<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:

    bool isValid(int x, int y, int n, int m) {
        return x >= 0 && y >= 0 && x < n && y < m;
    }

    int shortestPathBinaryMatrix(vector<vector<int>>& grid) {
        queue<pair<pair<int, int>, int>> q;
        vector<int> dir_x = {1, 1, 1, -1, -1, -1, 0, 0};
        vector<int> dir_y = {-1, 0, 1, -1, 0, 1, 1, -1};
        set<pair<int, int>> visited;
        if (grid[0][0] == 0) {
            q.push({{0, 0}, 1});
        }
        while (!q.empty()) {
            auto top = q.front();
            if (top.first.first == grid.size() - 1 && top.first.second == grid[0].size() - 1) {
                return top.second;
            }
            q.pop();
            if (visited.find(top.first) != visited.end()) {
                continue;
            } 
            visited.insert(top.first);
            for (int i = 0; i < 8; i++) {
                int x = dir_x[i] + top.first.first;
                int y = dir_y[i] + top.first.second;
                if (isValid(x, y, grid.size(), grid[0].size()) && grid[x][y] == 0) {
                    q.push({{x, y}, top.second + 1});
                }
            }
        }
        return -1;
    }
};
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