半平面交 n^2和nlogn的模板
n^2普通模板：
/*半平面相交（直线切割多边形）（点标号从1开始）*/
Point points[MAXN],p[MAXN],q[MAXN];
int n;
double r;
int cCnt,curCnt;
inline void getline(Point x,Point y,double &a,double &b,double &c){
a = y.y - x.y;
b = x.x - y.x;
c = y.x * x.y - x.x * y.y;
}
inline void initial(){
for(int i = 1; i <= n; ++i)p[i] = points[i];
p[n+1] = p[1];
p[0] = p[n];
cCnt = n;
}
inline Point intersect(Point x,Point y,double a,double b,double c){
double u = fabs(a * x.x + b * x.y + c);
double v = fabs(a * y.x + b * y.y + c);
return Point( (x.x * v + y.x * u) / (u + v) , (x.y * v + y.y * u) / (u + v) );
}
inline void cut(double a,double b ,double c){
curCnt = 0;
for(int i = 1; i <= cCnt; ++i){
if(a*p[i].x + b*p[i].y + c >= EPS)q[++curCnt] = p[i];
else {
if(a*p[i-1].x + b*p[i-1].y + c > EPS){
q[++curCnt] = intersect(p[i],p[i-1],a,b,c);
}
if(a*p[i+1].x + b*p[i+1].y + c > EPS){
q[++curCnt] = intersect(p[i],p[i+1],a,b,c);
}
}
}
for(int i = 1; i <= curCnt; ++i)p[i] = q[i];
p[curCnt+1] = q[1];p[0] = p[curCnt];
cCnt = curCnt;
}
inline void solve(){
//注意：默认点是顺时针，如果题目不是顺时针，规整化方向
initial();
for(int i = 1; i <= n; ++i){
double a,b,c;
getline(points[i],points[i+1],a,b,c);
cut(a,b,c);
}
/*
如果要向内推进r，用该部分代替上个函数
for(int i = 1; i <= n; ++i){
Point ta, tb, tt;
tt.x = points[i+1].y - points[i].y;
tt.y = points[i].x - points[i+1].x;
double k = r / sqrt(tt.x * tt.x + tt.y * tt.y);
tt.x = tt.x * k;
tt.y = tt.y * k;
ta.x = points[i].x + tt.x;
ta.y = points[i].y + tt.y;
tb.x = points[i+1].x + tt.x;
tb.y = points[i+1].y + tt.y;
double a,b,c;
getline(ta,tb,a,b,c);
cut(a,b,c);
}
*/
//多边形核的面积
double area = 0;
for(int i = 1; i <= curCnt; ++i)
area += p[i].x * p[i + 1].y - p[i + 1].x * p[i].y;
area = fabs(area / 2.0);
//此时cCnt为最终切割得到的多边形的顶点数，p为存放顶点的数组
}
inline void GuiZhengHua(){
//规整化方向，逆时针变顺时针，顺时针变逆时针
for(int i = 1; i < (n+1)/2; i ++)
swap(points[i], points[n-i]);//头文件加iostream
}
inline void init(){
for(int i = 1; i <= n; ++i)points[i].input();
points[n+1] = points[1];
}
接下来是大牛的一个nlogn模板，大意就是维护一个真正有用的点集，然后尽量把没用的删除以便把n降到最低。对于能否真正降到log还心存疑惑，如果数据不巧，nlogn时间复杂度不会比n^2的低，或者更高，总之 慎用！
#include<iostream>
#include<fstream>
#include<iomanip>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cstdlib>
#include<cmath>
#include<set>
#include<map>
#include<queue>
#include<stack>
#include<string>
#include<vector>
#include<sstream>
#include<cassert>
#define LL long long
#define eps 1e-10
#define inf 10000
#define zero(a) fabs(a)<eps
#define N 20005
using namespace std;
struct Point{
double x,y;
}p[N*2];
struct Segment{
Point s,e;
double angle;
void get_angle(){angle=atan2(e.y-s.y,e.x-s.x);}
}seg[N];
int m;
//叉积为正说明，p2在p0-p1的左侧
double xmul(Point p0,Point p1,Point p2){
return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}
Point Get_Intersect(Segment s1,Segment s2){
double u=xmul(s1.s,s1.e,s2.s),v=xmul(s1.e,s1.s,s2.e);
Point t;
t.x=(s2.s.x*v+s2.e.x*u)/(u+v);t.y=(s2.s.y*v+s2.e.y*u)/(u+v);
return t;
}
bool cmp(Segment s1,Segment s2){
//先按极角排序
if(s1.angle>s2.angle) return true;
//极角相等，内侧的在前
else if(zero(s1.angle-s2.angle)&&xmul(s2.s,s2.e,s1.e)>-eps) return true;
return false;
}
void HalfPlaneIntersect(Segment seg[],int n){
sort(seg,seg+n,cmp);
int tmp=1;
for(int i=1;i<n;i++)
if(!zero(seg[i].angle-seg[tmp-1].angle))
seg[tmp++]=seg[i];
n=tmp;
Segment deq[N];
deq[0]=seg[0];deq[1]=seg[1];
int head=0,tail=1;
for(int i=2;i<n;i++){
while(head<tail&&xmul(seg[i].s,seg[i].e,Get_Intersect(deq[tail],deq[tail-1]))<-eps) tail--;
while(head<tail&&xmul(seg[i].s,seg[i].e,Get_Intersect(deq[head],deq[head+1]))<-eps) head++;
deq[++tail]=seg[i];
}
while(head<tail&&xmul(deq[head].s,deq[head].e,Get_Intersect(deq[tail],deq[tail-1]))<-eps) tail--;
while(head<tail&&xmul(deq[tail].s,deq[tail].e,Get_Intersect(deq[head],deq[head+1]))<-eps) head++;
if(head==tail) return;
m=0;
for(int i=head;i<tail;i++)
p[m++]=Get_Intersect(deq[i],deq[i+1]);
if(tail>head+1)
p[m++]=Get_Intersect(deq[head],deq[tail]);
}
double Get_area(Point p[],int &n){
double area=0;
for(int i=1;i<n-1;i++)
area+=xmul(p[0],p[i],p[i+1]);
return fabs(area)/2.0;
}
int main(){
int n;
while(scanf("%d",&n)!=EOF){
seg[0].s.x=0;seg[0].s.y=0;seg[0].e.x=10000;seg[0].e.y=0;seg[0].get_angle();//设置边界
seg[1].s.x=10000;seg[1].s.y=0;seg[1].e.x=10000;seg[1].e.y=10000;seg[1].get_angle();
seg[2].s.x=10000;seg[2].s.y=10000;seg[2].e.x=0;seg[2].e.y=10000;seg[2].get_angle();
seg[3].s.x=0;seg[3].s.y=10000;seg[3].e.x=0;seg[3].e.y=0;seg[3].get_angle();
for(int i=0;i<n;i++){
scanf("%lf%lf%lf%lf",&seg[i+4].s.x,&seg[i+4].s.y,&seg[i+4].e.x,&seg[i+4].e.y);//读点
seg[i+4].get_angle();
}
HalfPlaneIntersect(seg,n+4);
printf("%.1f\n",Get_area(p,m));
}
return 0;
}
