poj 3384 Feng Shui (Half Plane Intersection)

3384 -- Feng Shui

　　构造半平面交，然后求凸包上最远点对。

　　这题的题意是给出一个凸多边形区域，要求在其中放置两个半径为r的圆（不能超出凸多边形区域），要求求出两个圆心，使得多边形中没有被覆盖的面积最小。反之就是求圆覆盖的区域最大。首先我们可以求出圆心放置的位置的区域，这个要利用半平面交，将原多边形区域向内收缩r的距离。要求两个圆覆盖的区域最大，也就是它们相交的面积最小，也就是两个圆心的距离要尽可能的大。这样就说明了，这题的做法是要求出凸包上面的最远点对。

　　做这题的时候犯了两个错误，一个是没有设置对精度，直接用了cout的默认输出，另一个则是没有想到收缩以后，剩余的多边形的顶点数会少于n。

代码如下：

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

 using namespace std;

 struct Point {
     double x, y;
     Point() {}
     Point(double x, double y) : x(x), y(y) {}
 } ;
 template<class T> T sqr(T x) { return x * x;}

 typedef Point Vec;
 Vec operator + (Vec a, Vec 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);}
 Vec operator / (Vec a, double p) { return Vec(a.x / p, a.y / p);}

 const double EPS = 1e-;
 const double PI = acos(-1.0);
 inline int sgn(double x) { return (x > EPS) - (x < -EPS);}
 bool operator < (Point a, Point b) { return sgn(a.x - b.x) <  || sgn(a.x - b.x) ==  && a.y < b.y;}
 bool operator == (Point a, Point b) { return sgn(a.x - b.x) ==  || sgn(a.y - b.y) == ;}

 inline double dotDet(Vec a, Vec b) { return a.x * b.x + a.y * b.y;}
 inline double crossDet(Vec a, Vec b) { return a.x * b.y - a.y * b.x;}
 inline double dotDet(Point o, Point a, Point b) { return dotDet(a - o, b - o);}
 inline double crossDet(Point o, Point a, Point b) { return crossDet(a - o, b - o);}
 inline double vecLen(Vec x) { return sqrt(dotDet(x, x));}
 inline double toRad(double deg) { return deg/ 180.0 * PI;}
 inline double angle(Vec v) { return atan2(v.y, v.x);}
 Vec normal(Vec x) {
     double len = vecLen(x);
     return Vec(-x.y, x.x) / len;
 }

 struct Poly {
     vector<Point> pt;
     Poly() { pt.clear();}
     ~Poly() {}
     Poly(vector<Point> &pt) : pt(pt) {}
     Point operator [] (int x) const { return pt[x];}
     int size() { return pt.size();}
     double area() {
         double ret = 0.0;
         int sz = pt.size();
         for (int i = ; i < sz; i++) {
             ret += crossDet(pt[i], pt[i - ]);
         }
         return fabs(ret / 2.0);
     }
 } ;

 struct DLine {
     Point p;
     Vec v;
     double ang;
     DLine() {}
     DLine(Point p, Vec v) : p(p), v(v) { ang = atan2(v.y, v.x);}
     bool operator < (const DLine &L) const { return ang < L.ang;}
     DLine move(double x) {
         Vec nor = normal(v);
         nor = nor * x;
         return DLine(p + nor, v);
     }
 } ;

 inline bool onLeft(DLine L, Point p) { return crossDet(L.v, p - L.p) > ;}
 Point dLineIntersect(DLine a, DLine b) {
     Vec u = a.p - b.p;
     double t = crossDet(b.v, u) / crossDet(a.v, b.v);
     return a.p + a.v * t;
 }

 Poly halfPlane(DLine *L, int n) {
     Poly ret = Poly();
     sort(L, L + n);
     int fi, la;
     Point *p = new Point[n];
     DLine *q = new DLine[n];
     q[fi = la = ] = L[];
     for (int i = ; i < n; i++) {
         while (fi < la && !onLeft(L[i], p[la - ])) la--;
         while (fi < la && !onLeft(L[i], p[fi])) fi++;
         q[++la] = L[i];
         if (fabs(crossDet(q[la].v, q[la - ].v)) < EPS) {
             la--;
             if (onLeft(q[la], L[i].p)) q[la] = L[i];
         }
         if (fi < la) p[la - ] = dLineIntersect(q[la - ], q[la]);
     }
     while (fi < la && !onLeft(q[fi], p[la - ])) la--;
     if (la < fi) return ret;
     p[la] = dLineIntersect(q[la], q[fi]);
     for (int i = fi; i <= la; i++) ret.pt.push_back(p[i]);
     return ret;
 }

 const int N = ;
 Point pt[N];
 DLine dl[N];

 int main() {
 //    freopen("in", "r", stdin);
     int n;
     double r;
     while (cin >> n >> r) {
         for (int i = ; i < n; i++) {
             cin >> pt[i].x >> pt[i].y;
             if (i) dl[i - ] = DLine(pt[i], pt[i - ] - pt[i]).move(r + EPS);
         }
         dl[n - ] = DLine(pt[], pt[n - ] - pt[]).move(r + EPS);
         Poly tmp = halfPlane(dl, n);
         if (tmp.size() <= ) {
             for (int i = ; i < n; i++) {
                 if (i) dl[i - ] = DLine(pt[i], pt[i - ] - pt[i]).move(r - EPS);
             }
             dl[n - ] = DLine(pt[], pt[n - ] - pt[]).move(r - EPS);
             tmp = halfPlane(dl, n);
         }
         double dis = 0.0;
         int id[] = { , };
         n = tmp.size();
         for (int i = ; i < n; i++) {
             for (int j = ; j < n; j++) {
                 if (dis < vecLen(tmp[i] - tmp[j])) {
                     dis = vecLen(tmp[i] - tmp[j]);
                     id[] = i;
                     id[] = j;
                 }
             }
         }
 //        cout << vecLen(tmp[id[0]] - tmp[id[1]]) << endl;
         cout.precision();
         cout << tmp[id[]].x << ' ' << tmp[id[]].y << ' ' << tmp[id[]].x << ' ' << tmp[id[]].y << endl;
     }
     return ;
 }

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——written by Lyon