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-7;

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

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=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]=LineIntersection(q[last-1],q[last]);
    }
    while(first<last && !onleft(q[first],p[last-1])) last--;
    if(last-first<=1) return 0;
    p[last]=LineIntersection(q[last],q[first]);
    int m=0;
    for(int i=first;i<=last;i++) poly[m++]=p[i];
    return m;
}

const int N = 200+10;
Pt p[N],poly[N];
Line L[N];
vec v[N] , v2[N]; 
int n;

int main() {
    while(scanf("%d",&n)==1 && n) {
        int m,x,y;
        for(int i=0;i<n;i++) {
            scanf("%d%d",&x,&y);
            p[i]=Pt(x,y);
        }
        for(int i=0;i<n;i++) {
            v[i]=p[(i+1)%n]-p[i];
            v2[i]=Normal(v[i]);
        }
        double left=0 , right=20000;
        while(right-left>eps) {
            double mid=left+(right-left)/2;
            for(int i=0;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
",left);
    }
    return 0;
}