<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 {
private:
    set<pair<int, int>> bfs(list<pair<int, int>> queue, vector<vector<int>>& heights, vector<vector<bool>> visited) {
      set<pair<int, int>> flow;
      vector<vector<int>> directions = {{1,0}, {-1,0}, {0,1}, {0,-1}};
      while (queue.size()) {
        auto pos = queue.front();
        queue.pop_front();
        int r = pos.first;
        int c = pos.second;
        visited[r][c] = true;
        flow.insert(make_pair(r,c));
        for (auto d : directions) {
          int new_r = r + d[0];
          int new_c = c + d[1];
          if (new_r < 0 || new_c < 0 || new_r >= heights.size() || new_c >= heights[0].size()) {
            continue;
          }
          if (visited[new_r][new_c]) {
            continue;
          }
          if (heights[r][c] > heights[new_r][new_c]) {
            continue;
          }
          queue.push_back(make_pair(new_r, new_c));
        }
      }
      return flow;
    }

public:
    vector<vector<int>> pacificAtlantic(vector<vector<int>>& heights) {
      list<pair<int, int>> pacific_starts, atlantic_starts;
      int rows = heights.size();
      int cols = heights[0].size();
      for (int r = 0; r < rows; r++) {
        pacific_starts.push_back(make_pair(r, 0));
        atlantic_starts.push_back(make_pair(r, cols - 1));
      }
      for (int c = 0; c < cols; c++) {
        pacific_starts.push_back(make_pair(0, c));
        atlantic_starts.push_back(make_pair(rows - 1, c));
      }
      
      vector<vector<bool>> visited(heights.size(), vector<bool>(heights[0].size(), false));
      auto pacific_nodes = bfs(pacific_starts, heights, visited);
      auto atlantic_nodes = bfs(atlantic_starts, heights, visited);

      // cout << "Pacific Nodes:\n";
      // for (auto node : pacific_nodes) {
      //   cout << node.first << "," << node.second << " ";
      // }
      // cout << "\n";

      // cout << "Atlantic Nodes:\n";
      // for (auto node : atlantic_nodes) {
      //   cout << node.first << "," << node.second << " ";
      // }
      // cout << "\n";

      vector<vector<int>> cells;
      for (auto node : pacific_nodes) {
        if (atlantic_nodes.find(node) != atlantic_nodes.end()) {
          cells.push_back({node.first, node.second});
        }
      }
      return cells;
    }
};
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