Codeforces 982E Billiard 扩展欧几里得+思维

最新推荐文章于 2019-04-16 13:18:00 发布

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最新推荐文章于 2019-04-16 13:18:00 发布

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分类专栏： ACM-思维文章标签： codeforces acm 扩展欧几里得思维

本文链接：https://blog.youkuaiyun.com/weixin_39399748/article/details/81047493

本文介绍了一道Codeforces编程题目，涉及台球在矩形桌面上的运动轨迹。根据初始位置和速度，需要判断球是否会落入袋中及落入哪个袋。通过分析球的反射路径和应用扩展欧几里得算法，可以找到问题的解决方案。

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E. Billiard

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Consider a billiard table of rectangular size $n \times m$ with four pockets. Let's introduce a coordinate system with the origin at the lower left corner (see the picture).

$\text{[math]}$

There is one ball at the point $(x, y)$ currently. Max comes to the table and strikes the ball. The ball starts moving along a line that is parallel to one of the axes or that makes a $45^{\circ}$ angle with them. We will assume that:

the angles between the directions of the ball before and after a collision with a side are equal,
the ball moves indefinitely long, it only stops when it falls into a pocket,
the ball can be considered as a point, it falls into a pocket if and only if its coordinates coincide with one of the pockets,
initially the ball is not in a pocket.

Note that the ball can move along some side, in this case the ball will just fall into the pocket at the end of the side.

Your task is to determine whether the ball will fall into a pocket eventually, and if yes, which of the four pockets it will be.

Input

The only line contains $6$