ZOJ 3717

这题是二分+2SAT.

总结一下SAT题的特征。首先，可能会存在二选一的情况，然后会给出一些矛盾。据这些矛盾加边，再用SAT判定。

这一道题好像不能直接用printf("%0.3lf")，因为这个是四舍五入的，这道题好像不能四舍五入，只好选减去0.0005再按这个格式输出了。

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <stdlib.h>
#define oo 1000000007
#define eps 1e-4
using namespace std;
const int MAXN=420;
const int MAXM=320000;
struct b{
    int x,y,z;
}ball[MAXN];
double dis[MAXN][MAXN];
int head[MAXN],dfn[MAXN],low[MAXN],tot,stop,indx,belong[MAXN],pat;
int st[MAXN];
bool stack[MAXN];
int n;
struct e{
    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];
            belong[v]=pat;
            stack[v]=false;
        }while(u!= v); 
    } 
}

bool slove(double leng){
    int a,b; tot=0; indx=0; stop=0; pat=-1;
    memset(head,-1,sizeof(head));
    for(int i=0;i<n;i++){
        a=i;
        for(int j=i+1;j<n;j++){
            b=j;
            if(leng*2>dis[a*2][b*2]){
                addedge(2*a+1,b*2);
                addedge(b*2+1,a*2);
            }
            if(leng*2>dis[a*2][b*2+1]){
                addedge(a*2+1,b*2+1);
                addedge(b*2,a*2);
            }
            if(leng*2>dis[a*2+1][b*2]){
                addedge(a*2,b*2);
                addedge(b*2+1,a*2+1);
            }
            if(leng*2>dis[a*2+1][b*2+1]){
                addedge(a*2,b*2+1);
                addedge(b*2,a*2+1);
            }
        }
    }
    memset(dfn,0,sizeof(dfn));
    memset(low,0,sizeof(low));
    memset(stack,false,sizeof(stack));
    memset(belong,-1,sizeof(belong));
    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[i*2]==belong[i*2+1]){
            flag=false;
            break;
        }
    }
    return flag;
}

int main(){
    double xi,yi,zi;
    while(scanf("%d",&n)!=EOF){
        for(int i=0;i<2*n;i++){
            scanf("%d%d%d",&ball[i].x,&ball[i].y,&ball[i].z);
            i++;
            scanf("%d%d%d",&ball[i].x,&ball[i].y,&ball[i].z);
        }
        double high=oo,lown=0; double tmp;
        for(int i=0;i<2*n;i++){
            for(int j=i;j<2*n;j++){
                xi=ball[i].x-ball[j].x;
                yi=ball[i].y-ball[j].y;
                zi=ball[i].z-ball[j].z;
                tmp=sqrt(xi*xi+yi*yi+zi*zi);
                dis[i][j]=dis[j][i]=tmp;
            }
        }
        double ans;
        while(lown<high-eps){
            double mid=(high+lown)/2;
            if(slove(mid)){
                ans=mid;
                lown=mid;
            }
            else high=mid;
        }
        printf("%0.3lf
",ans-0.0005);
    }
    return 0;
}