【題意】

凸多邊形的最大內切圓

【題解】

二分+半平面交判定。

【程式碼】

#include <iostream>
#include <cmath>
#define eps 1e-8
#define oo 1e5
using namespace std;
const int maxn=105;

struct point
{
       double x,y;
       point() {}
       point(double xx,double yy) 
       {
                    x=xx;y=yy;
       }
}p[maxn];
int n;

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

void get(const point& p1,const point& p2,double & a,double & b,double & c)
{
     a=p2.y-p1.y;
     b=p1.x-p2.x;
     c=p2.x*p1.y-p2.y*p1.x;
}

point intersect(point u,point v,double a,double b,double c)
{
      double d,e,f;
      get(u,v,d,e,f);
      point ret;
      ret.x=(b*f-c*e)/(a*e-b*d);
      ret.y=(a*f-c*d)/(b*d-a*e);
      return ret;
}

void cut(int& n,point* p,double a,double b,double c)
{
      int m=0,i,t;
      point pp[maxn];
      for (i=0;i<n;i++)
          if (sig(a*p[i].x+b*p[i].y+c)<=0) 
             pp[m++]=p[i];
          else
          {
              t=(i-1+n)%n;
              if (sig(a*p[t].x+b*p[t].y+c)<0) pp[m++]=intersect(p[t],p[i],a,b,c);
              t=(i+1)%n;
              if (sig(a*p[t].x+b*p[t].y+c)<0) pp[m++]=intersect(p[t],p[i],a,b,c);
          }
      for (i=0;i<m;i++)
          p[i]=pp[i];
      n=m;
}

bool ok(double mid)
{
     double a,b,c;
     int nn=4,i;
     point tp[maxn];
     tp[0]=point(-oo,oo);
     tp[1]=point(-oo,-oo);
     tp[2]=point(oo,-oo);
     tp[3]=point(oo,oo);
     for (i=0;i<n;i++)
     {
         get(p[i],p[(i+1)%n],a,b,c);
         c+=mid*sqrt(a*a+b*b);
         cut(nn,tp,a,b,c);
         if (nn==0) break;
     }
     return nn>0;
}

double work()
{
       double ll=0,rr=1e4,mid;
       while (rr-ll>=1e-6)
       {
             mid=(ll+rr)/2;
             if (ok(mid)) ll=mid;
             else rr=mid;
       }
       return ll;
}

int main()
{
    freopen("pin.txt","r",stdin);
    freopen("pou.txt","w",stdout);
    int i;
    while (1)
    {
          cin >> n;
          if (n==0) break;
          for (i=0;i<n;i++)
              cin >> p[i].x >> p[i].y;
          cout.setf(ios_base::fixed,ios_base::floatfield);
          cout.precision(7);
          cout << work() << endl;
    }
    return 0;
}