Leetcode 490. The Maze (BFS)

Leetcode 490. The Maze (BFS)
Leetcode problem 490, "The Maze," involves finding if a ball can stop at a certain position within a maze given initial position and direction. Here's an analysis for solving it using Breadth-First Search (BFS):
Problem Summary:
- You're given a maze represented by a 2D array where `0` represents an empty space and `1` represents a wall.
- The ball starts at `start` and has a specific direction (`[dx, dy]`).
- The ball can roll in the given direction until it hits a wall.
- Determine if the ball can stop at the `destination` cell.
Approach Using BFS:
1. *Initialize a Queue:* Start with a queue that contains the initial position (`start`) and direction.
2. *Explore Neighbors:* While the queue is not empty:
- Dequeue a position and direction from the queue.
- Roll the ball in the given direction until it hits a wall or reaches an edge.
- Check if the final position matches the `destination`. If yes, return `true`.
- Otherwise, mark the current position as visited and enqueue the new position and direction if it's not visited.
3. *Return Result:* If no position at the destination is found after exploration, return `false`.
Time Complexity:
- In the worst-case scenario, the entire maze is traversed, leading to a time complexity of O(m * n), where 'm' is the number of rows and 'n' is the number of columns in the maze.
Space Complexity:
- The space complexity is O(m * n) to store the visited status of cells in the maze.
This BFS approach explores the maze by simulating the ball's movement from the starting position in the given direction until it reaches a wall or the destination. If it reaches the destination cell, it returns `true`; otherwise, it returns `false`.