题目背景

C++ 解法, 执行用时: 4ms, 内存消耗: 548K, 提交时间: 2021-08-25 17:34:38

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

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 p) {return Vector(A.x*p,A.y*p);}
Vector operator /(Vector A,double p) {return Vector(A.x/p,A.y/p);}
bool operator < (const Point& a,const Point& b){
    return a.x<b.x||(a.x==b.x&&a.y<b.y);
}
const double eps=1e-6;
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.y-b.y)==0;
}
typedef vector<Point> Polygon;
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 GetLineIntersection(Point P,Vector v,Point Q,Vector w){
    Vector u=P-Q;
    double t=Cross(w,u)/Cross(v,w);
    return P+v*t;
}
bool OnSegment(Point p,Point a1,Point a2){
    return dcmp(Cross(a1-p,a2-p))==0&&dcmp(Dot(a1-p,a2-p))<0;
}

Polygon CutPolygon(Polygon poly,Point A,Point B){
    Polygon newpoly;
    int n=poly.size();
    for(int i=0;i<n;i++){
        Point C=poly[i];
        Point D=poly[(i+1)%n];
        if(dcmp(Cross(B-A,C-A))>=0) newpoly.push_back(C);
        if(dcmp(Cross(B-A,C-D))!=0){
            Point ip=GetLineIntersection(A,B-A,C,D-C);
            if(OnSegment(ip,C,D)) newpoly.push_back(ip);
        }
    }
    return newpoly;
}

double PolygonArea(Polygon p){
    int n=p.size();
    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 main(){
    ios::sync_with_stdio(false);
    
    int n;cin>>n;
    Polygon now;
    now.push_back(Point(0.0,0.0));
    now.push_back(Point(1000.0,0.0));
    now.push_back(Point(1000.0,1000.0));
    now.push_back(Point(0.0,1000.0));
    for(int i=0;i<n;i++){
        double a,b,c,d;cin>>a>>b>>c>>d;
        now=CutPolygon(now,Point(a,b),Point(c,d));
    }
    cout<<fixed<<setprecision(1)<<PolygonArea(now)<<endl;
}