UVA 3890 Most Distant Point from the Sea（二分法+半平面交）

题目链接：http://acm.hust.edu.cn/vjudge/problem/viewProblem.action?id=11358

【思路】

二分法+半平面交

二分与海边的的距离，由法向量可以得到平移后的各边，半平面交在特定精度判断是否有交集。

【代码】

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

 const double eps = 1e-;

 struct Pt {
     double x,y;
     Pt(double x=,double y=):x(x),y(y) {}
 };
 typedef Pt vec;
 struct Line {
     Pt P; vec v;
     double ang;
     Line () {};
     Line (Pt P,vec v):P(P),v(v) { ang=atan2(v.y , v.x); }
     bool operator < (const Line& rhs) const{
         return ang<rhs.ang;
     }
 };

 vec operator - (Pt A,Pt B) { return vec(A.x-B.x,A.y-B.y); }
 vec operator + (vec A,vec B) { return vec(A.x+B.x,A.y+B.y); }
 vec operator * (vec A,double p) { return vec(A.x*p,A.y*p); }
 double Dot(vec A,vec B) { return A.x*B.x+A.y*B.y; }
 double cross(Pt A,Pt B) { return A.x*B.y-A.y*B.x; }
 double Len(vec A) { return sqrt(Dot(A,A)); }
 vec Normal(vec A) { double L=Len(A); return vec(-A.y/L,A.x/L); }

 bool onleft(Line L,Pt P) { return cross(L.v,P-L.P)>; }

 Pt LineIntersection(Line a,Line b) {
     vec u=a.P-b.P;
     double t=cross(b.v,u)/cross(a.v,b.v);
     return a.P+a.v*t;
 }
 int HalfplaneIntersection(Line* L,int n,Pt* poly) {
     sort(L,L+n);
     int first,last;
     Pt *p=new Pt[n];
     Line *q=new Line[n];
     q[first=last=]=L[];
     for(int i=;i<n;i++) {
         while(first<last && !onleft(L[i],p[last-])) last--;
         while(first<last && !onleft(L[i],p[first])) first++;
         q[++last]=L[i];
         if(fabs(cross(q[last].v,q[last-].v))<eps) {
             last--;
             if(onleft(q[last],L[i].P)) q[last]=L[i];
         }
         if(first<last) p[last-]=LineIntersection(q[last-],q[last]);
     }
     while(first<last && !onleft(q[first],p[last-])) last--;
     if(last-first<=) return ;
     p[last]=LineIntersection(q[last],q[first]);
     int m=;
     for(int i=first;i<=last;i++) poly[m++]=p[i];
     return m;
 }

 const int N = +;
 Pt p[N],poly[N];
 Line L[N];
 vec v[N] , v2[N];
 int n;

 int main() {
     while(scanf("%d",&n)== && n) {
         int m,x,y;
         for(int i=;i<n;i++) {
             scanf("%d%d",&x,&y);
             p[i]=Pt(x,y);
         }
         for(int i=;i<n;i++) {
             v[i]=p[(i+)%n]-p[i];
             v2[i]=Normal(v[i]);
         }
         double left= , right=;
         while(right-left>eps) {
             double mid=left+(right-left)/;
             for(int i=;i<n;i++) L[i]=Line(p[i]+v2[i]*mid,v[i]);
             m=HalfplaneIntersection(L,n,poly);
             if(!m) right=mid; else left=mid;
         }
         printf("%.6lf\n",left);
     }
     return ;
 }