Introduction

In this blog post, we will explore how to solve the LeetCode problem "858" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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

Explanation

Here's the breakdown of the approach, complexity, and the Python code:

• High-Level Approach:

  • Simulate the laser beam's path by reflecting it across the room's walls. Instead of actually reflecting, we conceptually extend the room infinitely in all directions, treating reflections as moving the laser in a straight line through the extended grid.
  • Find the smallest multiples of p (room width) and q (initial height) that align on the grid. These multiples reveal how many 'rooms' the beam traverses horizontally and vertically.
  • Determine the target receptor based on the parity (even/odd) of the number of rooms traversed horizontally and vertically.

• Complexity:

  • Runtime: O(log(p, q)) due to the Euclidean algorithm for GCD. Storage: O(1).

• Python Code:

Code

    def mirrorRefletion(p: int, q: int) -> int:    """
    Calculates the receptor number the laser ray meets first.

    Args:
        p: The length of the square room's walls.
        q: The distance from the 0th receptor where the ray first meets the east wall.

    Returns:
        The receptor number (0, 1, or 2) that the ray meets first.
    """
    import math

    def gcd(a, b):
        while b:
            a, b = b, a % b
        return a

    lcm = (p * q) // gcd(p, q)
    m = lcm // p
    n = lcm // q

    if m % 2 == 0 and n % 2 == 1:
        return 0
    elif m % 2 == 1 and n % 2 == 1:
        return 1
    else:
        return 2