mirror-reflection

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Algorithms

There is a special square room with mirrors on each of the four walls. Except for the southwest corner, there are receptors on each of the remaining corners, numbered <code>0</code>, <code>1</code>, and <code>2</code>.

The square room has walls of length <code>p</code>&nbsp;and a laser ray from the southwest corner first meets the east wall at a distance <code>q</code> from the <code>0th</code> receptor.

Given the two integers <code>p</code> and <code>q</code>, return the number of the receptor that the ray meets first.

The test cases are guaranteed so that the ray will meet a receptor eventually.

&nbsp;
Example 1:
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/18/reflection.png" style="width: 218px; height: 217px;" />
<pre>
Input: p = 2, q = 1
Output: 2
Explanation: The ray meets receptor 2 the first time it gets reflected back to the left wall.
</pre>

Example 2:

<pre>
Input: p = 3, q = 1
Output: 1
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= q &lt;= p &lt;= 1000</code></li>
</ul>

mirrorReflection

Mirror Reflection

Geometry

Math

Number Theory

有一个特殊的正方形房间，每面墙上都有一面镜子。除西南角以外，每个角落都放有一个接受器，编号为&nbsp;<code>0</code>，&nbsp;<code>1</code>，以及&nbsp;<code>2</code>。

正方形房间的墙壁长度为&nbsp;<code>p</code>，一束激光从西南角射出，首先会与东墙相遇，入射点到接收器 <code>0</code> 的距离为 <code>q</code> 。

返回光线最先遇到的接收器的编号（保证光线最终会遇到一个接收器）。
&nbsp;

示例 1：
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/18/reflection.png" style="width: 218px; height: 217px;" />
<pre>
输入：p = 2, q = 1
输出：2
解释：这条光线在第一次被反射回左边的墙时就遇到了接收器 2 。
</pre>

示例 2：

<pre>
输入：p = 3, q = 1
输入：1
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= q &lt;= p &lt;= 1000</code></li>
</ul>