[LeetCode] Nearest Exit from Entrance in Maze

Problem: You are given an m x n matrix maze (0-indexed) with empty cells (represented as '.') and walls (represented as '+'). You are also given the entrance of the maze, where entrance = [entrancerow, entrancecol] denotes the row and column of the cell you are initially standing at.

In one step, you can move one cell up, down, left, or right. You cannot step into a cell with a wall, and you cannot step outside the maze. Your goal is to find the nearest exit from the entrance. An exit is defined as an empty cell that is at the border of the maze. The entrance does not count as an exit.

Return the number of steps in the shortest path from the entrance to the nearest exit, or -1 if no such path exists.

Example:

Input: maze = [["+","+",".","+"],[".",".",".","+"],["+","+","+","."]], entrance = [1,2]
Output: 1
Explanation: There are 3 exits in this maze at [1,0], [0,2], and [2,3].
Initially, you are at the entrance cell [1,2].
- You can reach [1,0] by moving 2 steps left.
- You can reach [0,2] by moving 1 step up.
It is impossible to reach [2,3] from the entrance.
Thus, the nearest exit is [0,2], which is 1 step away.

Input: maze = [["+","+","+"],[".",".","."],["+","+","+"]], entrance = [1,0]
Output: 2
Explanation: There is 1 exit in this maze at [1,2].
[1,0] does not count as an exit since it is the entrance cell.
Initially, you are at the entrance cell [1,0].
- You can reach [1,2] by moving 2 steps right.
Thus, the nearest exit is [1,2], which is 2 steps away.

Input: maze = [[".","+"]], entrance = [0,0]
Output: -1
Explanation: There are no exits in this maze.

Approach: This is clearly a Graph BFS problem where a cell is connected to another cell if the other cell is one of top, bottom, left or right cell of the current cell. We just need to find the shortest path from the given cell 'entrance' to any empty cell (contains '.') on the boundary. To get this path we can use BFS as there is same weight here on every edge.

That's all!

Implementation in C#:

    public int NearestExit(char[][] maze, int[] entrance)

    {

        int rows = maze?.Length ?? 0;

        if (rows == 0)

        {

            return -1;

        }

        int cols = maze[0].Length;

        var queue = new Queue<int[]>();

        maze[entrance[0]][entrance[1]] = '+';

        this.AddValidNeighboursToQueue(maze, queue, entrance[0], entrance[1]);

        int steps = 1;

        while (queue.Count > 0)

        {

            int size = queue.Count;

            for (int i = 0; i < size; ++i)

            {

                var cell = queue.Dequeue();

                if (this.IsBoundaryCell(cell, rows, cols))

                {

                    return steps;

                }

                this.AddValidNeighboursToQueue(maze, queue, cell[0], cell[1]);

            }

            ++steps;

        }

        return -1;

    }

    private bool IsBoundaryCell(int[] cell, int rows, int cols)

    {

        return cell[0] == 0 ||

               cell[0] == rows - 1 ||

               cell[1] == 0 ||

               cell[1] == cols - 1;

    }

    private void AddValidNeighboursToQueue(char[][] maze,

                                           Queue<int[]> queue,

                                           int row,

                                           int col)

    {

        // Left neighbour

        if (this.IsValidAndEmptyCell(maze, row, col - 1))

        {

            maze[row][col - 1] = '+';

            queue.Enqueue(new int[] {row, col - 1});

        }

        // Right neighbour

        if (this.IsValidAndEmptyCell(maze, row, col + 1))

        {

            maze[row][col + 1] = '+';

            queue.Enqueue(new int[] {row, col + 1});

        }

        // Top neighbour

        if (this.IsValidAndEmptyCell(maze, row - 1, col))

        {

            maze[row - 1][col] = '+';

            queue.Enqueue(new int[] {row - 1, col});

        }

        // Bottom neighbour

        if (this.IsValidAndEmptyCell(maze, row + 1, col))

        {

            maze[row + 1][col] = '+';

            queue.Enqueue(new int[] {row + 1, col});

        }

    }

    private bool IsValidAndEmptyCell(char[][] maze, int row, int col)

    {

        return row >= 0 &&

               row < maze.Length &&

               col >= 0 &&

               col < maze[0].Length &&

               maze[row][col] == '.';

    }

Complexity: O(n)