<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>

#include <vector>
#include <queue>


using namespace std;

class Solution {

public:
    int x[5] = {0, 0, -1, 1};
    int y[5] = {1, -1, 0, 0};

    bool check_limits(vector<vector<int>>& heights, int r, int c) {
        if(r >= 0 && r < heights.size() && c >= 0 && c < heights[0].size()) { return true;}
        return false;
    }

    void bfs(vector<vector<int>>& heights, vector<std::vector<bool>> &visited, pair<int, int> start_node) {
        
        queue<pair<int, int>> queue;
        queue.push(start_node); 
        
        visited[start_node.first][start_node.second] = true;
        
        while(!queue.empty()) {
            auto node = queue.front(); queue.pop();
            int r = node.first;
            int c = node.second;
            for(int i = 0; i < 4; i++) {
                int nr = r + x[i];
                int nc = c + y[i];
                if(check_limits(heights, nr, nc) && !visited[nr][nc] && heights[nr][nc] >= heights[r][c]) {
                    queue.push(make_pair(nr, nc));
                    visited[nr][nc] = true;
                }
            }
        }
    }

    vector<vector<int>> pacificAtlantic(vector<vector<int>>& heights) {
        
        vector<vector<bool>> visited_pacific(heights.size(), vector<bool> (heights[0].size(), false));  
        vector<vector<bool>> visited_atlantic(heights.size(), vector<bool> (heights[0].size(), false));  
        
        for(int r = 0; r < heights.size(); r++) {
            bfs(heights, visited_pacific, make_pair(r, 0));
            bfs(heights, visited_atlantic, make_pair(r, heights[0].size() - 1));
        }
        
        for(int c = 0; c < heights[0].size(); c++) {
            bfs(heights, visited_pacific, make_pair(0, c));
            bfs(heights, visited_atlantic, make_pair(heights.size() - 1, c));
        }
        
        vector<vector<int>> result;
        for(int r = 0; r < heights.size(); r++) {
            for(int c = 0; c < heights[0].size(); c++) {
                if(visited_atlantic[r][c] && visited_pacific[r][c]) {
                    vector<int> field = {r, c};
                    result.push_back(field);
                }
            }
        }

        return result;
    }
};
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