2016湖南省省赛 J 三角形和矩形（计算几何）

https://ac.nowcoder.com/acm/contest/1112/J

把三角形的顶点里在矩形里面的点放进数组；

把矩形的顶点里在三角形里面的点放进数组；

把三角形三条边和矩形四条边的交点放进数组（规范相交）；

对这个数组去重并求凸包然后求凸包面积就是答案。

#include <bits/stdc++.h>
using namespace  std;
#define ll long long
const int N=1e3+10;
double eps=1e-8;
double pi=acos(-1);
struct Point{
    double x,y;
    Point(double x=0,double y=0):x(x),y(y){}
};
typedef Point Vector;
Vector operator + (Vector A,Vector B){return Vector(A.x+B.x,A.y+B.y);}
Vector operator - (Vector A,Vector B){return Vector(A.x-B.x,A.y-B.y);}
Vector operator * (Vector A,double B){return Vector(A.x*B,A.y*B);}
Vector operator / (Vector A,double B){return Vector(A.x/B,A.y/B);}
int dcmp(double x){
    if(fabs(x)<eps)return 0;
    else return x<0?-1:1;
}
bool operator < (const Point &a,const Point &b){
    return dcmp(a.x-b.x)<0||(dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)<0);
}
bool operator == (const Point &a,const Point &b){
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
}
double Cross(Vector A,Vector B){
    return A.x*B.y-A.y*B.x;
}
double Dot(Vector A,Vector B){
    return A.x*B.x+A.y*B.y;
}
Point line_point(Point p,Vector v,Point q,Vector w){//直线交点 
    Vector u=p-q;
    double t=Cross(w,u)/Cross(v,w);
    return p+v*t;
}
bool onsegment(Point p,Point a1,Point a2){
    if(p==a1||p==a2)return true;
    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;
}
bool segmentcross(Point a1,Point a2,Point b1,Point b2){
    double c1=Cross(a2-a1,b1-a1),c2=Cross(a2-a1,b2-a1),
           c3=Cross(b2-b1,a1-b1),c4=Cross(b2-b1,a2-b1);
    return dcmp(c1)*dcmp(c2)<0&&dcmp(c3)*dcmp(c4)<0;
}
Point line_line(Point A,Point B,Point C,Vector D){//线段交点 
    if(segmentcross(A,B,C,D)){
        return line_point(A,B-A,C,D-C);
    }
    return Point(123.456,0);
}
int tubao(Point *p,int n,Point *ch){
    sort(p,p+n);
    n=unique(p,p+n)-p;
    int m=0;
    for(int i=0;i<n;i++){
        while(m>1&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=n-2;i>=0;i--){
        while(m>k&&Cross(ch[m-1]-ch[m-2],p[i]-ch[m-2])<=0)m--;
        ch[m++]=p[i];
    }
    if(n>1)m--;
    return m;
}
double tubaos(Point *p,int n){
    double area=0;
    for(int i=1;i<n-1;i++){
        area+=Cross(p[i]-p[0],p[i+1]-p[0]);
    }
    return area/2;
}
int intubao(Point *ch,int n,Point p){
    Vector A,B;
    int flag=0;
    for(int i=0;i<n;i++){
        A=ch[(i+1)%n]-ch[i];
        B=p-ch[i];
        if(onsegment(p,ch[i],ch[(i+1)%n])){
            flag=-1;
            break;
        }
        else if(Cross(A,B)>0){
            flag++;
        }
    }
    if(flag==-1||flag==n)return 1;
    return 0;
}

double x[N],y[N];
Point p[N],q[N],ch[N],ans[N];
int main(){
    while(~scanf("%lf%lf",&x[1],&y[1])){
        scanf("%lf%lf",&x[2],&y[2]);
        scanf("%lf%lf",&x[3],&y[3]);
        scanf("%lf%lf",&x[4],&y[4]);
        int n=0;
        p[n++]=Point(x[3],y[3]);
        p[n++]=Point(x[4],y[3]);
        p[n++]=Point(x[4],y[4]);
        p[n++]=Point(x[3],y[4]);

        int m=0;
        q[m++]=Point(x[1],y[1]);
        q[m++]=Point(x[1],y[2]);
        q[m++]=Point(x[2],y[1]);
        
        tubao(q,m,ch);
        int cnt=0;
        for(int i=0;i<n;i++){
            if(intubao(ch,m,p[i])){
                ans[cnt++]=p[i];
            }
        }
        for(int i=0;i<m;i++){
            if(intubao(p,n,q[i])){
                ans[cnt++]=q[i];
            }
        }
        p[n]=p[0];
        q[m]=q[0];
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                Point A=line_line(p[i],p[i+1],q[j],q[j+1]);
                if(dcmp(A.x-123.456)!=0)ans[cnt++]=A;
            }
        }
        int n1=tubao(ans,cnt,ch);
        if(n1<=2)printf("%.8lf
",0.0);
        else printf("%.8lf
",tubaos(ch,n1));
    }
}