平行四边形

做法

根据平行四边形的判定条件：
一组对边平行而相等

然后套用几何板子就能解决问题

代码

#include <bits/stdc++.h>
using namespace std;

const double eps=1e-8;
const double PI=acos(-1.0);
const double INF = 1e100;

int sgn(double x){
    if(fabs(x)<=eps)return 0;
    return x>0?1:-1;
}

int dcmp(const double& a, const double& b){
    if(fabs(a-b)<eps) return 0;
    else if(a>b) return 1;
    return -1;
}

//arccos(x)
double acs(double x){
    if(x > 1) x = 1;
    else if(x < -1) x = -1;
    return acos(x);
}

//arcsin(x)
double asn(double x){
    if(x > 1) x = 1;
    else if(x < -1) x = -1;
    return asin(x);
}

struct Point{
    double x,y,ang;
    Point(double x = 0, double y = 0):x(x),y(y){}
    void input(){
        cin>>x>>y;
    }
    void calcangle(){
        ang=atan2(y,x);
    }
    double len2() { //返回长度的平方
        return x * x + y * y;
    }
};

//计算两点距离
double distance(const Point& a, const Point& b){
    return hypot(a.x-b.x,a.y-b.y);
}



//求两点斜率
double slope(const Point& a, const Point& b){
    if(dcmp(a.x,b.x)==0) return INF;
    return (a.y-b.y)/(a.x-b.x);
}

//计算倾斜角
double gradient(const Point& a, const Point& b){
    if(dcmp(a.y,b.y)==0) return 0;
    if(dcmp(a.x,b.x)==0) return PI/2.0;
    return atan(slope(a,b));
}


typedef Point Vector;

//判断两点是否相等
bool operator == (const Point& a, const Point& b){
    return sgn(a.x-b.x)==0 && sgn(a.y-b.y)==0;
}

//向量点积
double operator * (const Vector& a, const Vector& b){
    return a.x*b.x+a.y*b.y;
}

//向量叉乘,返回结果向量的有向长度
//注意叉乘的绝对值也就是两向量围成的平行四边形的面积。
double operator ^ (const Vector& a, const Vector& b){
    return a.x*b.y-a.y*b.x;
}

//向量加法
Vector operator + (const Vector& a, const Vector& b){
    return Vector(a.x+b.x,a.y+b.y);
}

// 向量减法
Vector operator - (const Vector& a, const Vector& b){
    return Vector(a.x - b.x, a.y - b.y);
}

//向量数乘
Vector operator * (const Vector& a, const double& b){
    return Vector(a.x*b,a.y*b);
}
Vector operator * (const double& a,const Vector& b){
    return Vector(a*b.x,a*b.y);
}

Vector operator / (const Vector& a, const double& b){
    return Vector(a.x/b, a.y/b);
}

bool operator < (const Point& a, const Point& b){
    if(a.x==b.x) return a.y<b.y;
    return a.x<b.x;
}

//向量模长
double len(const Vector& x){
    return sqrt(x*x);
}

struct Line{
    Point s,e;
    Vector v;
    double ang;//直线极角
    Line(Point _s,Point _e){ //两点
        s = _s;
        e = _e;
        v = _e - _s;
    }
    Line(Point p,double ang){ //0<=angle<PI
        s=p;
        if(sgn(ang-PI/2)==0) e=(s+Point(0,1));
        else e=(s+Point(1,tan(ang)));
    }
    Line(double a,double b,double c){ //ax+by+c=0
        if(sgn(a)==0){
            s=Point(0,-c/b);
            e=Point(1,-c/b);
        }
        else if(sgn(b)==0){
            s=Point(-c/a,0);
            e=Point(-c/a,1);
        }
        else{
            s=Point(0,-c/b);
            e=Point(1,(-c-a)/b);
        }
    }
    void input(){
        s.input();
        e.input();
    }
    void clacangle(){
        double ang = atan2(e.y-s.y,e.x-s.x);
        if(sgn(ang)<0) ang+=PI;
        if(sgn(ang-PI)==0) ang-=PI;
    }
    double length(){
        return distance(s,e);
    }
};

bool operator == (const Line& l,const Line& v){ //判断两条线段是否相等
    return l.s == v.s && l.e == v.e;
}

//点和直线关系
//1 在左侧
//2 在右侧
//3 在直线上
int Relation(const Line& l,const Point& p){
    int c=sgn((p-l.s)^(l.e-l.s));
    if(c<0) return 1;
    else if(c>0) return 2;
    else return 3;
}

//两直线关系
//0 平行
//1 重合
//2 相交
int linecrossline(const Line& l,const Line& v){
    if(sgn((l.e-l.s)^(v.e-v.s)) == 0) return Relation(v,l.s)==3;
    return 2;
}

void solve(){
    Point a,b,c,d;
    a.input();b.input();c.input();d.input();
    if(!linecrossline(Line(a,b),Line(c,d))){
        cout<<"YES\n";
        return;
    }
    if(!linecrossline(Line(a,c),Line(b,d))){
        cout<<"YES\n";
        return;
    }
    if(!linecrossline(Line(a,d),Line(b,c))){
        cout<<"YES\n";
        return;
    }
    cout<<"NO\n";
}


int main(){
    ios::sync_with_stdio(0);cin.tie(0);
    int t;cin>>t;while(t--)
    solve();
    return 0;
}