4818 Largest Empty Circle on a Segment (几何+二分)

ACM-ICPC Live Archive

　　挺水的一道题，直接二分圆的半径即可。1y~

　　类似于以前半平面交求核的做法，假设半径已经知道，我们只需要求出线段周围哪些位置是不能放置圆心的即可。这样就转换为圆与直线，直线与直线交的问题了。

　　不知道这题能不能SAA过，有空试下。

代码如下：

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

 using namespace std;

 const double EPS = 1e-;
 inline int sgn(double x) { return (x > EPS) - (x < -EPS);}
 typedef pair<double, double> Point;
 #define x first
 #define y second
 template<class T> T sqr(T x) { return x * x;}
 Point operator + (Point a, Point b) { return Point(a.x + b.x, a.y + b.y);}
 Point operator - (Point a, Point b) { return Point(a.x - b.x, a.y - b.y);}
 Point operator * (Point a, double p) { return Point(a.x * p, a.y * p);}
 Point operator / (Point a, double p) { return Point(a.x / p, a.y / p);}

 inline double cross(Point a, Point b) { return a.x * b.y - a.y * b.x;}
 inline double dot(Point a, Point b) { return a.x * b.x + a.y * b.y;}
 inline double veclen(Point a) { return sqrt(dot(a, a));}
 inline Point vecunit(Point a) { return a / veclen(a);}
 inline Point normal(Point a) { return Point(-a.y, a.x) / veclen(a);}

 struct Line {
     Point s, t;
     Line() {}
     Line(Point s, Point t) : s(s), t(t) {}
     Point vec() { return t - s;}
     Point point(double p) { return s + vec() * p;}
     Line move(double p) { // + left - right
         Point nor = normal(vec());
         return Line(s + nor * p, t + nor * p);
     }
 } ;

 inline bool between(Point o, Point a, Point b) { return sgn(dot(a - o, b - o)) < ;}
 inline bool between(Point a, Line l) { return between(a, l.s, l.t);}
 inline Point llint(Line a, Line b) { return a.point(cross(b.vec(), a.s - b.s) / cross(a.vec(), b.vec()));}

 bool clint(Point a, double r, double *sol) {
     if (sgn(r - fabs(a.y)) <= ) return ;
     double d = sqrt(sqr(r) - sqr(a.y));
     //cout << "d " << d << endl;
     sol[] = a.x - d;
     sol[] = a.x + d;
     return ;
 }

 Line Y0 = Line(Point(, ), Point(, ));

 double L;
 inline void adjust(double &x) { x = max(0.0, min(L, x));}
 Point getseg(Line a, double r) {
     vector<double> sol;
     sol.clear();
     double t[];
     if (clint(a.s, r, t)) sol.push_back(t[]), sol.push_back(t[]);
     if (clint(a.t, r, t)) sol.push_back(t[]), sol.push_back(t[]);
     Line l1 = a.move(r), l2 = a.move(-r), l3 = Line(l1.s, l2.s), l4 = Line(l1.t, l2.t);
     Point p1 = llint(l1, Y0), p2 = llint(l2, Y0), p3 = llint(l3, Y0), p4 = llint(l4, Y0);
     if (between(p1, l1)) sol.push_back(p1.x);
     if (between(p2, l2)) sol.push_back(p2.x);
     if (between(p3, l3)) sol.push_back(p3.x);
     if (between(p4, l4)) sol.push_back(p4.x);
     if (sol.size() == ) return Point(-, -);
     sort(sol.begin(), sol.end());
     //cout << "sol ";
     //for (int i = 0; i < sol.size(); i++) cout << sol[i] << ' '; cout << endl;
     adjust(sol[]), adjust(sol[sol.size() - ]);
     return Point(sol[], sol[sol.size() - ]);
 }

 const int N = ;
 typedef pair<double, int> Event;
 Line l[N];
 int n;

 bool test(double r) {
     vector<Event> ev;
     ev.clear();
     for (int i = ; i < n; i++) {
         Point tmp = getseg(l[i], r);
         if (tmp.x <  || tmp.y < ) continue;
         //cout << tmp.x << '~' << tmp.y << endl;
         ev.push_back(Event(tmp.x, ));
         ev.push_back(Event(tmp.y, -));
     }
     sort(ev.begin(), ev.end());
     //cout << r << endl;
     //for (int i = 0; i < ev.size(); i++) cout << ev[i].x << '&' << ev[i].y << ' '; cout << endl;
     double last = ;
     int cnt = , sz = ev.size();
     for (int i = ; i < sz; i++) {
         if (ev[i].y == ) {
             if (cnt ==  && sgn(ev[i].x - last) > ) return ;
             cnt++;
         } else {
             if (cnt == ) last = ev[i].x;
             cnt--;
         }
     }
     return sgn(L - last) > ;
 }

 int main() {
     //freopen("in", "r", stdin);
     int T;
     cin >> T;
     while (T-- && cin >> n >> L) {
         for (int i = ; i < n; i++) cin >> l[i].s.x >> l[i].s.y >> l[i].t.x >> l[i].t.y;
         double lp = , rp = , mp;
         while (rp - lp > EPS) {
             mp = (lp + rp) / ;
             if (test(mp)) lp = mp;
             else rp = mp;
         }
         //puts("~~~~~~~~~~~~~~~~~~~~~~~~");
         //test(2.118);
         printf("%.3f\n", mp);
     }
     return ;
 }

——written by Lyon