POJ 2749

二分+2SAT的题

写错了HIGH和LOW与MID的变换，TLE了好几次。。

按HATE和LIKE关系先加边，再用距离的限制加边。

dist(i,S1)+dist(S1,j)>limit  Xi->~Xj  Xj->Xi

dist(i,S2)+dist(S2,j)>limit  ~Xi->Xj  ~Xj->Xi

dist(i,S1)+dist(S1,S2)+dist(S2,j)>limit Xi->Xj  ~Xj->~Xi

dist(i,S2)+dist(S2,S1)+dist(S1,j)>limit ~Xi->~Xj  Xj->Xi

用离散数学的知识就能推出来，以上借别人的一用。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>

using namespace std;

const int inf=8500000;
const int MAXN=1050;
const int MAXM=20000000;
int s1_s2,dis1[MAXN],dis2[MAXN],head[MAXN],dfn[MAXN],low[MAXN],belong[MAXN];
int st[MAXN],stop,indx,tot,pat;
bool stack[MAXN]; int leng;
int n,hn,ln;
struct d{
    int x,y;
}point[MAXN],s1,s2;
struct h{
    int u,v;
}hate[MAXN*2];
struct l{
    int u,v;
}like[MAXN*2];

struct ei{
    int u,v;
    int next;
}edge[MAXM];

void addedge(int u,int v){
    edge[tot].u=u;
    edge[tot].v=v;
    edge[tot].next=head[u];
    head[u]=tot++;
}

void tarjan(int u){
    int v;
    dfn[u]=low[u]=++indx;
    st[stop++]=u;
    stack[u]=true;
    for(int e=head[u];e!=-1;e=edge[e].next){
        v=edge[e].v;
        if(dfn[v]==0){
            tarjan(v);
            low[u]=min(low[u],low[v]);
        }
        else if(stack[v]){
            low[u]=min(low[u],dfn[v]);
        }
    }
    if(dfn[u]==low[u]){
        pat++;
        do{
            v=st[--stop];
            stack[v]=false;
            belong[v]=pat;
        }while(u!=v);
    }
}

bool slove(){
    int u,v;
    
    memset(head,-1,sizeof(head));
    memset(dfn,0,sizeof(dfn));
    memset(low,0,sizeof(low));
    memset(belong,0,sizeof(belong));
    stop=0; indx=0; tot=0; pat=0;
    memset(stack,false,sizeof(stack));
    
    
    for(int i=0;i<hn;i++){
        u=hate[i].u;
        v=hate[i].v;
        addedge(u*2,v*2+1);
        addedge(v*2,u*2+1);
        addedge(2*u+1,2*v);
        addedge(2*v+1,2*u);
    }
    for(int i=0;i<ln;i++){
        u=like[i].u;
        v=like[i].v;
        addedge(u*2,v*2);
        addedge(v*2,u*2);
        addedge(2*u+1,2*v+1);
        addedge(2*v+1,2*u+1);
    }
    for(int i=0;i<n;i++){
        for(int j=i+1;j<n;j++){
            if(dis1[i]+dis1[j]>leng){
                addedge(i*2,j*2+1);
                addedge(j*2,i*2+1);
            }
            if(dis2[i]+dis2[j]>leng){
                addedge(i*2+1,j*2);
                addedge(j*2+1,i*2);
            }
            if(dis1[i]+s1_s2+dis2[j]>leng){
                addedge(i*2,j*2);
                addedge(j*2+1,i*2+1);
            }
            if(dis2[i]+s1_s2+dis1[j]>leng){
                addedge(j*2,i*2);
                addedge(i*2+1,j*2+1);
            }
        }
    }
    for(int i=0;i<2*n;i++){
        if(dfn[i]==0)
        tarjan(i);
    }
    bool flag=true;
    for(int i=0;i<n;i++){
        if(belong[2*i]==belong[2*i+1]){
            flag=false;
            break;
        }
    }
    return flag;
}

int main(){
    int u,v; int tmp;
    while(scanf("%d%d%d",&n,&hn,&ln)!=EOF){
        scanf("%d%d%d%d",&s1.x,&s1.y,&s2.x,&s2.y);
        for(int i=0;i<n;i++){
        scanf("%d%d",&point[i].x,&point[i].y);
        }
        for(int i=0;i<hn;i++){
            scanf("%d%d",&u,&v);
            u--; v--;
            hate[i].u=u; hate[i].v=v;
        }
        for(int i=0;i<ln;i++){
            scanf("%d%d",&u,&v);
            u--; v--; 
            like[i].u=u; like[i].v=v;
        }
        for(int i=0;i<n;i++){
            tmp=abs(point[i].x-s1.x)+abs(point[i].y-s1.y);
            dis1[i]=tmp;
            tmp=abs(point[i].x-s2.x)+abs(point[i].y-s2.y);
            dis2[i]=tmp;
        }
        s1_s2=abs(s1.x-s2.x)+abs(s1.y-s2.y);
        int lown=1,high=inf,ans=-1;
        while(lown<=high){
            int mid=(lown+high)/2;
            leng=mid;
            if(slove()){
                ans=mid;
                high=mid-1;
            }
            else lown=mid+1;
        }
        printf("%d
",ans);
    }
    return 0;
}