<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(const vector<vector<int>>& heights, const vector<vector<int>> &sources, set<vector<int>>& canReachOcean) {
        stack<vector<int>> q;
        set<vector<int>> discovered;
        for (auto& source : sources) {
            int r = source[0];
            int c = source[1];
            discovered.insert({r, c});
            q.push({r, c});
        }
        
        while (!q.empty()) {
            vector<int> cell = q.top();
            int cellR = cell[0];
            int cellC = cell[1];
            q.pop();
            canReachOcean.insert({cell[0], cell[1]});
        
            if (cellR + 1 < heights.size() && discovered.find({cellR + 1, cellC}) == discovered.end()) {
                if (heights[cellR + 1][cellC] >= heights[cellR][cellC]) {
                    q.push({cellR + 1, cellC});
                    discovered.insert({cellR + 1, cellC});
                }
            }
            if (cellR - 1 >= 0 && discovered.find({cellR - 1, cellC}) == discovered.end()) {
                if (heights[cellR - 1][cellC] >= heights[cellR][cellC]) {
                    q.push({cellR - 1, cellC});
                    discovered.insert({cellR - 1, cellC});
                }
            }
            if (cellC + 1 < heights[0].size() && discovered.find({cellR, cellC + 1}) == discovered.end()) {
                if (heights[cellR][cellC + 1] >= heights[cellR][cellC]) {
                    q.push({cellR, cellC + 1});
                    discovered.insert({cellR, cellC + 1});
                }
            }
            if (cellC - 1 >= 0 && discovered.find({cellR, cellC - 1}) == discovered.end()) {
                if (heights[cellR][cellC - 1] >= heights[cellR][cellC]) {
                    q.push({cellR, cellC - 1});
                    discovered.insert({cellR, cellC - 1});
                }
            }
            
        }
    }

    void dfs(vector<vector<int>>& heights, int cellR, int cellC, set<vector<int>>& discovered) {
        discovered.insert({cellR, cellC});
        if (cellR + 1 < heights.size() && discovered.find({cellR + 1, cellC}) == discovered.end() ) {
                if (heights[cellR + 1][cellC] >= heights[cellR][cellC]) {
                    dfs(heights, cellR + 1, cellC, discovered);
                }
            }
            if (cellR - 1 >= 0 && discovered.find({cellR - 1, cellC}) == discovered.end()) {
                if (heights[cellR - 1][cellC] >= heights[cellR][cellC]) {
                    dfs(heights, cellR - 1, cellC, discovered);
                }
            }
            if (cellC + 1 < heights[0].size() && discovered.find({cellR, cellC + 1}) == discovered.end()) {
                if (heights[cellR][cellC + 1] >= heights[cellR][cellC]) {
                    dfs(heights, cellR, cellC + 1, discovered);
                }
            }
            if (cellC - 1 >= 0 && discovered.find({cellR, cellC - 1}) == discovered.end()) {
                if (heights[cellR][cellC - 1] >= heights[cellR][cellC]) {
                    dfs(heights, cellR, cellC - 1, discovered);
                }
            }

    }
    vector<vector<int>> pacificAtlantic(vector<vector<int>>& heights) {
        vector<vector<int>> res;
        set<vector<int>> canReachPacific;
        set<vector<int>> canReachAtlantic;

        int m = heights.size();
        int n = heights[0].size();
        
        // pacific
        for (int i = 0; i < heights.size(); i++) {
            dfs(heights, i, 0, canReachPacific);
        }
        for (int j = 1; j < heights[0].size(); j++) {
            dfs(heights, 0, j, canReachPacific);
        }
        // atlantic
        for (int i = 0; i < heights.size(); i++) {
            dfs(heights, i, n - 1, canReachAtlantic);
        }
        for (int j = 0; j < heights[0].size() - 1; j++) {
            dfs(heights, m - 1, j, canReachAtlantic);
        }

        set_intersection(canReachPacific.begin(), canReachPacific.end(), canReachAtlantic.begin(), canReachAtlantic.end(), back_inserter(res));
        return res;

    }

    vector<vector<int>> pacificAtlantic2(vector<vector<int>>& heights) {
        vector<vector<int>> res;
        set<vector<int>> canReachPacific;
        set<vector<int>> canReachAtlantic;
        vector<vector<int>> pacificSources;
        vector<vector<int>> atlanticSources;

        int m = heights.size();
        int n = heights[0].size();
        
        // pacific
        for (int i = 0; i < heights.size(); i++) {
            pacificSources.push_back({i, 0});
        }
        for (int j = 1; j < heights[0].size(); j++) {
            pacificSources.push_back({0, j});
        }
        bfs(heights, pacificSources, canReachPacific);
        // atlantic
        for (int i = 0; i < heights.size(); i++) {
            atlanticSources.push_back({i, n - 1});
        }
        for (int j = 0; j < heights[0].size() - 1; j++) {
            atlanticSources.push_back({m - 1, j});
        }
        bfs(heights, atlanticSources, canReachAtlantic);

        set_intersection(canReachPacific.begin(), canReachPacific.end(), canReachAtlantic.begin(), canReachAtlantic.end(), back_inserter(res));
        return res;

    }
};
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