18上海大都会赛G

卡epssm
先判是不是个凸包，
显然我们要旋转点，
显然在一定范围内是有单调性的，
这个范围不太好找，我们把2pi分成若干小段，其中这些小段里有单调性，最后取min就行，eps太大会wa，推荐1e-11.
注意check的时候不能是『那样的形状』自己脑补去吧

#include <bits/stdc++.h>
using namespace std;
typedef double db;
const db eps=1e-11;
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);}
struct point{
    db x,y;
    point operator + (const point &k1) const{return (point){k1.x+x,k1.y+y};}
    point operator - (const point &k1) const{return (point){x-k1.x,y-k1.y};}
    point operator * (db k1) const{return (point){x*k1,y*k1};}
    point operator / (db k1) const{return (point){x/k1,y/k1};}
    int operator == (const point &k1) const{return cmp(x,k1.x)==0&&cmp(y,k1.y)==0;}
    // 逆时针旋转
    point turn(db k1){return (point){x*cos(k1)-y*sin(k1),x*sin(k1)+y*cos(k1)};}
    point turn90(){return (point){-y,x};}
    bool operator < (const point k1) const{
        int a=cmp(x,k1.x);
        if (a==-1) return 1; else if (a==1) return 0; else return cmp(y,k1.y)==-1;
    }
    db abs(){return sqrt(x*x+y*y);}
    db abs2(){return x*x+y*y;}
    db dis(point k1){return ((*this)-k1).abs();}
    point unit(){db w=abs(); return (point){x/w,y/w};}
    void scan(){double k1,k2; scanf("%lf%lf",&k1,&k2); x=k1; y=k2;}
    void print(){printf("%.11lf %.11lf
",x,y);}
    db getw(){return atan2(y,x);}
    point getdel(){if (sign(x)==-1||(sign(x)==0&&sign(y)==-1)) return (*this)*(-1); else return (*this);}
    int getP() const{return sign(y)==1||(sign(y)==0&&sign(x)==-1);}
};
db cross(point k1,point k2){return k1.x*k2.y-k1.y*k2.x;}
vector<point> ConvexHull(vector<point>A,int flag=1){ // flag=0 不严格 flag=1 严格
    int n=A.size(); vector<point>ans(n*2);
    sort(A.begin(),A.end()); int now=-1;
    for (int i=0;i<A.size();i++){
        while (now>0&&sign(cross(ans[now]-ans[now-1],A[i]-ans[now-1]))<flag) now--;
        ans[++now]=A[i];
    } int pre=now;
    for (int i=n-2;i>=0;i--){
        while (now>pre&&sign(cross(ans[now]-ans[now-1],A[i]-ans[now-1]))<flag) now--;
        ans[++now]=A[i];
    } ans.resize(now); return ans;
}
int t;
vector<point> p,s;
db check(db x){
    for(int i=0;i<4;i++)
        s[i]=p[i].turn(x);
    db mnx=1e404,mxx=-1e404,mny=1e404,mxy=-1e404;
    int mxxid,mxyid,mnyid,mnxid;
    for(int i=0;i<4;i++){
        if (s[i].x < mnx)mnx = s[i].x, mnxid = i;
        if (s[i].x > mxx)mxx = s[i].x, mxxid = i;
        if (s[i].y < mny)mny = s[i].y, mnyid = i;
        if (s[i].y > mxy)mxy = s[i].y, mxyid = i;
    }
    if (mnxid == mnyid || mnxid == mxyid)return 11111;
    if (mxxid == mxyid || mxxid == mnyid)return 11111;
    return fabs(mxy-mny-(mxx-mnx));
}
db slove(db l,db r){//三回啊三回
    while (l+eps<=r){
        db lm = l+(r-l)/3;
        db rm = r-(r-l)/3;
        if(check(lm)>=check(rm))l=lm;
        else r=rm;
    }
    return check(l);
}
int main(){
    scanf("%d",&t);int cas=0;
    while (t--){
        p.resize(4);
        s.resize(4);
        for(int i=0;i<4;i++){
            scanf("%lf%lf",&p[i].x,&p[i].y);
        }
        p=ConvexHull(p);
        if(p.size()!=4){
            printf("Case %d: No
",++cas);
            continue;
        }
        db s = 1e18;
        for(db i=0;i<2*pi;i+=pi/3){
            s = min(s,slove(i,i+pi/3));
        }
        if(s<=1e-8)printf("Case %d: Yes
",++cas);
        else printf("Case %d: No
",++cas);
    }
}

可能这就是我单身的原因吧。
最近几天情绪大概会很失落。