luogu4196 [CQOI2006]凸多边形 半平面交
据说pkusc出了好几年半平面交了,我也来水一发
ref
#include <algorithm>
#include <iostream>
#include <cstdio>
#include <cmath>
using namespace std;
int n, cnt, tot;
const double eps=1e-7;
struct Point{
double x, y;
Point(double u=0.0, double v=0.0){
x = u; y = v;
}
Point operator+(const Point &u)const{
return Point(x+u.x, y+u.y);
}
Point operator-(const Point &u)const{
return Point(x-u.x, y-u.y);
}
double crs(Point u){
return x*u.y-y*u.x;
}
}pt[55], a[1005];
struct Line{
Point x, y;
double ang;
Line(){}
Line(Point u, Point v){
x = u; y = v;
ang = atan2(v.y-u.y, v.x-u.x);
}
}l[1005], d[1005];
Point operator*(double x, Point u){
return Point(x*u.x, x*u.y);
}
bool cmp(Line u, Line v){
if(fabs(u.ang-v.ang)>=eps) return u.ang<v.ang;
return (u.y-u.x).crs(v.y-u.x)>eps;
}
Point inter(Line u, Line v){
double t=(v.x-u.x).crs(v.y-u.x)/((v.x-u.x).crs(v.y-u.x)+(v.y-u.y).crs(v.x-u.y));
return u.x+t*(u.y-u.x);
}
bool isLeft(Point u, Line v){
return (v.y-v.x).crs(u-v.x)>eps;
}
void halfPlaneIntersection(){
sort(l+1, l+1+cnt, cmp);
for(int i=1; i<=cnt; i++){
if(i==1 || fabs(l[i].ang-l[i-1].ang)>=eps) tot++;
l[tot] = l[i];
}
cnt = tot; tot = 0;
int ll=1, rr=0;
d[++rr] = l[1]; d[++rr] = l[2];
for(int i=3; i<=cnt; i++){
while(ll<rr && !isLeft(inter(d[rr-1], d[rr]), l[i])) rr--;
while(ll<rr && !isLeft(inter(d[ll+1], d[ll]), l[i])) ll++;
d[++rr] = l[i];
}
while(ll<rr && !isLeft(inter(d[rr-1], d[rr]), d[ll])) rr--;
while(ll<rr && !isLeft(inter(d[ll+1], d[ll]), d[rr])) ll++;
d[rr+1] = d[ll];
for(int i=ll; i<=rr; i++)
a[++tot] = inter(d[i], d[i+1]);
}
double ans(){
if(tot<3) return 0.0;
a[tot+1] = a[1];
double re=0;
for(int i=1; i<=tot; i++)
re += a[i].crs(a[i+1]);
return re/2;
}
int main(){
cin>>n;
while(n--){
int mi;
scanf("%d", &mi);
for(int i=1; i<=mi; i++)
scanf("%lf %lf", &pt[i].x, &pt[i].y);
pt[mi+1] = pt[1];
for(int i=1; i<=mi; i++)
l[++cnt] = (Line){pt[i], pt[i+1]};
}
halfPlaneIntersection();
printf("%.3f\n", ans());
return 0;
}
拙いものと思えども、
その手に握る其れこそが、
いつか幻想を生んでいく。