<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) 
    {
        const size_t SIZE{grid.size()};

        size_t source_row{0};
        size_t source_col{0};

        size_t target_row{SIZE -1};
        size_t target_col{SIZE -1};

        if(grid[source_row][source_col] == 1 ||
           grid[target_row][target_col] == 1)
        {
            return -1;
        }

        else if(source_row == target_row && 
                source_col == target_col)
        {
            return 1;
        }

        std::vector<std::vector<std::pair<size_t,size_t>>>
        parent_coordinates(SIZE, std::vector<std::pair<size_t, size_t>>(SIZE));

        parent_coordinates[source_row][source_col] = {source_row, source_col};

        std::function<void(size_t, size_t)>
        print_path = [&](size_t cur_row, size_t cur_col) ->void
        {
            while(cur_row != source_row && 
                  cur_col != source_col)
            {
                std::cout << "[" << cur_row << " , " << cur_col << "]\n";

                auto [parent_row, parent_col] = parent_coordinates[cur_row][cur_col];
                
                cur_row = parent_row;
                cur_col = parent_col;
            }

            std::cout << "[" << cur_row << " , " << cur_col << "]\n";
        }; // End of print_path() lambda function.


        std::vector<std::vector<int>> DIRECTIONS
        {            
            {0,1},
            {0,-1},
            {-1,0},
            {-1,1},
            {-1,-1},
            {1,0},
            {1,1},
            {1,-1}
        };
        constexpr int NUM_DIRECTIONS{8};

        std::queue<std::pair<size_t, size_t>> coordinate_queue{};
        coordinate_queue.emplace(source_row, source_col);    

        int result_shortest_clear_path_length{0};

        while(!coordinate_queue.empty())
        {
            ++result_shortest_clear_path_length;

            size_t num_nodes_at_cur_level{coordinate_queue.size()};
            while(num_nodes_at_cur_level--)
            {
                auto [cur_row, cur_col] = coordinate_queue.front();
                coordinate_queue.pop();

                if(cur_row == target_row && 
                   cur_col == target_col)
                {
                    print_path(cur_row, cur_col);

                    return result_shortest_clear_path_length;
                }

                for(size_t dir_pos{0}; dir_pos < NUM_DIRECTIONS; ++dir_pos)
                {
                    size_t new_row{DIRECTIONS[dir_pos][0] + cur_row};
                    size_t new_col{DIRECTIONS[dir_pos][1] + cur_col};

                    if(new_row >= SIZE || new_col >= SIZE || grid[new_row][new_col] == 1)
                    {
                        continue;
                    }

                    grid[new_row][new_col] = 1;

                    parent_coordinates[new_row][new_col] = {cur_row, cur_col};

                    coordinate_queue.emplace(new_row, new_col);
                }
            }

        }

        return -1;
    }
};
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