Peaceful Commission 2-sat

Posted 2021-11-26 bxd123

　　n个国家  每个国家有两个代表  桥求选出 n个人成立世界和平委员会    有m条关系    a与b 关系差不能同时选中    求选中人的最小字典序 

 

2-sat的入门题

调试了半天发现那个博客就是错的心态崩了

#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;
}

View Code

 

贴上2-sat模板：

//546MS 2136K   1427 B  C++
#include<iostream>
#include<cstring>
#include<cstdio>
const int MAXN=8010*2;
const int MAXM=80010;
using namespace std;
int n,m;
int s[MAXN],cnt;
bool mark[MAXN];
struct Edge{
    int to,next;
}edge[MAXM<<1];int head[MAXN],tot;
void addedge(int u,int v){
    edge[tot].to=v;edge[tot].next=head[u];head[u]=tot++;
}
void init(){
    tot=0;
    memset(head,0xff,sizeof(head));
}
bool dfs(int u){
    if(mark[u^1]) return false;
    if(mark[u]) return true;
    s[cnt++]=u;
    mark[u]=1;
    for(int i=head[u];i!=-1;i=edge[i].next){
        if(!dfs(edge[i].to))
            return false;
    }
    return true;
}
bool twosat(){
    memset(mark,0,sizeof(mark));
    for(int i=0;i<2*n;i+=2){
        if(!mark[i]&&!mark[i+1]){
            cnt=0;
            if(!dfs(i)){
                while(cnt) mark[s[--cnt]]=false;
                if(!dfs(i^1)) return false;
            }
        }
    }
    return true;
}
int main()
{
    int u,v;
    while(scanf("%d%d",&n,&m)!=EOF){
        init();
        while(m--){
            scanf("%d%d",&u,&v);
            u--,v--;
            addedge(u,v^1);
            addedge(v,u^1);
        }
        if(twosat()){
            for(int i=0;i<2*n;i+=2){
                if(mark[i]) printf("%d\n",i+1);
                else printf("%d\n",i+2);
            }
        }else{
            puts("NIE");
        }

    }
    return 0;
}

View Code