uva 1475

半平面交，二分；

注意，题目的点是顺时针给出的；

#include<cstdio>
#include<algorithm>
#include<cmath>
#define maxn 50010
#define eps 1e-6
using namespace std;

int dcmp(double x)
{
    return fabs(x) < eps ? 0 : (x > 0 ? 1 : -1);
}

struct Point
{
    double x;
    double y;
    Point(double x = 0, double y = 0):x(x), y(y) {}
};
typedef Point Vector;

Vector operator + (Point A, Point B)
{
    return Vector(A.x + B.x, A.y + B.y);
}

Vector operator - (Point A, Point B)
{
    return Vector(A.x - B.x, A.y - B.y);
}

Vector operator * (Point A, double p)
{
    return Vector(A.x * p, A.y * p);
}

Vector operator / (Point A, double p)
{
    return Vector(A.x / p, A.y / p);
}
double dot(Point a,Point b)
{
    return a.x*b.x+a.y*b.y;
}
double cross(Point a,Point b)
{
    return a.x*b.y-a.y*b.x;
}

Vector nomal(Vector a)
{
    double l=sqrt(dot(a,a));
    return Vector(-a.y/l,a.x/l);
}

struct line
{
    Point p;
    Vector v;
    double ang;
    line() {}
    line(Point p,Vector v):p(p),v(v)
    {
        ang=atan2(v.y,v.x);
    }
    bool operator<(const line &t)const
    {
        return ang<t.ang;
    }
};

bool onleft(line l,Point p)
{
    return (cross(l.v,p-l.p)>0);
}

Point getintersection(line a,line b)
{
    Vector u=a.p-b.p;
    double t=cross(b.v,u)/cross(a.v,b.v);
    return a.p+a.v*t;
}

int halfplanintersection(line *l,int n,Point *poly)
{
    sort(l,l+n);
    int first,last;
    Point *p=new Point[n];
    line *q=new line[n];
    q[first=last=0]=l[0];
    for(int i=1; i<n; i++)
    {
        while(first<last && !onleft(l[i],p[last-1]))last--;
        while(first<last && !onleft(l[i],p[first]))first++;
        q[++last]=l[i];
        if(fabs(cross(q[last].v,q[last-1].v))<eps)
        {
            last--;
            if(onleft(q[last],l[i].p))q[last]=l[i];
        }
        if(first<last)p[last-1]=getintersection(q[last-1],q[last]);
    }
    while(first<last && !onleft(q[first],p[last-1]))last--;
    if((last-first )<=1)return 0;
    p[last]=getintersection(q[last],q[first]);
    int m=0;
    for(int i=first; i<=last; i++)poly[m++]=p[i];
    return m;
}

Point p[maxn],poly[maxn],v[maxn];
line l[maxn];

int main()
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        for(int i=0;i<n;i++)scanf("%lf%lf",&p[i].x,&p[i].y);
        for(int i=1;i<=n/2;i++) swap(p[i],p[n-i]);
        int left=0,right=n-2;
        int ans;
        while(left<=right)
        {
            int mid=(left+right)>>1;
            for(int i=0;i<n;i++)
            {
                v[i]=p[(i+mid+1)%n]-p[i];
                l[i]=line(p[i],v[i]);
            }
            int m=halfplanintersection(l,n,poly);
            if(!m){ans=mid;right=mid-1;}
            else left=mid+1;
        }
        printf("%d
",ans);
    }
}