Nearest Exit from Entrance in Maze - Solution & Explanation

In this approach, we use the Breadth-First Search (BFS) algorithm to explore the maze. BFS is suitable because it explores nodes layer by layer, ensuring that the shortest path is found. We initialize a queue with the entrance cell and explore its neighbors (up, down, left, right). If a neighbor is an unvisited empty cell and is on the boundary (except the entrance), it can be considered as an exit.

Each time we explore a cell, we mark it as visited by changing its state to '+'. This prevents revisiting nodes, which ensures that we won't traverse the same path multiple times. We keep track of steps taken from the entrance to the current cell, and if we reach an exit, we return the number of steps. If the queue is exhausted without finding an exit, we return -1.

This implementation uses a queue to facilitate the BFS. It starts by enqueuing the entrance and marking it as visited by changing it to '+'. Four possible movement directions are considered (right, down, left, up). As each cell is processed, its unvisited neighbors are enqueued. If a neighbor is a border cell but not the entrance, it is considered the closest exit, and the steps taken are returned.

In this approach, we use the Depth-First Search (DFS) algorithm to explore the maze. DFS might not be as efficient as BFS for finding the shortest path, but for educational purposes, it demonstrates another way to traverse the maze. We recursively explore each path, marking cells as visited and backtracking when dead-ends or exits are encountered.

This approach keeps a global minimum step count, updating it whenever an exit (that isn't the entrance) is found. Through recursive calls, each possible path is explored until all directions are exhausted. The main objective is to identify the closest exit with respect to steps taken from the entrance cell.

This C implementation of DFS explores each cell using recursive function calls. Directions are processed one by one, checking validity and boundary conditions for a potential exit. Dead-ends lead to recursive backtracking, unmarking visited cells to ensure every path combination is checked. The shortest path's steps are stored in a global variable, updated when an exit is found.