858. Mirror Reflection

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 0, 1, and 2.

The square room has walls of length p, and a laser ray from the southwest corner first meets the east wall at a distance q from the 0th receptor.

Return the number of the receptor that the ray meets first.  (It is guaranteed that the ray will meet a receptor eventually.)

 

Example 1:

Input: p = 2, q = 1
Output: 2
Explanation: The ray meets receptor 2 the first time it gets reflected back to the left wall.

Note:

1. 1 <= p <= 1000
2. 0 <= q <= p

思路：数学解法肯定是有的，但是想不到；直接模拟又太烦了；其实只需要一个维度（离目标出口0或1或2的竖直距离）描述即可

class Solution:
    def mirrorReflection(self, p, q):
        """
        :type p: int
        :type q: int
        :rtype: int
        """
        verticalDistanceToTarget = p
        up = right = True
        while 1:
            verticalDistanceToTarget -= q
            
            if verticalDistanceToTarget==0:
                if up: return 1 if right else 2
                elif right: return 0
            
            if verticalDistanceToTarget<0:
                verticalDistanceToTarget = p - (-verticalDistanceToTarget)
                up = not up
            right = not right
            
s=Solution()
print(s.mirrorReflection(2, 1))