<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>


using node = std::pair<std::pair<int, int>, int>;

struct cmp
{
    bool operator()(node n1, node n2)
    {
        return n1.second > n2.second;
    }
};

std::vector<std::pair<int, int>> getCandidate(int width, int x, int y)
{
    std::vector<std::pair<int, int>> Candidate;
    if(x != 0)
    {
        Candidate.push_back(std::make_pair(x-1, y));
        if(y != 0)
        {
            Candidate.push_back(std::make_pair(x-1, y-1));
        }
        if(y < width-1)
        {
            Candidate.push_back(std::make_pair(x-1, y+1));
        }
    }

    if(x < width - 1)
    {
        Candidate.push_back(std::make_pair(x+1, y));
        if(y != 0)
        {
            Candidate.push_back(std::make_pair(x+1, y-1));
        }
        if(y<width-1)
        {
            Candidate.push_back(std::make_pair(x+1, y+1));
        }
    }

    if(y != 0)
    {
        Candidate.push_back(std::make_pair(x, y-1));
    }
    if(y < width-1)
    {
        Candidate.push_back(std::make_pair(x, y+1));
    }
    return Candidate;
}

class Solution {
public:
    int shortestPathBinaryMatrix(vector<vector<int>>& grid) {
        int width = grid.size();
        // matrix to store path length
        std::vector<std::vector<int>> pathlength(width, vector<int> (width, std::numeric_limits<int>::max()));
        // priority queue for extract mean
        std::priority_queue<node, std::vector<node>, cmp> pq;
        // first node

        if(grid[0][0] == 1 || grid[width-1][width-1] == 1)
            return -1;
        pq.push(std::make_pair(std::make_pair(0,0), 1));

        while(!pq.empty())
        {
            node np = pq.top();
            pq.pop();
            int x = np.first.first;
            int y = np.first.second;
            int length = np.second;
            // std::cout << "x:" << x << "\ty:" << y << "\tlength: " << length << std::endl;
            if(pathlength[x][y] > length)
            {
                // set path length
                pathlength[x][y] = length;
                if(x == width -1 && y == width -1)
                {
                    return length;
                }

                // extend
                std::vector<std::pair<int, int>> candidates = getCandidate(width, x, y);
                for(int i=0; i<candidates.size(); i++)
                {
                    int tx = candidates[i].first;
                    int ty = candidates[i].second;
                    // std::cout << "\ttx:" << tx << "\tty:" << ty << std::endl;
                    // collision test
                    if(grid[tx][ty] == 0 && pathlength[tx][ty] > length + 1)
                    {
                        pq.push(std::make_pair(std::make_pair(tx,ty), length + 1));
                    }
                }
            }
            
        }
        return -1;

    }
};
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