BZOJ 2618 CQOI 2006 凸多边形 半平面交

题目大意：给出n个凸多边形，求这些多边形的面积的交。

思路：犯傻了。。以后看到凸多边形第一时间就要想到半平面交啊。。多明显啊，半天愣着没想出来。

CODE：

#include <cmath>#include <cstdio>#include <iomanip>#include <cstring>#include <iostream>#include <algorithm>#define MAX 6100#define EPS 1e-10#define DCMP(a) (fabs(a) < EPS)using namespace std;struct Point{double x,y;Point(double _ = .0,double __ = .0):x(_),y(__) {}Point operator -(const Point &a)const {return Point(x - a.x,y - a.y);}Point operator +(const Point &a)const {return Point(x + a.x,y + a.y);}Point operator *(double a)const {return Point(x * a,y * a);}void Read() {scanf("%lf%lf",&x,&y);}}p[MAX],temp[600];struct Line{Point p,v;double alpha;Line(Point _,Point __):p(_),v(__) {}Line() {}bool operator <(const Line &a)const {return alpha < a.alpha;}void Calc() {alpha = atan2(v.y,v.x);}}line[MAX],q[MAX];int k,cnt;int lines;inline double Cross(const Point &a,const Point &b){return a.x * b.y - a.y * b.x;}inline void MakeLine(const Point &a,const Point &b){line[++lines] = Line(a,b - a);}inline bool OnLeft(const Point &p,const Line &l){return Cross(l.v,p - l.p) > 0;}inline Point GetIntersection(const Line &l1,const Line &l2){Point u = l1.p - l2.p;double t = Cross(l2.v,u) / Cross(l1.v,l2.v);return l1.p + l1.v * t;}double HalfplanIntersection(){int front = 1,tail = 1;q[1] = line[1];for(int i = 2; i <= lines; ++i) {while(front < tail && !OnLeft(p[tail - 1],line[i]))--tail;while(front < tail && !OnLeft(p[front],line[i]))++front;if(DCMP(Cross(q[tail].v,line[i].v)))q[tail] = OnLeft(q[tail].p,line[i]) ? q[tail]:line[i];elseq[++tail] = line[i];if(front < tail)p[tail - 1] = GetIntersection(q[tail],q[tail - 1]);}while(front < tail && !OnLeft(p[tail - 1],q[front]))--tail;p[tail] = GetIntersection(q[tail],q[front]);if(tail - front <= 1)return .0;double re = .0;for(int i = front; i < tail; ++i)re += Cross(p[i],p[i + 1]);re += Cross(p[tail],p[front]);return re / 2.0;}int main(){cin >> k;for(int i = 1; i <= k; ++i) {scanf("%d",&cnt);for(int j = 1; j <= cnt; ++j)temp[j].Read();for(int j = 1; j < cnt; ++j)MakeLine(temp[j],temp[j + 1]);MakeLine(temp[cnt],temp[1]);}for(int i = 1; i <= lines; ++i)line[i].Calc();sort(line + 1,line + lines + 1);cout << fixed << setprecision(3) << HalfplanIntersection() << endl;return 0;}