POJ 3525 半平面交+二分

二分所能形成圆的最大距离，然后将每一条边都向内推进这个距离，最后所有边组合在一起判断时候存在内部点

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#include <cmath>

using namespace std;
#define N 105
#define ll long long
#define eps 1e-7

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

struct Point{
    double x,y;
    Point(double x=0 , double y=0):x(x),y(y){}
}p[N] , poly[N];

typedef Point Vector;

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 &m) const{
        return dcmp(ang-m.ang)<0;
    }
}line[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);}
Vector operator/(Vector a , double b){return Vector(a.x/b , a.y/b);}

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 Len(Vector a){return sqrt(Dot(a,a));}

bool OnLeft(Line L , Point P)
{
    return dcmp(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;
}

Vector Normal(Vector a)
{
    double l = Len(a);
    return Vector(-a.y , a.x)/l;
}

int HalfplaneIntersection(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;
}

double calArea(Point *p , int n)
{
    if(!n) return 0;
    double ret = 0;
    for(int i=2 ; i<n ; i++){
        ret += Cross(p[i-1]-p[0],p[i]-p[0]);
    }
    return ret/2;
}

double bin_search(Point *p , int n)
{
    double l = 0 , r = 1e8 , m;
    Vector unit;
    while(r-l>=eps)
    {
        m = (l+r)/2;
        for(int i=1 ; i<=n ; i++){
            unit = Normal(p[i]-p[i-1]);
            line[i-1] = Line(p[i-1]+unit*m , p[i]-p[i-1]);
        }
        if(HalfplaneIntersection(line , n , poly)) l=m;
        else r=m;
    }
    return l;
}

int main()
{
   // freopen("in.txt" , "r" , stdin);
    int n ;
    while(scanf("%d" , &n) , n)
    {
        for(int i=0 ; i<n ; i++) scanf("%lf%lf" , &p[i].x , &p[i].y);
        p[n] = p[0];
        printf("%.6f
" , bin_search(p , n));
    }
}