>
#include<iostream>
#include<cstring>
#include<cstdio>
using namespace std;
//input by bxd
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define repp(i,a,b) for(int i=(a);i>=(b);--i)
#define RI(n) scanf("%d",&(n))
#define RII(n,m) scanf("%d%d",&n,&m)
#define RIII(n,m,k) scanf("%d%d%d",&n,&m,&k)
#define RS(s) scanf("%s",s);
#define ll long long
#define pb push_back
#define REP(i,N)  for(int i=0;i<(N);i++)
#define CLR(A,v)  memset(A,v,sizeof A)
//////////////////////////////////
#define inf 0x3f3f3f3f
const int N=8005*2;
const int M=90000;
int n,m;
int head[M<<1],pos;
struct Edge
{
    int to,nex;
}edge[M<<1];
void add(int a,int b)
{
    edge[++pos].nex=head[a];
    head[a]=pos;
    edge[pos].to=b;
}
void init()
{
    pos=0;
    CLR(head,0);
}
int cnt,vis[N],s[N];
bool dfs(int x)
{
    if(vis[x^1])return 0;
    if(vis[x])return 1;
    s[cnt++]=x;
    vis[x]=1;
    for(int i=head[x];i;i=edge[i].nex)
        if(!dfs(edge[i].to))
        return 0;
    return 1;
}
bool twosat()
{
    CLR(vis,0);
    for(int i=0;i<2*n;i+=2)
    if(!vis[i]&&!vis[i+1]){
        cnt=0;
        if(!dfs(i)){
        while(cnt)vis[ s[--cnt] ]=0;
        if(!dfs(i^1))return 0;
        }
    }
    return 1;
}
int main()
{
    int a,b;
    while(RII(n,m)!=EOF)
    {
        init();
        rep(i,1,m)
        {
            RII(a,b);
            a--;b--;
            add(a,b^1);
            add(b,a^1);
        }
        if(twosat())
        {
            for(int i=0;i<2*n;i+=2)
            {
                if(vis[i])printf("%d\n",i+1);
                else printf("%d\n",i+2);
            }
        }
        else printf("NIE\n");
    }
    return 0;
}

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