LA 4973 Ardenia (3D Geometry + Simulation)

　　三维几何，题意是要求求出两条空间线段的距离。题目难度在于要求用有理数的形式输出，这就要求写一个有理数类了。
　　开始的时候写出来的有理数类就各种疯狂乱套，TLE的结果是显然的。后来发现，在计算距离前都是不用用到有理数类的，所以就将开始的部分有理数改成直接用long long。其实好像可以用int来做的，不过我的方法比较残暴，中间运算过程居然爆int了。所以就只好用long long了。
代码如下，附带debug以及各种强的数据：
  1 #include <cstdio>
  2 #include <iostream>
  3 #include <cstring>
  4 #include <algorithm>
  5 #include <cmath>
  6 
  7 using namespace std;
  8 
  9 template<class T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a;}
 10 template <class T> T sqr(T x) { return x * x;}
 11 typedef long long LL;
 12 struct Rat {
 13     LL a, b;
 14     Rat() {}
 15     Rat(LL x) { a = x, b = 1;}
 16     Rat(LL _a, LL _b) {
 17         LL GCD = gcd(_b, _a);
 18         a = _a / GCD, b = _b / GCD;
 19     }
 20     double val() { return (double) a / b;}
 21     bool operator < (Rat x) const { return a * x.b < b * x.a;}
 22     bool operator > (Rat x) const { return a * x.b > b * x.a;}
 23     bool operator == (Rat x) const { return a * x.b == b * x.a;}
 24     bool operator < (LL x) const { return Rat(a, b) < Rat(x);}
 25     bool operator > (LL x) const { return Rat(a, b) > Rat(x);}
 26     bool operator == (LL x) const { return Rat(a, b) == Rat(x);}
 27     Rat operator + (Rat x) {
 28         LL tb = b * x.b, ta = a * x.b + b * x.a;
 29         LL GCD = gcd(abs(tb), abs(ta));
 30         return Rat(ta / GCD, tb / GCD);
 31     }
 32     Rat operator - (Rat x) {
 33         LL tb = b * x.b, ta = a * x.b - b * x.a;
 34         LL GCD = gcd(abs(tb), abs(ta));
 35         return Rat(ta / GCD, tb / GCD);
 36     }
 37     Rat operator * (Rat x) {
 38         if (a * x.a == 0) return Rat(0, 1);
 39 //        if (b * x.b == 0) { puts("..."); while (1) ;}
 40         LL tb = b * x.b, ta = a * x.a;
 41         LL GCD = gcd(abs(tb), abs(ta));
 42         return Rat(ta / GCD, tb / GCD);
 43     }
 44     Rat operator / (Rat x) {
 45         if (a * x.b == 0) return Rat(0, 1);
 46 //        if (b * x.a == 0) { puts("!!!"); while (1) ;}
 47         LL GCD, tb = b * x.a, ta = a * x.b;
 48         GCD = gcd(abs(tb), abs(ta));
 49         return Rat(ta / GCD, tb / GCD);
 50     }
 51     void fix() {
 52         a = abs(a), b = abs(b);
 53         LL GCD = gcd(b, a);
 54         a /= GCD, b /= GCD;
 55     }
 56 } ;
 57 
 58 struct Point {
 59     LL x[3];
 60     Point operator + (Point a) {
 61         Point ret;
 62         for (int i = 0; i < 3; i++) ret.x[i] = x[i] + a.x[i];
 63         return ret;
 64     }
 65     Point operator - (Point a) {
 66         Point ret;
 67         for (int i = 0; i < 3; i++) ret.x[i] = x[i] - a.x[i];
 68         return ret;
 69     }
 70     Point operator * (LL p) {
 71         Point ret;
 72         for (int i = 0; i < 3; i++) ret.x[i] = x[i] * p;
 73         return ret;
 74     }
