<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>> directions = {{0, 1}, {0, -1}, {1, 0}, {-1, 0}};
    vector<vector<int>> heights;

    bool isValid(const vector<int>& node) {
        if (node[0] < 0 || node[0] >= heights.size()) {
            return false;
        }

        if (node[1] < 0 || node[1] >= heights[0].size()) {
            return false;
        }

        return true;
    }

    void dfs(const vector<int>& node, set<vector<int>>& ocean) {
        if (!isValid(node)) {
            return;
        }

        if (!ocean.count(node)) {
            ocean.insert(node);
            for (const auto& direction: directions) {
                const vector<int> neighbor = {node[0] + direction[0], node[1] + direction[1]};
                if (!isValid(neighbor)) {
                    continue;
                }
                if (heights[neighbor[0]][neighbor[1]] >= heights[node[0]][node[1]]) {
                    dfs(neighbor, ocean);
                }
            }
        }
    }

    vector<vector<int>> pacificAtlantic(vector<vector<int>>& heights) {
        this->heights = heights;
        int n = heights.size();
        int m = heights[0].size();
        set<vector<int>> pacific;
        set<vector<int>> pacific_visited;
        set<vector<int>> atlantic;
        set<vector<int>> atlantic_visited;        

        for (int j = 0; j < m; j++) {
            pacific.insert({0, j});
            atlantic.insert({n - 1, j});
        }

        for (int j = 0; j < n; j++) {
            pacific.insert({j, 0});
            atlantic.insert({j, m - 1});            
        }

        for (const auto& p_start: pacific) {
            dfs(p_start, pacific_visited);
        }

        for (const auto& a_start: atlantic) {
            dfs(a_start, atlantic_visited);
        }

        vector<vector<int>> result;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (pacific_visited.count({i, j}) and atlantic_visited.count({i, j})) {
                    result.push_back({i, j});
                }
            }
        }

        return result;
    }
};
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