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-;
 const db pi = acos(-);
 int sign(db k){if(k>eps)return ;else if(k<-eps)return -;return ;}
 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)<=;}// 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,)+pow(a.y-b.y,)+pow(a.z-b.z,));
 }
 struct line{
     point p[];
     line (point k1,point k2){p[]=k1; p[]=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[],p-l[]).length())==&&(l[].x-p.x)*(l[].x-p.x)<eps&&
            (l[].y-p.y)*(l[].y-p.y)<eps&&(l[].z-p.z)*(l[].z-p.z)<eps;
 }
 struct plane{
     point p[];
     plane(point k1,point k2,point k3){p[]=k1,p[]=k2,p[]=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[],s[],s[]);}
 int dot_inplane_in(point p,plane s){
     return sign(det(s[]-s[],s[]-s[]).length()-det(p-s[],p-s[]).length()-
                 det(p-s[],p-s[]).length()-det(p-s[],p-s[]).length())==;
 }
 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[])*dot(pvec(s),p2-s[])>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[],l[],s)&&
             !sameside(s[],s[],plane{l[],l[],s[]})&&
            !sameside(s[],s[],plane{l[],l[],s[]})&&
            !sameside(s[],s[],plane{l[],l[],s[]});
 }
 point intersection(line l,plane s){//直线与平面的交点
     point ret = pvec(s);
     db t = ((ret.x*(s[].x-l[].x)+ret.y*(s[].y-l[].y))+ret.z*(s[].z-l[].z))/
            ((ret.x*(l[].x-l[].x)+ret.y*(l[].y-l[].y))+ret.z*(l[].z-l[].z));
     ret = l[]+(l[]-l[])*t;return ret;
 }
 int t;
 point p[];
 int check(plane a,plane b){//check 0;
     bool f=;
     if(intersect_in({a[],a[]},b))f=;
     if(intersect_in({a[],a[]},b))f=;
     if(intersect_in({a[],a[]},b))f=;
     if(intersect_in({b[],b[]},a))f=;
     if(intersect_in({b[],b[]},a))f=;
     if(intersect_in({b[],b[]},a))f=;
     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[],b[]+x};
     point xx = intersection(s0,a);
     if(dot_inplane_in(xx,a))
         ans = min(ans,(xx-b[]).length());
     line s1 = {b[],b[]+x};
     xx = intersection(s1,a);
     if(dot_inplane_in(xx,a))
         ans = min(ans,(xx-b[]).length());
     line s2 = {b[],b[]+x};
     xx = intersection(s2,a);
     if(dot_inplane_in(xx,a))
         ans = min(ans,(xx-b[]).length());
     return ans;
 }
 db ptoline(point p,line l){//点到直线的距离
     return (det(p-l[],l[]-l[])/dis(l[],l[])).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[]-b[],v2=a-b[],v3=a-b[];
     if(sign(dot(v1,v2)<))return v2.length();
     else if(sign(dot(v1,v3))>)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[],p[]}),slove2(a,{p[],p[]})),slove2(a,{p[],p[]}));
 }
 db slove3(line a,plane b){
     point l=a[],r=a[];
     for(int i=;i<;i++){
         point mid = (l+r)/,lm=(l+mid)/,rm=(r+mid)/;
         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=;i<=;i++){
             scanf("%lf%lf%lf",&x,&y,&z);
             p[i]={x,y,z};
         }
         plane a = {p[],p[],p[]},b = {p[],p[],p[]};
 //        if(check(a,b)){
 //            printf("%.11f\n",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=;i<;i++){
                 ans = min(ans,slove3({a[i],a[(i+)%]},b));
                 ans = min(ans,slove3({b[i],b[(i+)%]},a));
             }
             printf("%.11f\n",ans);
 //        }
     }
 }
 /**
 1
 0 0 0 1 0 0 0 1 0
 2 2 1 3 2 1 2 3 1
  */