 75     bool operator == (Point a) const {
 76         for (int i = 0; i < 3; i++) if (!(x[i] == a.x[i])) return false;
 77         return true;
 78     }
 79     void print() {
 80         for (int i = 0; i < 3; i++) cout << x[i] << ' ';
 81         cout << endl;
 82     }
 83 } ;
 84 typedef Point Vec;
 85 
 86 struct Line {
 87     Point s, t;
 88     Line() {}
 89     Line (Point s, Point t) : s(s), t(t) {}
 90     Vec vec() { return t - s;}
 91 } ;
 92 typedef Line Seg;
 93 
 94 LL dotDet(Vec a, Vec b) {
 95     LL ret = 0;
 96     for (int i = 0; i < 3; i++) ret = ret + a.x[i] * b.x[i];
 97     return ret;
 98 }
 99 
100 Vec crossDet(Vec a, Vec b) {
101     Vec ret;
102     for (int i = 0; i < 3; i++) {
103         ret.x[i] = a.x[(i + 1) % 3] * b.x[(i + 2) % 3] - a.x[(i + 2) % 3] * b.x[(i + 1) % 3];
104     }
105     return ret;
106 }
107 
108 inline LL vecLen(Vec x) { return dotDet(x, x);}
109 inline bool parallel(Line a, Line b) { return vecLen(crossDet(a.vec(), b.vec())) == 0;}
110 inline bool onSeg(Point x, Point a, Point b) { return parallel(Line(a, x), Line(b, x)) && dotDet(a - x, b - x) < 0;}
111 inline bool onSeg(Point x, Seg s) { return onSeg(x, s.s, s.t);}
112 
113 Rat pt2Seg(Point p, Point a, Point b) {
114     if (a == b) return Rat(vecLen(p - a));
115     Vec v1 = b - a, v2 = p - a, v3 = p - b;
116     if (dotDet(v1, v2) < 0) return Rat(vecLen(v2));
117     else if (dotDet(v1, v3) > 0) return Rat(vecLen(v3));
118     else return Rat(vecLen(crossDet(v1, v2)), vecLen(v1));
119 }
120 inline Rat pt2Seg(Point p, Seg s) { return pt2Seg(p, s.s, s.t);}
121 inline Rat pt2Plane(Point p, Point p0, Vec n) { return Rat(sqr(dotDet(p - p0, n)), vecLen(n));}
122 inline bool segIntersect(Line a, Line b) {
123     Vec v1 = crossDet(a.s - b.s, a.t - b.s);
124     Vec v2 = crossDet(a.s - b.t, a.t - b.t);
125     Vec v3 = crossDet(b.s - a.s, b.t - a.s);
126     Vec v4 = crossDet(b.s - a.t, b.t - a.t);
127 //    v1.print();
128 //    v2.print();
129 //    cout << dotDet(v1, v2).val() << "= =" << endl;
130     return dotDet(v1, v2) < 0 && dotDet(v3, v4) < 0;
131 }//        cout << "same plane" << endl;
132 
133 pair<Rat, Rat> getIntersect(Line a, Line b) {
134     Point p = a.s, q = b.s;
135     Vec v = a.vec(), u = b.vec();
136     LL uv = dotDet(u, v), vv = dotDet(v, v), uu = dotDet(u, u);
137     LL pv = dotDet(p, v), qv = dotDet(q, v), pu = dotDet(p, u), qu = dotDet(q, u);
138     if (uv == 0) return make_pair(Rat(qv - pv, vv), Rat(pu - qu, uu));
139 //    if (vv == 0 || uv == 0 || uv / vv - uu / uv == 0) { puts("shit!"); while (1) ;}
140     Rat y = (Rat(pv - qv, vv) - Rat(pu - qu, uv)) / (Rat(uv, vv) - Rat(uu, uv));
141     Rat x = (y * uv - pv + qv) / vv;
142 //    cout << x.a << ' ' << x.b << ' ' << y.a << ' ' << y.b << endl;
143     return make_pair(x, y);
