<p>Given an <code>n x n</code> binary matrix <code>grid</code>, return <em>the length of the shortest <strong>clear path</strong> in the matrix</em>. If there is no clear path, return <code>-1</code>.</p>

<p>A <strong>clear path</strong> in a binary matrix is a path from the <strong>top-left</strong> cell (i.e., <code>(0, 0)</code>) to the <strong>bottom-right</strong> cell (i.e., <code>(n - 1, n - 1)</code>) such that:</p>

<ul>
	<li>All the visited cells of the path are <code>0</code>.</li>
	<li>All the adjacent cells of the path are <strong>8-directionally</strong> connected (i.e., they are different and they share an edge or a corner).</li>
</ul>

<p>The <strong>length of a clear path</strong> is the number of visited cells of this path.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/18/example1_1.png" style="width: 500px; height: 234px;" />
<pre>
<strong>Input:</strong> grid = [[0,1],[1,0]]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/02/18/example2_1.png" style="height: 216px; width: 500px;" />
<pre>
<strong>Input:</strong> grid = [[0,0,0],[1,1,0],[1,1,0]]
<strong>Output:</strong> 4
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,0,0],[1,1,0],[1,1,0]]
<strong>Output:</strong> -1
</pre>

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

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 100</code></li>
	<li><code>grid[i][j] is 0 or 1</code></li>
</ul>

class Solution {
public:
    int shortestPathBinaryMatrix(vector<vector<int>>& grid) {
        int n=grid.size();
        if(n==1 && grid[0][0]==0) return 1;
        if(grid[0][0]!=0 || grid[n-1][n-1]==1) return -1;
        vector<vector<int>> mov = {{0,1},{1,0},{-1,0},{0,-1},{-1,-1},{1,1},{-1,1},{1,-1}}; 
        // queue<pair<int,pair<int,int>>> pq;
        set<pair<int,pair<int,int>>> pq;

        pq.insert({0,{0,0}});
        vector<vector<int>> dist(n, vector<int>(n, INT_MAX));
        dist[0][0]=0;
        while(!pq.empty()){
            auto t = *(pq.begin());
            pq.erase(t);
            int w=t.first;
            int j=t.second.second;
            int i=t.second.first;
            // if(w>dist[i][j]) continue;
            // cout << i << " " << j << " " << w << endl;
            for(int x=0; x<8; x++){
                if(i+mov[x][0]<n && i+mov[x][0]>-1 && j+mov[x][1]<n && j+mov[x][1]>-1 && grid[i+mov[x][0]][j+mov[x][1]]==0){
                    if(dist[i+mov[x][0]][j+mov[x][1]]>w+1){
                        if(i+mov[x][0]==n-1 && j+mov[x][1]==n-1) return w+2;
                        if(dist[i+mov[x][0]][j+mov[x][1]]!=INT_MAX) pq.erase({dist[i+mov[x][0]][j+mov[x][1]],{i+mov[x][0], j+mov[x][1]}});
                        dist[i][j]=w+1;
                        pq.insert({w+1, {i+mov[x][0], j+mov[x][1]}});
                    }
                }
            }
        }
        return -1;
    }
};
49141