BZOJ 1137 半平面交

半平面交的板子

//By SiriusRen
#include <bits/stdc++.h>
#define double long double
using namespace std;
const int N=100050;
const double eps=1e-10;
int n,m,xx,yy,tot;
double Ans;
vector<int>vec[N];
struct Point{double x,y;}point[N];
struct Line{Point a,b;double angle;}line[N],q[N];
void addline(Line &l,Point a,Point b){
    l.a=a,l.b=b,l.angle=atan2(b.y-a.y,b.x-a.x);
}
Point operator-(Point a,Point b){
    Point c;c.x=a.x-b.x,c.y=a.y-b.y;return c;
}
double operator*(Point a,Point b){
    return a.x*b.y-a.y*b.x;
}
bool operator<(Line a,Line b){
    if(a.angle==b.angle)return (b.b-a.a)*(b.a-a.a)>0;
    return a.angle<b.angle;
}
Point inter(Line a,Line b){
    double k1,k2,t;
    k1=(a.b-b.a)*(b.b-b.a);
    k2=(b.b-b.a)*(a.a-b.a);
    t=k1/(k1+k2);
    Point ans;
    ans.x=a.b.x+(a.a.x-a.b.x)*t;
    ans.y=a.b.y+(a.a.y-a.b.y)*t;
    return ans;
}
double dis(Point x,Point y){
    x=y-x;
    return sqrt(x.x*x.x+x.y*x.y);
}
bool judge(Line a,Line b,Line t){
    Point p=inter(a,b);
    return (t.a-p)*(t.b-p)<0;
}
void bpmj(){
    sort(line+1,line+1+tot);
    n=0;
    for(int i=1;i<=tot;i++){
        if(abs(line[i].angle-line[i-1].angle)>eps)n++;
        line[n]=line[i];
    }
    int r=1,l=0;
    q[0]=line[1],q[1]=line[2];
    for(int i=3;i<=n;i++){
        while(l<r&&judge(q[r],q[r-1],line[i]))r--;
        while(l<r&&judge(q[l],q[l+1],line[i]))l++;
        q[++r]=line[i];
    }
    while(l<r&&judge(q[r],q[r-1],q[l]))r--;
    while(l<r&&judge(q[l],q[l+1],q[r]))l++;
    q[r+1]=q[l],tot=0;
    for(int i=l;i<=r;i++)point[++tot]=inter(q[i],q[i+1]);
    point[++tot]=point[1];
    for(int i=1;i<tot;i++)Ans+=dis(point[i],point[i+1]);
}
int main(){
    scanf("%d%d",&n,&m);
    for(int i=1;i<=n;i++)
        scanf("%Lf%Lf",&point[i].x,&point[i].y);
    Ans=-dis(point[1],point[n]);
    for(int i=1;i<=m;i++){
        scanf("%d%d",&xx,&yy);
        if(xx>yy)swap(xx,yy);
        vec[xx].push_back(yy);
    }
    for(int i=1,j,k;i<=n;i++){
        sort(vec[i].begin(),vec[i].end());
        for(j=n,k=vec[i].size()-1;j>i&&~k;j--,k--)
            if(vec[i][k]!=j)break;
        if(i==1&&j==n){printf("%.10Lf\n",dis(point[1],point[n]));return 0;}
        if(j>i)addline(line[++tot],point[j],point[i]);
    }addline(line[++tot],point[1],point[n]);
    bpmj();
    printf("%.10Lf\n",Ans);
}