<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:
    vector<vector<int>> pacificAtlantic(vector<vector<int>>& heights) {
        int h = heights.size();
        int w = heights[0].size();

        vector<vector<char>> atlantic(h, vector<char>(w, '_'));
        vector<vector<char>> pacific(h, vector<char>(w, '_'));;
        vector<vector<int>> coords;
        
        for(int i = 0; i < w; i++){
            propagateRain(atlantic, heights, 'a', h-1, i);
            propagateRain(pacific, heights, 'p', 0, i);
        }
        for(int i = 0; i < h; i++){
            propagateRain(atlantic, heights, 'a', i, w-1);
            propagateRain(pacific, heights, 'p', i, 0);
        }
        
        for(int i = 0; i < h; i++){
            for(int j = 0; j < w; j++){
                if(atlantic[i][j] == 'a' && pacific[i][j] == 'p'){
                    coords.push_back({i, j});
                }
            }
        }

        return coords;
    }

    void propagateRain(vector<vector<char>> &area, vector<vector<int>> &heights, char c, int row, int col){
        if(area[row][col] != '_') return;
        cout << "Visiting [" <<row << ", " << col << "]" << endl; 
        area[row][col] = c;

        int h = heights.size();
        int w = heights[0].size();
        
        vector<pair<int, int>> neighbors = getNeighbors(w,h,row,col);
        for(pair<int,int> n:neighbors){
            if(heights[row][col] <= heights[n.first][n.second]){
                propagateRain(area, heights, c, n.first, n.second);
            }
        }
    }

    vector<pair<int, int>> getNeighbors(int width, int height, int row, int col){
        vector<pair<int, int>> neighbors;
        if(row > 0){
            neighbors.push_back(make_pair(row-1, col));
        }
        if(row < height - 1){
            neighbors.push_back(make_pair(row+1, col));
        }
        if(col > 0){
            neighbors.push_back(make_pair(row, col-1));
        }
        if(col < width - 1){
            neighbors.push_back(make_pair(row, col+1));
        }
        return neighbors;
    }
};
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