UVALive4974 CERC2010B Beasts

思想是半平面交+旋转卡壳，关于X轴取一次对称再求包围(0, -10^10)点的部分后再对称回来可以少写点针对性代码。左右的射线单独处理了。

  1 #include<stdio.h>
  2 #include<string.h>
  3 #include<stdlib.h>
  4 #include<algorithm>
  5 #include<iostream>
  6 #include<math.h>
  7 using namespace std;
  8 const int maxn = 211111;
  9 const double eps = 1e-9;
 10 typedef double PELEM;
 11 typedef long long LL;
 12 struct Point
 13 {
 14     PELEM x, y;
 15     Point()
 16     {
 17         x = y = 0;
 18     }
 19     Point(PELEM a, PELEM b)
 20     {
 21         x = a, y = b;
 22     }
 23     PELEM cross(const Point &b, const Point &c)const
 24     {
 25         return (b.x - x) * (c.y - y)
 26                - (c.x - x) * (b.y - y);
 27     }
 28     PELEM dot(const Point &p)const
 29     {
 30         return x * p.x + y * p.y;
 31     }
 32     Point operator-(const Point &p)const
 33     {
 34         return Point(x - p.x, y - p.y);
 35     }
 36     Point operator+(const Point &p)const
 37     {
 38         return Point(x + p.x, y + p.y);
 39     }
 40     Point operator-()const
 41     {
 42         return Point(-x, -y);
 43     }
 44 } p[2][maxn << 1];
 45 struct Line
 46 {
 47     LL a, b, c;
 48     bool operator<(const Line &l)const
 49     {
 50         if(a *l.b == b * l.a)
 51             return l.c * b < c * l.b;
 52         return a * l.b > b * l.a;
 53     }
 54     int CmXL(const Line &l)const
 55     {
 56         if(a * l.b < b * l.a) return 1;
 57         else if(a * l.b > b * l.a) return -1;
 58         return 0;
 59     }
 60     bool paral(const Line &l)const
 61     {
 62         return a * l.b == b * l.a;
 63     }
 64     bool high(const Point &p)const
 65     {
 66         return p.x * a + p.y * b - c > eps;
 67     }
 68     Point CrossP(const Line &l)const
 69     {
 70         return Point((double)(c * l.b - l.c * b) / (a * l.b - l.a * b),
 71                      (double)(c * l.a - l.c * a) / (b * l.a - l.b * a));
 72     }
 73 };
 74 void HPC(Line l[], int n, Point p[], Line nl[], int &pm, int &lm)
 75 {
 76     int i, tn;
 77     sort(l, l + n);
 78     pm = lm = 0;
 79     nl[lm ++] = l[0];
 80     for(i = 1; i < n; ++ i)
 81     {
 82         if(lm && nl[lm - 1].paral(l[i])) continue;
 83         while(pm && !l[i].high(p[pm - 1]))
 84             -- pm, -- lm;
 85         p[pm ++] = nl[lm - 1].CrossP(l[i]);
 86         nl[lm ++] = l[i];
 87     }
 88     if(pm == 0) p[pm ++] = Point(0, (double)nl[0].c / nl[0].b);
 89 }
 90 int n, pn1, pn2, ln1, ln2;
 91 Line l[maxn], l1[maxn], l2[maxn];
 92 Point p1[maxn], p2[maxn];
 93 Point CrossPoint(Point a, Point b, Point c, Point d)
 94 {
 95     double u = a.cross(b, c), v = b.cross(a, d);
 96     return Point((c.x * v + d.x * u) / (u + v), (c.y * v + d.y * u) / (u + v));
 97 }
 98 double DisPtoP(Point a, Point b)
 99 {
100     return (a - b).dot(a - b);
101 }
102 
103 double DisPtoS(Point p, Point a, Point b, bool mk)
104 {
105     Point t = Point(p.x + a.y - b.y, p.y + b.x - a.x);
106     if(mk && (t - a).dot(b - a) > eps || t.cross(a, p) * t.cross(b, p) < -eps)
107         return DisPtoP(p, CrossPoint(t, p, a, b));
108     return min(DisPtoP(p, a), DisPtoP(p, b));
109 }
110 double DisStoS(Point a, Point b, Point c, Point d)
111 {
112     double ans = 1e30;
113     ans = min(ans, DisPtoS(a, c, d, 0));
114     ans = min(ans, DisPtoS(b, c, d, 0));
115     ans = min(ans, DisPtoS(c, a, b, 0));
116     ans = min(ans, DisPtoS(d, a, b, 0));
117     return ans;
118 }
119 int main()
120 {
121     int t, i, j, k;
122     double ans;
123     Point ts, te;
124     for(scanf("%d", &t); t --; )
125     {
126         ans = 1e30;
127         scanf("%d", &n);
128         for(i = 0; i < n; ++ i)
129         {
130             scanf("%lld%lld%lld", &l[i].a, &l[i].b, &l[i].c), l[i].c = -l[i].c;
131             if(l[i].b < 0) l[i].a = -l[i].a, l[i].b = -l[i].b, l[i].c = -l[i].c;
132         }
133         HPC(l, n, p1, l1, pn1, ln1);
134         for(i = 0; i < n; ++ i)
135             l[i].a = -l[i].a, l[i].c = -l[i].c;
136         HPC(l, n, p2, l2, pn2, ln2);
137         for(i = 0; i < ln2; ++ i)
138             l2[i].a = -l2[i].a, l2[i].c = -l2[i].c;
139         for(i = 0; i < pn2; ++ i)
140             p2[i].y = -p2[i].y;
141         for(i = 0, j = pn2 - 1; i + 1 < pn1 || j;)
142         {
143             if(j && (i == pn1 - 1 || l1[i + 1].CmXL(l2[j]) == 1))
144                 ans = min(ans, DisPtoS(p1[i], p2[j - 1], p2[j], 0)), -- j;
145             else if(i < pn1 - 1 && (!j || l1[i + 1].CmXL(l2[j]) == -1))
146                 ans = min(ans, DisPtoS(p2[j], p1[i], p1[i + 1], 0)), ++ i;
147             else
148             {
149                 ans = min(ans, DisStoS(p1[i], p1[i + 1], p2[j - 1], p2[j]));
150                 ++ i, -- j;
151             }
152         }
153         ts = Point(p2[0].x - 1, (l2[0].c - l2[0].a * (p2[0].x - 1)) / l2[0].b);
154         te = Point(p2[pn2 - 1].x + 1, (l2[pn2].c - l2[pn2].a * (p2[pn2 - 1].x + 1)) / l2[pn2].b);
155         for(i = 0; i < pn1; ++ i)
156         {
157             ans = min(ans, DisPtoS(p1[i], p2[0], ts, 1));
158             ans = min(ans, DisPtoS(p1[i], p2[pn2 - 1], te, 1));
159         }
160         ts = Point(p1[0].x - 1, (l1[0].c - l1[0].a * (p1[0].x - 1)) / l1[0].b);
161         te = Point(p1[pn1 - 1].x + 1, (l1[pn1].c - l1[pn1].a * (p1[pn1 - 1].x + 1)) / l1[pn1].b);
162         for(i = 0; i < pn2; ++ i)
163         {
164             ans = min(ans, DisPtoS(p2[i], p1[0], ts, 1));
165             ans = min(ans, DisPtoS(p2[i], p1[pn1 - 1], te, 1));
166         }
167         printf("%.6f\n", ans);
168     }
169     return 0;
170 }
posted @ 2012-08-27 21:00  CSGrandeur  阅读(404)  评论(0)  编辑  收藏  举报