UVALive 3890 Most Distant Point from the Sea

https://vjudge.net/problem/UVALive-3890

 

题意：凸n边形小岛，求岛上距海的最远的一点距海的最短距离（凸包内切圆半径）

 

二分+半平面交判断是否存在这样的点

 

#include<cmath>
#include<cstdio>
#include<algorithm>

#define N 101

using namespace std;

const double eps=1e-6;

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

typedef Point Vector;

Point P[N],Poly[N];
Vector v[N],v2[N];

Vector operator - (Vector A,Vector B) {  return Vector(A.x-B.x,A.y-B.y); }
Vector operator + (Vector A,Vector B) {  return Vector(A.x+B.x,A.y+B.y); }
Vector operator * (Vector A,double b) {  return Vector(A.x*b,A.y*b); }

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 < (Line L) const 
    {
        return ang<L.ang;
    }
};

Line L[N];

double Cross(Vector A,Vector B)
{
    return A.x*B.y-A.y*B.x;
}

double Dot(Vector A,Vector B)
{
    return A.x*B.x+A.y*B.y;
}

double Length(Vector A)
{
    return sqrt(Dot(A,A));
}

Vector Normal(Vector A)
{
    double L=Length(A);
    return Vector(-A.y/L,A.x/L);
}

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;
}

bool HalfplaneIntersection(Line *L,int n)
{
    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--;
    return last-first>1;
}

int main()
{
    int n,m;
    int x,y;
    double l,r,mid;
    while(scanf("%d",&n)!=EOF)
    {
        if(!n) return 0;
        for(int i=0;i<n;++i) 
        {
            scanf("%d%d",&x,&y);
            P[i]=Point(x,y);
        }
        for(int i=0;i<n;++i)
        {
            v[i]=P[(i+1)%n]-P[i];
            v2[i]=Normal(v[i]);
        }
        l=0; r=20000;
        while(r-l>eps)
        {
            mid=(l+r)/2;
            for(int i=0;i<n;++i) 
            L[i]=Line(P[i]+v2[i]*mid,v[i]);
            if(HalfplaneIntersection(L,n)) l=mid;
            else r=mid;
        }
        printf("%.6lf\n",l);
    }
}