G102040I

傻逼题。我从来没见过eps这样的。。。

打破了我对计算几何美好的幻想。

eps=1e-6=>wa3  eps=1e-8->wa2  eps 1e-4->AC

真的自闭，真的猜不到eps要设成1e-4，最后看了先杭电的代码，发现他们是1e-4,我就改了下，然后？？？？过了？？？？

nmsl

nmsl

nmsl

思路正确无比。赛后发现板子错了，把板子删了，tle3，把三分套三分换成了三分+板子，就开始无限WA制了

精简一下就是一句话：求线段到三角形的距离。

前置技能：三分，点到三角形的距离，点到线段的距离，点到平面的投影，点是否在三角形内

然后就没了。赛时-13赛后+37

#include <bits/stdc++.h>
using namespace std;
typedef double db;
const db eps = 1e-4;
const db pi = acos(-1);
int sign(db k){if(k>eps)return 1;else if(k<-eps)return -1;return 0;}
int cmp(db k1,db k2){return sign(k1-k2);}
int inmid(db k1,db k2,db k3){return sign(k1-k3)*sign(k2-k3)<=0;}// k3 在 [k1,k2] 内
struct point{
    db x,y,z;
    point operator + (point k1){return (point){x+k1.x,y+k1.y,z+k1.z};}
    point operator - (point k1){return (point){x-k1.x,y-k1.y,z-k1.z};}
    point operator * (db k1){return (point){x*k1,y*k1,z*k1};}
    point operator / (db k1){return (point){x/k1,y/k1,z/k1};}
    db length()const {return sqrt(x*x+y*y+z*z);}
    db len2()const {return x*x+y*y+z*z;}
};
point det(const point &a,const point &b){
    return point{a.y*b.z-a.z*b.y,a.z*b.x-a.x*b.z,a.x*b.y-a.y*b.x};
}
db dis(const point &a,const point &b){//距离
    return sqrt(pow(a.x-b.x,2)+pow(a.y-b.y,2)+pow(a.z-b.z,2));
}
struct line{
    point p[2];
    line (point k1,point k2){p[0]=k1; p[1]=k2;}
    point& operator [] (int k){return p[k];}
};
db dot(point k1,point k2){return k1.x*k2.x+k1.y*k2.y+k1.z*k2.z;}
int dot_online_in(point p,line l){//点在线段上，包括端点
    return sign(det(p-l[0],p-l[1]).length())==0&&(l[0].x-p.x)*(l[1].x-p.x)<eps&&
           (l[0].y-p.y)*(l[1].y-p.y)<eps&&(l[0].z-p.z)*(l[1].z-p.z)<eps;
}
struct plane{
    point p[3];
    plane(point k1,point k2,point k3){p[0]=k1,p[1]=k2,p[2]=k3;}
    point& operator [] (int k){return p[k];}
};
point pvec(point s1,point s2,point s3){
    return det(s1-s2,s2-s3);
}
point pvec(plane s){return pvec(s[0],s[1],s[2]);}
int dot_inplane_in(point p,plane s){
    return sign(det(s[0]-s[1],s[0]-s[2]).length()-det(p-s[0],p-s[1]).length()-
                det(p-s[1],p-s[2]).length()-det(p-s[2],p-s[0]).length())==0;
}
int sameside(point p1,point p2,plane s){//两点在平面同侧
//    point tmp = pvec(s);
    return dot(pvec(s),p1-s[0])*dot(pvec(s),p2-s[0])>eps;
}
int intersect_in(line l,plane s){//线段和三角形是否有交点包含边界
    return !sameside(l[0],l[1],s)&&
            !sameside(s[2],s[0],plane{l[0],l[1],s[1]})&&
           !sameside(s[0],s[1],plane{l[0],l[1],s[2]})&&
           !sameside(s[1],s[2],plane{l[0],l[1],s[0]});
}
point intersection(line l,plane s){//直线与平面的交点
    point ret = pvec(s);
    db t = ((ret.x*(s[0].x-l[0].x)+ret.y*(s[0].y-l[0].y))+ret.z*(s[0].z-l[0].z))/
           ((ret.x*(l[1].x-l[0].x)+ret.y*(l[1].y-l[0].y))+ret.z*(l[1].z-l[0].z));
    ret = l[0]+(l[1]-l[0])*t;return ret;
}
int t;
point p[22];
int check(plane a,plane b){//check 0;
    bool f=0;
    if(intersect_in({a[0],a[1]},b))f=1;
    if(intersect_in({a[1],a[2]},b))f=1;
    if(intersect_in({a[0],a[2]},b))f=1;
    if(intersect_in({b[0],b[1]},a))f=1;
    if(intersect_in({b[0],b[2]},a))f=1;
