Shortest Path in Binary Matrix (BFS)

To solve the shortest clear path in a binary matrix, I would use Breadth-First Search, which is ideal for finding the minimum steps in an unweighted grid. First, I'd validate edge cases: if the matrix is empty, or if the start or end cell is blocked, I'd return -1 immediately. Next, I initialize a queue with the top-left coordinate and set the current path length to 1. I also maintain a visited structure, either by modifying the input matrix to mark visited cells as 0 or using a separate boolean matrix, to prevent cycles. Then, I process the queue level by level. For each cell, I explore all eight possible neighbors. If a neighbor is within bounds, is a clear path (value 1), and hasn't been visited, I add it to the queue with an incremented distance. This ensures we find the destination via the shortest route first. Once the bottom-right corner is dequeued, I return the accumulated distance. If the queue empties without reaching the target, it means no valid path exists, so I return -1. This approach runs in O(N^2) time and space, which is optimal since we may need to visit every cell once. This method aligns well with engineering standards at companies like LinkedIn where efficiency and correctness are paramount.