HDU2468 Experiment on a … “Cable”

如图，横坐标为时间轴，纵坐标为相对起点的位移，斜率为速度。

设C为起点发出的包，发出时间为1，速度为1~2。

设D为终点发出的包，发出时间为2，速度为1~2。

A、B为探测器发出时间范围2~5，速度为4。

由图可看出，发包的时间-位移相叠的范围为可能全部抓包的范围，称有效范围。

在探测器的时间-位移范围内的有效范围/探测器时间-位移范围即探测器全部抓包的平均工作效率。

对所有速度区间、探测器时间-位移区间、起点终点区间 做半平面交，得到凸包面积除以探测器时间-位移区间面积可得解。

精度要求挺高的，eps注意一下。

  1 #include<stdio.h>

  2 #include<stdlib.h>

  3 #include<string.h>

  4 #include<math.h>

  5 #include<algorithm>

  6 using namespace std;

  7 const int maxn = 5111;

  8 const double eps = 1e-12;

  9 const double pi = acos(-1.0);

 10 typedef struct{double x, y;}Point;

 11 int dcmp(double x) {return (x > eps) - (x < -eps);}

 12 inline double det(double x1, double y1, double x2, double y2)

 13 {return x1 * y2 - x2 * y1;}

 14 double cross(Point a, Point b, Point c)

 15 {return det(b.x -a.x, b.y - a.y, c.x - a.x, c.y - a.y);}

 16 bool EqualPoint(Point a, Point b)

 17 {return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;}

 18 typedef struct{Point s, e;double ang, d;}Line;

 19 Point MakePoint(double xx, double yy)

 20 {Point res;res.x = xx, res.y = yy;return res;}

 21 void SetLine(Point a, Point b, Line &l)

 22 {

 23     l.s = a;

 24     l.e = b;

 25     l.ang = atan2(b.y - a.y, b.x - a.x);

 26     if(dcmp(a.x - b.x)) l.d = (a.x * b.y - b.x * a.y) / fabs(a.x - b.x);

 27     else l.d = (a.x * b.y - b.x * a.y) / fabs(a.y - b.y);

 28 }

 29 bool Parallel(const Line &la, const Line &lb)

 30 {

 31     return !dcmp( (la.e.x - la.s.x) * (lb.e.y - lb.s.y) -

 32             (la.e.y - la.s.y) * (lb.e.x - lb.s.x) );

 33 }

 34 Point CrossPoint(const Line &la, const Line &lb)

 35 {

 36     Point res;

 37     double u = cross(la.s, la.e, lb.s), v = cross(la.e, la.s, lb.e);

 38     res.x = (lb.s.x * v + lb.e.x * u) / (u + v);

 39     res.y = (lb.s.y * v + lb.e.y * u) / (u + v);

 40     return res;

 41 }

 42 int CompL(const void *a, const void *b)

 43 {

 44     Line la = *(Line*)a, lb = *(Line*)b;

 45     if(dcmp(la.ang - lb.ang)) return la.ang > lb.ang ? 1 : -1;

 46     return la.d > lb.d ? 1 : -1;

 47 }

 48 

 49 Line deq[maxn];

 50 bool HalfPanelCross(Line l[], int n, Point cp[], int &m)

 51 {

 52     int i, tn;

 53     m = 0;

 54     qsort(l, n, sizeof(Line), CompL);

 55     for(i = tn = 1; i < n; ++ i)

 56         if(dcmp(l[i].ang - l[i - 1].ang))

 57             l[tn ++] = l[i];

 58     n = tn;

 59     int front = 0, rear = 1;

 60     deq[0] = l[0], deq[1] = l[1];

 61     for(i = 2; i < n; ++ i)

 62     {

 63         if(Parallel(deq[rear], deq[rear - 1]) ||

 64             Parallel(deq[front], deq[front + 1]))

 65             return false;

 66         while(front < rear && dcmp( cross(l[i].s, l[i].e,

 67             CrossPoint(deq[rear], deq[rear - 1])) ) < 0) -- rear;

 68         while(front < rear && dcmp( cross(l[i].s, l[i].e,

 69             CrossPoint(deq[front], deq[front + 1])) ) < 0) ++ front;

 70         deq[++ rear] = l[i];

 71     }

 72     while(front < rear && dcmp( cross(deq[front].s, deq[front].e,

 73         CrossPoint(deq[rear], deq[rear - 1])) ) < 0) -- rear;

 74     while(front < rear && dcmp( cross(deq[rear].s, deq[rear].e,

 75         CrossPoint(deq[front], deq[front + 1])) ) < 0) ++ front;

 76     if(rear <= front + 1) return false;

 77     for(i = front; i < rear; ++ i)

 78         cp[m ++] = CrossPoint(deq[i], deq[i + 1]);

 79     if(front < rear + 1)

 80         cp[m ++] = CrossPoint(deq[front], deq[rear]);

 81     m = unique(cp, cp + m, EqualPoint) - cp;

 82     for(i = 0; i < m; ++ i)

 83     {

 84         if(dcmp(cp[i].x) == 0) cp[i].x = 0;

 85         if(dcmp(cp[i].y) == 0) cp[i].y = 0;

 86     }

 87     return true;

 88 }

 89 double PolygonArea(Point p[], int n)

 90 {

 91     if(n < 3) return 0.0;

 92     double s = p[0].y * (p[n - 1].x - p[1].x);

 93     p[n] = p[0];

 94     for(int i = 1; i < n; ++ i)

 95         s += p[i].y * (p[i - 1].x - p[i + 1].x);

 96     return fabs(s * 0.5);

 97 }

 98 Line l[maxn << 2];

 99 Point p[maxn << 2];

100 double len;

101 int n, m, ltp;

102 double maxv, minv, ti;

103 double start, end, v;

104 int main()

105 {

106     int ca = 0;

107     while(scanf("%lf", &len), dcmp(len))

108     {

109         ltp = 0;

110         scanf("%d", &n);

111         while(n --)

112         {

113             scanf("%lf%lf%lf", &minv, &maxv, &ti);

114             SetLine(MakePoint(ti, 0), MakePoint(ti + 1, minv), l[ltp ++]);

115             SetLine(MakePoint(ti + 1, maxv), MakePoint(ti, 0), l[ltp ++]);

116         }

117         scanf("%d", &m);

118         while(m --)

119         {

120             scanf("%lf%lf%lf", &minv, &maxv, &ti);

121             SetLine(MakePoint(ti + 1, len - minv), MakePoint(ti, len), l[ltp ++]);

122             SetLine(MakePoint(ti, len), MakePoint(ti + 1, len - maxv), l[ltp ++]);

123         }

124         scanf("%lf%lf%lf", &start, &end, &v);

125         printf("Case #%d: ", ++ ca);

126         SetLine(MakePoint(0, 0), MakePoint(1, 0), l[ltp ++]);

127         SetLine(MakePoint(1, len), MakePoint(0, len), l[ltp ++]);

128         SetLine(MakePoint(start + 1, v), MakePoint(start, 0), l[ltp ++]);

129         SetLine(MakePoint(end, 0), MakePoint(end + 1, v), l[ltp ++]);

130         if(!HalfPanelCross(l, ltp, p, n)){printf("0.00000\n"); continue;}

131         printf("%.5f\n", PolygonArea(p, n) / (end - start) / len + eps);

132     }

133     return 0;

134 }