mirror-reflection.md

Code

func gcd(a, b int) int {
	for a > 0 && b > 0 {
		if a == b {
			return a
		} else if a > b {
			a = a % b
		} else {
			b = b % a
		}
	}

	if a == 0 {
		return b
	} else {
		return a
	}

	return 0
}

func mirrorReflection(p int, q int) int {
	g := gcd(p, q)

	p /= g
	p %= 2

	q /= g
	q %= 2

	if p == 1 && q == 1 {
		return 1
	}

	if p != 1 {
		return 2
	}

	return 0

}

Solution in mind

• Implemented Mathematical solution as given here

• Instead of modelling the ray as a bouncing line, model it as a straight line through reflections of the room.

• For example, if p = 2, q = 1, then we can reflect the room horizontally, and draw a straight line from (0, 0) to (4, 2). The ray meets the receptor 2, which was reflected from (0, 2) to (4, 2).

• In general, the ray goes to the first integer point (kp, kq) where k is an integer, and kp and kq are multiples of p. Thus, the goal is just to find the smallest k for which kq is a multiple of p.

• The mathematical answer is k = p / gcd(p, q).