Leetcode 858. Mirror Reflection

Problem

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.

Given the two integers p and q, 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.

Algorithm

Number theory. The final position is the LCM of p and q. Unfold the mirror and a grid will form with all the points alternating. Use the remainder to determine the final receptor.

Code

class Solution:
    def mirrorReflection(self, p: int, q: int) -> int:
        def gcd(a, b):
            r = a % b
            if not r:
                return b
            return gcd(b, r)
        
        id = [[-1, 0], [2, 1]]
        lcm = p * q // gcd(p, q)
        x = lcm // q % 2
        y = lcm // p % 2
        return id[y][x]
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