<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();

        vector<vector<int>> dist(n, vector<int>(n, 1e9));

        set<vector<int>> st;
        if(grid[0][0] == 0) {
            dist[0][0] = 1;
            st.insert({1, 0, 0});
        }
        vector<int> movements;
        movements = {1, -1, 0};

        auto is_valid = [&](int i, int j, int d){
            int ans = 0;
            if(i >= 0 and i < n and j >= 0 and j < n and dist[i][j] > d + 1 and grid[i][j] == 0) ans = 1;
            return ans;
        };
        while(st.size()){
            auto vec = *st.begin();
            st.erase(st.begin());
            int d = vec[0];
            printf("%d,", d);
            int i = vec[1];
            int j = vec[2];
            for(auto i1 : movements){
                for(auto j1 : movements){
                    if(j1 == 0 and i1 == 0) continue;
                    if(is_valid(i+i1, j+j1, d)){
                        dist[i+i1][j+j1] = d + 1;
                        st.insert({d+1, i+i1, j+j1});
                    }
                }
            }

            // if(j+1 < n and dist[i][j+1] > d + 1 and grid[i][j+1] == 0){
            //     dist[i][j+1] = d + 1;
            //     st.insert({d+1, i, j+1});
            // }
            // if(j-1 >= 0 and dist[i][j-1] > d + 1 and grid[i][j-1] == 0){
            //     dist[i][j-1] = d + 1;
            //     st.insert({d+1, i, j-1});
            // }
            // if(i+1<n and dist[i+1][j] > d+1 and grid[i+1][j] == 0){
            //     dist[i+1][j] = d + 1;
            //     st.insert({d+1, i+1, j});
            // }
            // if(i-1 >= 0 and dist[i-1][j] > d+1 and grid[i-1][j] == 0){
            //     dist[i-1][j] = d + 1;
            //     st.insert({d+1, i-1, j});
            // }
            
            // if(i+1 < n and j + 1 < n and dist[i+1][j+1] > d+1 and grid[i+1][j+1] == 0){
            //     dist[i+1][j+1] = d+1;
            //     st.insert({d+1, i+1, j+1});
            // }

            // if(i-1>=0 and j+1<n and dist[i-1][j+1] > d + 1 and grid[i-1][j+1] == 0){
            //     dist[i-1][j+1] = d + 1;
            //     st.insert({d+1, i-1, j+1});
            // }

            // if(i-1>=0 and j-1>=0 and dist[i-1][j-1] > d + 1 and grid[i-1][j-1] == 0){
            //     dist[i-1][j-1] = d + 1;
            //     st.insert({d+1, i-1, j-1});
            // }

            // if(i+1< n and j-1>=0 and dist[i+1][j-1] > d + 1 and grid[i+1][j-1] == 0){
            //     dist[i+1][j-1] = d + 1;
            //     st.insert({d+1, i+1, j-1});
            // }
        }


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