1 #include<iostream>
2 #include<cstdio>
3 #include<cstring>
4 #include<queue>
5 #include<map>
6 #include<set>
7 #include<cmath>
8 using namespace std;
9 typedef long long LL;
10 const double eps = 1e-8;
11 int sgn(double x) {
12 if(fabs(x) < eps) return 0;
13 if(x < 0) return -1;
14 else return 1;
15 }
16 struct Point {
17 double x, y;
18 Point(double x = 0, double y = 0) : x(x), y(y) {}
19 Point operator - (const Point& t) const {
20 return Point(x - t.x, y - t.y);
21 }
22 double operator ^ (const Point& t) const {
23 return x * t.y - y * t.x;
24 }
25 double operator * (const Point& t) const {
26 return x * t.x + y * t.y;
27 }
28 Point operator * (const double& k) const {
29 return Point(x * k, y * k);
30 }
31 Point operator / (const double& k) const {
32 return Point(x / k, y / k);
33 }
34 Point operator + (const Point& t) const {
35 return Point(x + t.x, y + t.y);
36 }
37 double distance(Point p) {
38 return hypot(x - p.x, y - p.y);
39 }
40 double len() {
41 return hypot(x, y);
42 }
43 double len2() {
44 return x * x + y * y;
45 }
46 Point trunc(double r) {
47 double l = len();
48 if(!sgn(l)) return *this;
49 r /= l;
50 return Point(x * r, y * r);
51 }
52 };
53 struct Line {
54 Point s, e;
55 Line() {}
56 Line(Point s, Point e) {
57 this->s = s; this->e = e;
58 }
59 double length() {
60 return sqrt((s.x - e.x) * (s.x - e.x) + (s.y - e.y) * (s.y - e.y));
61 }
62 int relation(Point p) {
63 int c = sgn((p - s) ^ (e - s));
64 if(c < 0) return 1;
65 else if(c > 0) return 2;
66 else return 3;
67 }
68 double dispointtoline(Point p) {
69 return fabs((p - s) ^ (e - s)) / length();
70 }
71 double dispointtoseg(Point p) {
72 if(sgn((p - s) * (e - s)) < 0 || sgn((p - e) * (s - e)) < 0)
73 return min(p.distance(s), p.distance(e));
74 return dispointtoline(p);
75 }
76 Point lineprog(Point p) {
77 return s + (((e - s) * ((e - s) * (p - s))) / ((e - s).len2()));
78 }
79 Point symmetrypoint(Point p) {
80 Point q = lineprog(p);
81 return Point(2 * q.x - p.x, 2 * q.y - p.y);
82 }
83 };
84 struct Circle {
85 Point p;
86 double r;
87 Circle(double x, double y, double r) {
88 p = Point(x, y);
89 this->r = r;
90 }
91 int relationline(Line v) {
92 double dst = v.dispointtoline(p);
93 if(sgn(dst - r) < 0) return 2;
94 else if(sgn(dst - r) == 0) return 1;
95 else return 0;
96 }
97 int relationseg(Line v) {
98 double dst = v.dispointtoseg(p);
99 if(sgn(dst - r) < 0) return 2;
100 else if(sgn(dst - r) == 0) return 1;
101 else return 0;
102 }
103 int pointcrossline(Line v, Point& p1, Point& p2) {
104 if(!(*this).relationline(v)) return 0;
105 Point a = v.lineprog(p);
106 double d = v.dispointtoline(p);
107 d = sqrt(r * r - d * d);
108 if(sgn(d) == 0) {
109 p1 = a; p2 = a;
110 return 1;
111 }
112 p1 = a + (v.e - v.s).trunc(d);
113 p2 = a - (v.e - v.s).trunc(d);
114 return 2;
115 }
116 };
117 int main() {
118 int T; scanf("%d", &T);
119 int ca(1);
120 while(T--) {
121 int ox, oy, r;
122 int ax, ay, vx, vy;
123 int bx, by;
124 scanf("%d%d%d", &ox, &oy, &r);
125 scanf("%d%d%d%d", &ax, &ay, &vx, &vy);
126 scanf("%d%d", &bx, &by);
127 Line l(Point(ax, ay), Point(ax + vx, ay + vy));
128 Circle c(ox, oy, r);
129 Point d(bx, by);
130 Line t(Point(ax, ay), Point(bx, by));
131 if(l.relation(d) == 3 && c.relationseg(t) <= 1 && sgn(Point(bx - ax, by - ay) ^ Point(vx, vy)) == 0) printf("Case #%d: Yes\n", ca++);
132 else {
133 Point a, b;
134 if(c.pointcrossline(l, a, b) != 2) printf("Case #%d: No\n", ca++);
135 else {
136 Point cut;
137 if(a.distance(Point(ax, ay)) > b.distance(Point(ax, ay))) cut = b;
138 else cut = a;
139 Line mid(cut, c.p);
140 Point en = mid.symmetrypoint(Point(ax, ay));
141 Line aft(cut, en);
142 if(aft.e.distance(d) > aft.s.distance(d)) swap(aft.s, aft.e);
143 if(sgn((aft.e - aft.s) ^ Point(d.x - cut.x, d.y - cut.y)) == 0) printf("Case #%d: Yes\n", ca++);
144 else printf("Case #%d: No\n", ca++);
145 }
146 }
147 }
148 return 0;
149 }
醉了，，现场读错题了，分反弹和不反弹两种情况讨论就好了，加点特判
时间： 2024-11-18 00:24:37