144 }
145 
146 void work(Point *pt) {
147     Line a = Line(pt[0], pt[1]);
148     Line b = Line(pt[2], pt[3]);
149     if (parallel(a, b)) {
150         if (onSeg(pt[0], b) || onSeg(pt[1], b)) { puts("0 1"); return ;}
151         if (onSeg(pt[2], a) || onSeg(pt[3], a)) { puts("0 1"); return ;}
152 //        cout << "parallel" << endl;
153         Rat tmp = min(min(pt2Seg(pt[0], b), pt2Seg(pt[1], b)), min(pt2Seg(pt[2], a), pt2Seg(pt[3], a)));
154         tmp.fix();
155         printf("%lld %lld\n", tmp.a, tmp.b);
156         return ;
157     }
158     Vec nor = crossDet(a.vec(), b.vec());
159     Rat ans = pt2Plane(pt[0], pt[2], nor);
160 //    cout << "~~~" << endl;
161     if (ans == 0) {
162 //        cout << "same plane" << endl;
163         if (segIntersect(a, b)) { puts("0 1"); return ;}
164         Rat tmp = min(min(pt2Seg(pt[0], b), pt2Seg(pt[1], b)), min(pt2Seg(pt[2], a), pt2Seg(pt[3], a)));
165         tmp.fix();
166         printf("%lld %lld\n", tmp.a, tmp.b);
167         return ;
168     } else {
169 //        cout << "diff plane" << endl;
170         pair<Rat, Rat> tmp = getIntersect(a, b);
171 //        cout << tmp.first.val() << "= =" << tmp.second.val() << endl;
172 //        cout << (tmp.first > 0) << endl;
173         if (tmp.first > 0 && tmp.first < 1 && tmp.second > 0 && tmp.second < 1) {
174 //            cout << "cross" << endl;
175             ans.fix();
176             printf("%lld %lld\n", ans.a, ans.b);
177         } else {
178 //            cout << "not cross" << endl;
179             Rat t = min(min(pt2Seg(pt[0], b), pt2Seg(pt[1], b)), min(pt2Seg(pt[2], a), pt2Seg(pt[3], a)));
180             t.fix();
181             printf("%lld %lld\n", t.a, t.b);
182         }
183     }
184 }
185 
186 int main() {
187 //    freopen("in", "r", stdin);
188 //    freopen("out", "w", stdout);
189     Point pt[4];
190     int T;
191     cin >> T;
192     while (T--) {
193         for (int i = 0; i < 4; i++) {
194             for (int j = 0; j < 3; j++) {
195                 scanf("%lld", &pt[i].x[j]);
196             }
197         }
198         work(pt);
199     }
200     return 0;
201 }
202 
203 /*
204 13
205 
206 -20 -20 -20 20 20 19
207 0 0 0 1 1 1
208 
209 -20 -20 -20 20 19 20
210 -20 -20 20 20 20 -20
211 
212 0 0 0 20 20 20
213 0 0 10 0 20 10
214 
215 0 0 0 1 1 1
216 2 3 4 1 2 2
217 
218 0 0 0 0 0 0
219 0 1 1 1 2 3
220 
221 0 0 0 10 10 10
222 11 12 13 10 11 11
223 
224 0 0 0 1 1 1
225 1 1 1 2 2 2
226 
227 1 0 0 0 1 0
228 1 1 0 2 2 0
229 
230 1 0 0 0 1 0
231 0 0 0 1 1 0
232 
233 0 0 0 0 0 20
234 20 0 10 0 20 10
235 
236 0 0 0 20 20 20
237 1 1 2 1 1 2
238 
239 0 0 0 20 20 20
240 0 20 20 0 20 20
241 
242 0 0 0 0 0 20
243 20 20 0 20 20 20
244 */
View Code
——written by Lyon
posted @ 2013-06-30 21:36 LyonLys 阅读(414) 评论(0) 编辑收藏举报
刷新页面返回顶部