    if(intersect_in({b[1],b[2]},a))f=1;
    return f;
}
db slove(plane a,plane b){//b三个点到a的距离
    db ans = 1e18;
    point x = pvec(a);
    line s0 = {b[0],b[0]+x};
    point xx = intersection(s0,a);
    if(dot_inplane_in(xx,a))
        ans = min(ans,(xx-b[0]).length());
    line s1 = {b[1],b[1]+x};
    xx = intersection(s1,a);
    if(dot_inplane_in(xx,a))
        ans = min(ans,(xx-b[1]).length());
    line s2 = {b[2],b[2]+x};
    xx = intersection(s2,a);
    if(dot_inplane_in(xx,a))
        ans = min(ans,(xx-b[2]).length());
    return ans;
}
db ptoline(point p,line l){//点到直线的距离
    return (det(p-l[0],l[1]-l[0])/dis(l[0],l[1])).length();
}
point proj(point k1,point k2,point q){ // q 到直线 k1,k2 的投影
    point k=k2-k1; return k1+k*(dot(q-k1,k)/k.len2());
}
int inmid(point k1,point k2,point k3){
    return inmid(k1.x,k2.x,k3.x)&&inmid(k1.y,k2.y,k3.y)&&inmid(k1.z,k2.z,k3.z);
}
db slove2(point a,line b){//点到线段的距离
    point v1=b[1]-b[0],v2=a-b[0],v3=a-b[1];
    if(sign(dot(v1,v2)<0))return v2.length();
    else if(sign(dot(v1,v3))>0)return v3.length();
    else return det(v1,v2).length()/v1.length();
//    point x = proj(b[0],b[1],a);
//    if(dot_online_in(x,b))
//        return (a-x).length();
//    return min((a-b[0]).length(),(a-b[1]).length());
}
db dis_point_plane(point a,plane p){
    point xx = pvec(p);
    line l = {a,a+xx};
    point xxx = intersection(l,p);
    if(dot_inplane_in(xxx,p))
        return (a-xxx).length();
    return min(min(slove2(a,{p[0],p[1]}),slove2(a,{p[1],p[2]})),slove2(a,{p[2],p[0]}));
}
db slove3(line a,plane b){
    point l=a[0],r=a[1];
    for(int i=0;i<90;i++){
        point mid = (l+r)/2,lm=(l+mid)/2,rm=(r+mid)/2;
        if(dis_point_plane(lm,b)<=dis_point_plane(rm,b)){
            r=rm;
        } else
            l=lm;
    }
    return dis_point_plane(l,b);
}
double x,y,z;
int main(){
    scanf("%d",&t);
    while (t--){
        for(int i=1;i<=6;i++){
            scanf("%lf%lf%lf",&x,&y,&z);
            p[i]={x,y,z};
        }
        plane a = {p[1],p[2],p[3]},b = {p[4],p[5],p[6]};
//        if(check(a,b)){
//            printf("%.11f
",0.0);
//        }else{
            db ans = 1e18;
//            ans = min(ans,slove(a,b));
//            ans = min(ans,slove(b,a));
//            for(int i=0;i<3;i++) {
//                for(int k=0;k<3;k++) {
//                    point l=a[i],r=a[(i+1)%3],lm,rm;
//                    line t=(line){b[k],b[(k+1)%3]};
//                    for(int j=0;j<90;j++) {
//                        lm=l+(r-l)/3,rm=r-(r-l)/3;
//                        if(slove2(lm,t)<=slove2(rm,t)) r=rm;
//                        else l=lm;
//                    }
//                    ans=std::min(ans,slove2(r,t));
//                }
//            }
            for(int i=0;i<3;i++){
                ans = min(ans,slove3({a[i],a[(i+1)%3]},b));
                ans = min(ans,slove3({b[i],b[(i+1)%3]},a));
            }
            printf("%.11f
",ans);
//        }
    }
}
/**
1
0 0 0 1 0 0 0 1 0
2 2 1 3 2 1 2 3 1
 */