Mirror Reflection — LeetCode 858 Python Solution

The 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.

Example

Input

p = 2, q = 1

Output

2

Explanation

The ray meets receptor 2 the first time it gets reflected back to the left wall.

Python solution

class Solution:
    def mirrorReflection(self, p: int, q: int) -> int:
        g = gcd(p, q)
        p = (p // g) % 2
        q = (q // g) % 2
        if p == 1 and q == 1:
            return 1
        return 0 if p == 1 else 2

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 858. Mirror Reflection is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math, Number Theory and Geometry.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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