<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(grid[0][0] == 1 or grid[n-1][n-1] == 1){ return -1;}
        vector<vector<int>> dist(n,vector<int>(n,1e9+2));
        set<vector<int>> st;
        dist[0][0] = 0;
        st.insert({0,0,0});
        int deltarow[8] = {-1,-1,0,1,1,1,0,-1};
        int deltacol[8] = {0,1,1,1,0,-1,-1,-1};
        while(!st.empty()){
            auto it = *(st.begin());
            int x = it[0];
            int y = it[1];
            int currdist = it[2];
            st.erase(it);
            for(int i = 0 ; i < 8 ; i++){
                int xnew = x+deltarow[i];
                int ynew = y+deltacol[i];
                if( xnew >= 0 and xnew <= n-1 and ynew >= 0 and ynew <= n-1 and grid[xnew][ynew] == 0){
                    if(dist[xnew][ynew] > currdist + 1){
                        dist[xnew][ynew] = currdist+1;
                        st.insert({xnew,ynew,dist[xnew][ynew]});
                    }
                }
            }

        }
        if(dist[n-1][n-1] == 1e9+2){
            return -1;
        }
        return dist[n-1][n-1]+1;

    }
};
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