<p>There is an <code>m x n</code> rectangular island that borders both the <strong>Pacific Ocean</strong> and <strong>Atlantic Ocean</strong>. The <strong>Pacific Ocean</strong> touches the island&#39;s left and top edges, and the <strong>Atlantic Ocean</strong> touches the island&#39;s right and bottom edges.</p>

<p>The island is partitioned into a grid of square cells. You are given an <code>m x n</code> integer matrix <code>heights</code> where <code>heights[r][c]</code> represents the <strong>height above sea level</strong> of the cell at coordinate <code>(r, c)</code>.</p>

<p>The island receives a lot of rain, and the rain water can flow to neighboring cells directly north, south, east, and west if the neighboring cell&#39;s height is <strong>less than or equal to</strong> the current cell&#39;s height. Water can flow from any cell adjacent to an ocean into the ocean.</p>

<p>Return <em>a <strong>2D list</strong> of grid coordinates </em><code>result</code><em> where </em><code>result[i] = [r<sub>i</sub>, c<sub>i</sub>]</code><em> denotes that rain water can flow from cell </em><code>(r<sub>i</sub>, c<sub>i</sub>)</code><em> to <strong>both</strong> the Pacific and Atlantic oceans</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/08/waterflow-grid.jpg" style="width: 400px; height: 400px;" />
<pre>
<strong>Input:</strong> heights = [[1,2,2,3,5],[3,2,3,4,4],[2,4,5,3,1],[6,7,1,4,5],[5,1,1,2,4]]
<strong>Output:</strong> [[0,4],[1,3],[1,4],[2,2],[3,0],[3,1],[4,0]]
<strong>Explanation:</strong> The following cells can flow to the Pacific and Atlantic oceans, as shown below:
[0,4]: [0,4] -&gt; Pacific Ocean 
&nbsp;      [0,4] -&gt; Atlantic Ocean
[1,3]: [1,3] -&gt; [0,3] -&gt; Pacific Ocean 
&nbsp;      [1,3] -&gt; [1,4] -&gt; Atlantic Ocean
[1,4]: [1,4] -&gt; [1,3] -&gt; [0,3] -&gt; Pacific Ocean 
&nbsp;      [1,4] -&gt; Atlantic Ocean
[2,2]: [2,2] -&gt; [1,2] -&gt; [0,2] -&gt; Pacific Ocean 
&nbsp;      [2,2] -&gt; [2,3] -&gt; [2,4] -&gt; Atlantic Ocean
[3,0]: [3,0] -&gt; Pacific Ocean 
&nbsp;      [3,0] -&gt; [4,0] -&gt; Atlantic Ocean
[3,1]: [3,1] -&gt; [3,0] -&gt; Pacific Ocean 
&nbsp;      [3,1] -&gt; [4,1] -&gt; Atlantic Ocean
[4,0]: [4,0] -&gt; Pacific Ocean 
       [4,0] -&gt; Atlantic Ocean
Note that there are other possible paths for these cells to flow to the Pacific and Atlantic oceans.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> heights = [[1]]
<strong>Output:</strong> [[0,0]]
<strong>Explanation:</strong> The water can flow from the only cell to the Pacific and Atlantic oceans.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == heights.length</code></li>
	<li><code>n == heights[r].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 200</code></li>
	<li><code>0 &lt;= heights[r][c] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    void bfs(std::deque<std::pair<int, int>>& q, std::vector<bool>& s, vector<vector<int>>& heights)
    {
        std::array<int, 5> const directions = { 0, 1, 0, -1, 0 };

        int const rows = heights.size();
        int const cols = heights[0].size();        

        while (!q.empty())
        {
            auto [row, col] = q.back();
            q.pop_back();

            if (s[(row * cols) + col])
            {
                continue;
            }

            s[(row * cols) + col] = true;

            for (int i = 0; i < 4; ++i)
            {
                int const rr = row + directions[i], cc = col + directions[i + 1];
                if ((0 <= rr && rr < rows) && 
                    (0 <= cc && cc < cols) && 
                    !s[(rr * cols) + cc])
                {
                    if (heights[rr][cc] >= heights[row][col])
                    {
                        q.push_front(std::pair{ rr, cc });
                    }
                }
            }            
        }      
    }

    vector<vector<int>> pacificAtlantic(vector<vector<int>>& heights) {
        int const rows = heights.size();
        int const cols = heights[0].size();

        std::vector<std::vector<int>> result;
        std::deque<std::pair<int, int>> pacificQueue;
        std::deque<std::pair<int, int>> atlanticQueue;

        std::vector<bool> pacificSet(rows * cols, false);
        std::vector<bool> atlanticSet(rows * cols, false);

        for (int row = 0; row < heights.size(); ++row)
        {
            pacificQueue.push_back(std::pair{ row, 0 });
            atlanticQueue.push_back(std::pair{ row, heights[0].size() - 1 });
        }

        for (int col = 0; col < heights[0].size(); ++col)
        {
            pacificQueue.push_back(std::pair{ 0, col });
            atlanticQueue.push_back(std::pair{ heights.size() - 1, col });             
        }

        bfs(pacificQueue, pacificSet, heights);
        bfs(atlanticQueue, atlanticSet, heights);
        
        for (int r = 0; r < rows; ++r)
        {
            for (int c = 0; c < cols; ++c)
            {
                if (atlanticSet[(r * cols) + c] && pacificSet[(r * cols) + c])
                {
                    std::vector<int> coord = { r, c };
                    result.push_back(std::move(coord));
                }
            }
        }

        return result;
    }
};
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