0858.go

// Source: https://leetcode.com/problems/mirror-reflection
// Title: Mirror Reflection
// Difficulty: Medium
// Author: Mu Yang <http://muyang.pro>

////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
// 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.
//
// Example 1:
//
//   https://s3-lc-upload.s3.amazonaws.com/uploads/2018/06/18/reflection.png
//
//   Input: p = 2, q = 1
//   Output: 2
//   Explanation: The ray meets receptor 2 the first time it gets reflected back to the left wall.
//
// Example 2:
//
//   Input: p = 3, q = 1
//   Output: 1
//
// Constraints:
//
//   1 <= q <= p <= 1000
//
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

package main

// Find receptor by GCD of p and q
func mirrorReflection(p int, q int) int {
	gcd := _gcd(p, q)

	x := p / gcd
	y := q / gcd

	if y%2 == 0 {
		return 0
	}
	if x%2 == 0 {
		return 2
	}
	return 1
}

func _gcd(a int, b int) int {
	for b != 0 {
		a, b = b, a%b
	}
	return a
}