[原创]【待补】华中农业大学第五届程序设计大赛 F Escape from the Darkness [解析几何]【数学】
2017-05-26 21:39:29 Tabris_ 阅读数：343
1204: Escape from the Darkness
Time Limit: 1 Sec Memory Limit: 1280 MB
Submit: 99 Solved: 3
Xiao Ming, a high school student, learnt blackbody radiation from the physics class. The black body on the book is indicated approximately by black body cavity as below:
from the small hole if total reflection occurs on the surface of the cavity.
Assuming in the two-dimensional coordinates, the center of the oval is at origin, and the vertexes of it is respectively (a, 0), (-a, 0), (0, b), (0, -b). There is a small hole at (a/2,sqrt(3)*b/2) (whose areas can be ignored). A beam of light (whose diameter can be ignored) shoot into the oval through the small hole. The direction of the light is (-1, 0). Assuming the light totally mirror reflects on the surface of the oval, the question is how many times can the light reflect before shooting out through the small hole. (If a point is away from the small hole less than 0.01, we think light shoot out from that point.)
The first line is a positive integer T (1 <= T <= 55) which indicates the numbers of the test cases. Then flowing next T lines, there are two positive integer a, b (1 <= b<= a<= 10) in each line as a group of cases.
The output of each case is one line with a positive integer which indicates the times of reflects.
The path of the light in the sample is looked as the picture shows. The light reflected five times.