<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 {
private:
    void djikstra(int sr, int sc, vector<vector<char>>& maze, vector<vector<int>>& dis){
        priority_queue<pair<int, pair<int, int>>, vector<pair<int, pair<int, int>>>, greater<pair<int, pair<int, int>>>> pq;
        pq.push({0, {sr, sc}});
        dis[sr][sc] = 0;
        int dr[] = {0, 1, 0, -1};
        int dc[] = {-1, 0, 1, 0};
        while(!pq.empty()){
            auto it = pq.top();
            pq.pop();
            int d = it.first;
            int r = it.second.first;
            int c = it.second.second;

            for(int i=0; i<4; i++){
                int nr = r+dr[i];
                int nc = c+dc[i];
                if(nr>=0 && nc>=0 && nr<maze.size() && nc<maze[0].size() && maze[nr][nc] == '.'){
                    if(dis[nr][nc]>d+1){
                        dis[nr][nc] = d+1;
                        pq.push({d+1, {nr, nc}});
                    }
                }
            }
        }
    }
public:
    int nearestExit(vector<vector<char>>& maze, vector<int>& entrance) {
        int n = maze.size();
        int m = maze[0].size();

        map<vector<int>, int> borders;
        for(int i=0; i<n; i++){
            for(int j=0; j<m; j++){
                if(i == 0 || i==n-1 || j==0 || j==m-1){
                    if(maze[i][j] == '.'){
                        borders[{i, j}]++;
                    }
                }
            }
        }
        int sr = entrance[0];
        int sc = entrance[1];
        if(maze[sr][sc] == '+') return -1;
        vector<vector<int>> dis(n, vector<int>(m, 1e9));
        djikstra(entrance[0], entrance[1], maze, dis);
        int mini = 1e9;
        for(int i=0; i<n; i++){
            for(int j=0; j<m; j++){
                if(borders.find({i, j})!=borders.end()){
                    if(dis[i][j]<1e9 && dis[i][j]!=0){
                        mini = min(mini, dis[i][j]);
                    }
                }
            }
        }
        return mini==1e9?-1:mini;
    }
};
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