poj1584（判断凸包+求点到线段的距离）

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

const double eps=1e-8;
const double inf=1e20;int sgn(double x){
    if(abs(x)<eps) return 0;
    if(x<0) return -1;
    return 1;
}

struct Point{
    double x,y;
    Point(){}
    Point(double xx,double yy):x(xx),y(yy){}
    Point operator + (const Point& b)const{
        return Point(x+b.x,y+b.y);
    }
    Point operator - (const Point& b)const{
        return Point(x-b.x,y-b.y);
    }
    double operator * (const Point& b)const{
        return x*b.x+y*b.y;
    }
    double operator ^ (const Point& b)const{
        return x*b.y-b.x*y;
    }
    //绕原点旋转角度b（弧度值），后x、y的变化
    void transXY(double b){
        double tx=x,ty=y;
        x=tx*cos(b)-ty*sin(b);
        y=tx*sin(b)+ty*cos(b);
    }
};

struct Line{
    Point s,e;
    Line(){}
    Line(Point ss,Point ee){
        s=ss,e=ee;
    }
    //两直线相交求交点
    //第一个值为0表示直线重合，为1表示平行，为2表示相交
    //只有第一个值为2时，交点才有意义
    pair<int,Point> operator &(const Line &b)const{
        Point res = s;
        if(sgn((s-e)^(b.s-b.e)) == 0)
        {
            if(sgn((s-b.e)^(b.s-b.e)) == 0)
                return make_pair(0,res);//重合
            else return make_pair(1,res);//平行
        }
        double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e));
        res.x += (e.x-s.x)*t;
        res.y += (e.y-s.y)*t;
        return make_pair(2,res);
    }
};
//判断线段相交
bool inter(Line l1,Line l2){
    return
        max(l1.s.x,l1.e.x)>=min(l2.s.x,l2.e.x)&&
        max(l2.s.x,l2.e.x)>=min(l1.s.x,l1.e.x)&&
        max(l1.s.y,l1.e.y)>=min(l2.s.y,l2.e.y)&&
        max(l2.s.y,l2.e.y)>=min(l1.s.y,l1.e.y)&&
        sgn((l1.s-l2.s)^(l2.e-l2.s))*sgn((l1.e-l2.s)^(l2.e-l2.s))<=0&&
        sgn((l2.s-l1.s)^(l1.e-l1.s))*sgn((l2.e-l1.s)^(l1.e-l1.s))<=0;
}

double dis(Point a,Point b){
    return sqrt((b-a)*(b-a));
}
//判断点在线段上
bool OnSeg(Point P,Line L){
    return
        sgn((L.s-P)^(L.e-P))==0&&
        sgn((P.x-L.s.x)*(P.x-L.e.x))<=0&&
        sgn((P.y-L.s.y)*(P.y-L.e.y))<=0;
}
//判断点在凸多边形内，复杂度O(n)
//点形成一个凸包，而且按逆时针排序（如果是顺时针把里面的<0改为>0）
//点的编号:0~n-1
//返回值：
//-1:点在凸多边形外
//0:点在凸多边形边界上
//1:点在凸多边形内
int inConvexPoly(Point a,Point p[],int n){
    for(int i=0;i<n;++i)
        if(sgn((p[i]-a)^(p[(i+1)%n]-a))<0) return -1;
        else if(OnSeg(a,Line(p[i],p[(i+1)%n]))) return 0;
    return 1;
}
//判断点在任意多边形内,复杂度O(n)
//射线法，poly[]的顶点数要大于等于3,点的编号0~n-1，按逆时针或顺时针排序
//返回值
//-1:点在凸多边形外
//0:点在凸多边形边界上
//1:点在凸多边形内
int inPoly(Point a,Point p[],int n){
    int cnt=0;
    Line ray,side;
    ray.s=a;
    ray.e.y=a.y;
    ray.e.x=-inf;
    for(int i=0;i<n;++i){
        side.s=p[i];
        side.e=p[(i+1)%n];
        if(OnSeg(a,side)) return 0;
        if(sgn(side.s.y-side.e.y)==0) continue;
        if(OnSeg(side.s,ray)){
            if(sgn(side.s.y-side.e.y)>0) ++cnt;
        }
        else if(OnSeg(side.e,ray)){
            if(sgn(side.e.y-side.s.y)>0) ++cnt;
        }
        else if(inter(ray,side)) ++cnt;
    }
    if(cnt%2==1) return 1;
    else return -1;
}
//判断凸多边形
//允许共线边
//点可以是顺时针给出也可以是逆时针给出
//点的编号是0～n-1
bool isconvex(Point poly[],int n){
    bool s[3];
    memset(s,false,sizeof(s));
    for(int i=0;i<n;++i){
        s[sgn((poly[(i+1)%n]-poly[i])^(poly[(i+2)%n]-poly[i]))+1]=true;
        if(s[0]&&s[2]) return false;
    }
    return true;
}
//点到线段的距离
//返回点到线段最近的点
Point NearestPointToLineSeg(Point P,Line L){
    Point result;
    double t=((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s));
    if(t>=0&&t<=1){
        result.x=L.s.x+(L.e.x-L.s.x)*t;
        result.y=L.s.y+(L.e.y-L.s.y)*t;
    }
    else{
        if(dis(P,L.s)<dis(P,L.e))
            return L.s;
        else 
            return L.e;
    }
    return result;
}

int n;
double R,X,Y;
Point pt[110];

int main(){
    while(scanf("%d",&n),n>=3){
        scanf("%lf%lf%lf",&R,&X,&Y);
        for(int i=0;i<n;++i)
            scanf("%lf%lf",&pt[i].x,&pt[i].y);
        if(!isconvex(pt,n)){
            printf("HOLE IS ILL-FORMED
");
            continue;
        }
        Point P=Point(X,Y);
        if(inPoly(P,pt,n)==-1){
            printf("PEG WILL NOT FIT
");
            continue;
        }
        int flag=1;
        for(int i=0;i<n;++i){
            if(sgn(dis(P,NearestPointToLineSeg(P,Line(pt[i],pt[(i+1)%n])))-R)<0){
                flag=0;
                break;
            }
        }
        if(flag) printf("PEG WILL FIT
");
        else printf("PEG WILL NOT FIT
");
    }
    return 0;
}