<p>You are given an <code>m x n</code> matrix <code>maze</code> (<strong>0-indexed</strong>) with empty cells (represented as <code>&#39;.&#39;</code>) and walls (represented as <code>&#39;+&#39;</code>). You are also given the <code>entrance</code> of the maze, where <code>entrance = [entrance<sub>row</sub>, entrance<sub>col</sub>]</code> denotes the row and column of the cell you are initially standing at.</p>

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

<p>Return <em>the <strong>number of steps</strong> in the shortest path from the </em><code>entrance</code><em> to the nearest exit, or </em><code>-1</code><em> if no such path exists</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/04/nearest1-grid.jpg" style="width: 333px; height: 253px;" />
<pre>
<strong>Input:</strong> maze = [[&quot;+&quot;,&quot;+&quot;,&quot;.&quot;,&quot;+&quot;],[&quot;.&quot;,&quot;.&quot;,&quot;.&quot;,&quot;+&quot;],[&quot;+&quot;,&quot;+&quot;,&quot;+&quot;,&quot;.&quot;]], entrance = [1,2]
<strong>Output:</strong> 1
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/04/nearesr2-grid.jpg" style="width: 253px; height: 253px;" />
<pre>
<strong>Input:</strong> maze = [[&quot;+&quot;,&quot;+&quot;,&quot;+&quot;],[&quot;.&quot;,&quot;.&quot;,&quot;.&quot;],[&quot;+&quot;,&quot;+&quot;,&quot;+&quot;]], entrance = [1,0]
<strong>Output:</strong> 2
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/04/nearest3-grid.jpg" style="width: 173px; height: 93px;" />
<pre>
<strong>Input:</strong> maze = [[&quot;.&quot;,&quot;+&quot;]], entrance = [0,0]
<strong>Output:</strong> -1
<strong>Explanation:</strong> There are no exits in this maze.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>maze.length == m</code></li>
	<li><code>maze[i].length == n</code></li>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
	<li><code>maze[i][j]</code> is either <code>&#39;.&#39;</code> or <code>&#39;+&#39;</code>.</li>
	<li><code>entrance.length == 2</code></li>
	<li><code>0 &lt;= entrance<sub>row</sub> &lt; m</code></li>
	<li><code>0 &lt;= entrance<sub>col</sub> &lt; n</code></li>
	<li><code>entrance</code> will always be an empty cell.</li>
</ul>

class Solution {
public:
    int nearestExit(vector<vector<char>>& maze, vector<int>& entrance) {
        vector<vector<int>> dist(maze.size(), vector<int>(maze[0].size(), -1));
        queue<vector<int>> q;
        dist[entrance[0]][entrance[1]] = 0;
        q.push(entrance);
        int d = BFS(entrance, maze, dist, q);
        return d;
    }

private:
    int BFS(vector<int>& entrance, vector<vector<char>>& maze, vector<vector<int>>& dist, queue<vector<int>>& q) {

        while (!q.empty()) {
            vector<int> v = q.front();
            q.pop();
            if (isExit(v, maze, entrance)) {
                return dist[v[0]][v[1]];
            }

            vector<int> up{v[0] - 1, v[1]};
            vector<int> down{v[0] + 1, v[1]};
            vector<int> left{v[0], v[1] - 1};
            vector<int> right{v[0], v[1] + 1};

            int d = dist[v[0]][v[1]];

            if (up[0] >= 0 && maze[up[0]][up[1]] == '.' && dist[up[0]][up[1]] == -1) {
                dist[up[0]][up[1]] = d + 1;
                q.push(up);
            }

            if (down[0] < maze.size() && maze[down[0]][down[1]] == '.' && dist[down[0]][down[1]] == -1) {
                dist[down[0]][down[1]] = d + 1;
                q.push(down);
            }

            if (left[1] >= 0 && maze[left[0]][left[1]] == '.' && dist[left[0]][left[1]] == -1) {
                dist[left[0]][left[1]] = d + 1;
                q.push(left);
            }

            if (right[1] < maze[0].size() && maze[right[0]][right[1]] == '.' && dist[right[0]][right[1]] == -1) {
                dist[right[0]][right[1]] = d + 1;
                q.push(right);
            }

        }

        return -1;

    }

    bool isExit(vector<int>& u, vector<vector<char>>& maze, vector<int>& entrance) {
        if (u == entrance) {
            return false;
        }
        else if (u[0] == 0 || u[1] == 0 || u[0] == maze.size() - 1|| u[1] == maze[0].size() - 1) {
            return true;
        }
        else {
            return false;
        }
    }
};
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