<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]!=0 || grid[n-1][n-1]!=0) return -1;
        map<pair<int,int>,int>mpp;
        int cnt=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==0){
                    mpp[{i,j}]=cnt;
                    cnt++;
                }
            }
        }

        // for(auto it:mpp) cout<<it.first.first<<" "<<it.first.second<<"-> "<<it.second<<endl;
        // cout<<endl;

        vector<vector<int>>adj(cnt);
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==0){
                    if(i+1<n && grid[i+1][j]==0) adj[mpp[{i,j}]].push_back(mpp[{i+1,j}]);
                    if(i-1>=0 && grid[i-1][j]==0) adj[mpp[{i,j}]].push_back(mpp[{i-1,j}]);
                    if(j+1<n && grid[i][j+1]==0) adj[mpp[{i,j}]].push_back(mpp[{i,j+1}]);
                    if(j-1>=0 && grid[i][j-1]==0) adj[mpp[{i,j}]].push_back(mpp[{i,j-1}]);

                    if(i+1<n && j+1<n && grid[i+1][j+1]==0) adj[mpp[{i,j}]].push_back(mpp[{i+1,j+1}]);
                    if(i-1>=0 && j+1<n && grid[i-1][j+1]==0) adj[mpp[{i,j}]].push_back(mpp[{i-1,j+1}]);
                    if(j-1>=0 && i-1>=0 && grid[i-1][j-1]==0) adj[mpp[{i,j}]].push_back(mpp[{i-1,j-1}]);
                    if(j-1>=0 && i+1<n && grid[i+1][j-1]==0) adj[mpp[{i,j}]].push_back(mpp[{i+1,j-1}]);
                }
            }
        }

        // for(int i=0;i<adj.size();i++){
        //     cout<<i<<"-> ";
        //     for(int j=0;j<adj[i].size();j++){
        //         cout<<adj[i][j]<<" ";
        //     }
        //     cout<<endl;
        // }

        queue<int>q;
        vector<int>ans(cnt,INT_MAX);
        ans[0]=0;
        q.push(0);
        while(!q.empty()){
            int node=q.front();
            q.pop();
            for(auto it:adj[node]){
                if(ans[node]+1<ans[it]){
                    ans[it]=ans[node]+1;
                    q.push(it);
                }
            }
        }

        // cout<<endl;
        // for(int i=0;i<ans.size();i++) cout<<ans[i]<<" ";
        // cout<<endl;
        if(ans[cnt-1]==INT_MAX) return -1;
        return ans[cnt-1]+1;
    }
};
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