poj A Round Peg in a Ground Hole

http://poj.org/problem?id=1584

#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;

const int maxn=50000;
const double pi=acos(-1.0);
const double eps=10e-8;

int cmp(double x)
{
   if(fabs(x)<eps) return 0;
   if(x>0) return 1;
   return -1;
}

double sqr(double x)
{
    return x*x;
}

struct point
{
    double x,y;
    point(){}
    point(double a,double b):x(a),y(b){}
    bool operator <(const point &a)const
    {
        return (x<a.x)||(x==a.x&&y<a.y);
    }
    friend point operator -(const point &a,const point &b){
        return point(a.x-b.x,a.y-b.y);
    }
    double norm(){
        return sqrt(sqr(x)+sqr(y));
    }
}p[maxn],ch[maxn];

struct line
{
   point a,b;
   line(){}
   line(point x,point y):a(x),b(y){}
};

double det(point a,point b,point c)
{
    return ((b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y));
}

double cross(point a,point b,point c)
{
    return ((b.x-a.x)*(c.y-b.y)-(c.x-b.x)*(b.y-a.y));
}
double det1(const point &a,const point &b)
{
    return a.x*b.y-a.y*b.x;
}

double dot(const point &a,const point &b)
{
    return a.x*b.x+a.y*b.y;
}

double dis(point a,point b)
{
    return sqrt(sqr(a.x-b.x)+sqr(a.y-b.y));
}

double dis_point_segment(const point p,const point s,const point t)
{
    if(cmp(dot(p-s,t-s))<0) return (p-s).norm();
    if(cmp(dot(p-t,s-t))<0) return (p-t).norm();
    return fabs(det1(s-p,t-p)/dis(s,t));
}

bool pointonsegment(point p,point s,point t)
{
    return cmp(det1(p-s,t-s))==0&&cmp(dot(p-s,p-t))<=0;
}

int convex_hull(point *p,int n,point *ch)
{
    sort(p,p+n);
    int m=0;
    for(int i=0; i<n; i++)
    {
        while(m>1&&det(ch[m-2],ch[m-1],p[i])<=0) m--;
        ch[m++]=p[i];
    }
    int k=m;
    for(int i=n-2; i>=0; i--)
    {
        while(m>k&&det(ch[m-2],ch[m-1],p[i])<=0) m--;
        ch[m++]=p[i];
    }
    if(n>1) m--;
    return m;
}


bool convex_hull1(point *p,int n)
{
    int flag=0;
    p[n]=p[0];
    for(int i=2; i<=n; i++)
    {
        //printf("%lf%lf %lf%lf %lf%lf\n",p[i-2].x,p[i-2].y,p[i-1].x,p[i-1].y,p[i].x,p[i].y);
        int t=cmp(cross(p[i-2],p[i-1],p[i]));
        //printf("%d\n",t);
        if(!flag) flag=t;
        if(flag*t<0) return false;
    }
    return true;
}
int point_in(point t,point *ch,int n)
{
    int num=0,d1,d2,k;
    ch[n]=ch[0];
    for(int i=0; i<n; i++)
    {
        if(pointonsegment(t,ch[i],ch[i+1])) return 2;
        k=cmp(det1(ch[i+1]-ch[i],t-ch[i]));
        d1=cmp(ch[i].y-t.y);
        d2=cmp(ch[i+1].y-t.y);
        if(k>0&&d1<=0&&d2>0) num++;
        if(k<0&&d2<=0&&d1>0) num--;
    }
    return num!=0;
}
int main()
{
    int n;
    double r,x,y;
    //freopen("sb.txt","w",stdout);
    while(scanf("%d",&n)!=EOF)
    {
        if(n<3) break;
        scanf("%lf%lf%lf",&r,&x,&y);
        point t(x,y);
        for(int i=0; i<n; i++)
        {
            scanf("%lf%lf",&p[i].x,&p[i].y);
        }

        if(!convex_hull1(p,n))
        {
            printf("HOLE IS ILL-FORMED\n");
            continue;
        }
        int cn=convex_hull(p,n,ch);
        if(point_in(t,ch,cn))
        {
            double max1=dis_point_segment(t,ch[0],ch[1]);
            for(int i=1; i<cn+1; i++)
            {
                max1=min(max1,dis_point_segment(t,ch[i-1],ch[i]));
            }
            if(max1-r>=0) printf("PEG WILL FIT\n");
            else printf("PEG WILL NOT FIT\n");
        }
        else printf("PEG WILL NOT FIT\n");
    }
    return 0;
}