UVa 10387 Billiard：计算几何&反射

UVa 10387 Billiard：计算几何&反射2014-07-29 csdn博客 synapse710387 - Billiard

Time limit: 3.000 seconds

http://uva.onlinejudge.org/index.php？option=com_onlinejudge&Itemid=8&category=101&page=show_problem&problem=1328

In a billiard table with horizontal side a inches and vertical side b inches, a ball is launched from the middle of the table. After s > 0 seconds the ball returns to the point from which it was launched, after having made m bounces off the vertical sides and n bounces off the horizontal sides of the table. Find the launching angle A （measured from the horizontal）, which will be between 0 and 90 degrees inclusive, and the initial velocity of the ball.

Assume that the collisions with a side are elastic （no energy loss）, and thus the velocity component of the ball parallel to each side remains unchanged. Also, assume the ball has a radius of zero. Remember that, unlike pool tables, billiard tables have no pockets.

Input

Input consists of a sequence of lines, each containing five nonnegative integers separated by whitespace. The five numbers are: a, b, s, m, and n, respectively. All numbers are positive integers not greater than 10000.

Input is terminated by a line containing five zeroes.

Output

For each input line except the last, output a line containing two real numbers （accurate to two decimal places） separated by a single space. The first number is the measure of the angle A in degrees and the second is the velocity of the ball measured in inches per second, according to the description above.

Sample Input

100 100 1 1 1200 100 5 3 4201 132 48 1900 1560 0 0 0 0

Sample Output

45.00 141.4233.69 144.223.09 7967.81

思路：小球的运动轨迹可以转化为一条直线。如何转化？

如上图所示，想象小球在一个无限扩展的台球面上运动，即把小球的运动轨迹“拼接”起来。

这样我们就得到了一条直线，后面的就好算了。

完整代码：

/*0.018s*/#include<cstdio>#include<cmath>const double one_radian = 90.0 / acos（0）;///1弧度对应的角度值int main（）{int a, b, s, m, n;while （scanf（"%d%d%d%d%d", &a, &b, &s, &m, &n）, a）printf（"%.2f %.2f
", one_radian * atan（（double）b * n / a / m）, hypot（b * n, a * m） / s）;return 0;}