Mirror reflection

Math Geometry Number Theory

61.9% acceptance

Feb 22, 2026

1151

2561

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.

Solution

Rust

Time O(2^n)

Space O(n)

LeetCode

solution.rs

/*
 * 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:
 * 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
 */

impl Solution {
  pub fn mirror_reflection(p: i32, q: i32) -> i32 {
    fn gcd(a: i32, b: i32) -> i32 { if b == 0 { a } else { gcd(b, a % b) } }
    let g = gcd(p, q);
    let m = p / g; // number of "bounces" in terms of p
    let n = q / g; // number of "bounces" in terms of q
    if n % 2 == 0 { 0 }
    else if m % 2 == 0 { 2 }
    else { 1 }
  }
}