<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:
    const vector<pair<int, int>> dirs = {{0, 1}, {1, 0}, {-1,0}, {0, -1}};

    void processHeights(deque<pair<int, int>>& to_visit,
                        std::set<std::pair<int, int>>& can_flow,
                        vector<vector<int>>& heights, int n, int m,
                        std::set<std::pair<int, int>>& visited) {
        while (!to_visit.empty()) {

            auto cell = to_visit.front();
            to_visit.pop_front();
            int i = cell.first, j = cell.second;
            if (visited.contains({i, j})) {
                continue;
            }
            visited.insert({i,j});
            for (const auto& dir : dirs) {
                int x = dir.first, y = dir.second;
                int new_x = i + x;
                int new_y = j + y;
                // cout << "new: [" << new_x << " " << new_y << "] vs  old: "
                //      << "[" << i << " " << j << "]\n";
                if (new_x < 0 || new_x >= n || new_y < 0 || new_y >= m) {
                    continue;
                }
                if (visited.contains({new_x, new_y})) {
                    continue;
                }
                if (heights[new_x][new_y] >= heights[i][j]) {
                    can_flow.insert({new_x, new_y});
                    // cout << "yes\n";
                    to_visit.push_back({new_x, new_y});
                }
            }
        }
    }

    vector<vector<int>> pacificAtlantic(vector<vector<int>>& heights) {
        vector<vector<int>> result;

        const int n = heights.size();
        const int m = heights[0].size();

        auto tmp(heights);

        std::set<std::pair<int, int>> can_pac;
        std::set<std::pair<int, int>> visited_pac;
        std::set<std::pair<int, int>> can_atl;
        std::set<std::pair<int, int>> visited_atl;

        deque<pair<int, int>> to_visit_pac;
        deque<pair<int, int>> to_visit_atl;
        queue<pair<int, int>> to_visit;

        for (int i = 0; i < n; ++i) {
            to_visit_pac.push_back({i, 0});
            can_pac.insert({i, 0});
            to_visit_atl.push_back({i, m - 1});
            can_atl.insert({i, m - 1});
        }

        for (int i = 0; i < m; ++i) {
            can_pac.insert({0, i});
            to_visit_pac.push_back({0, i});
            can_atl.insert({n - 1, i});
            to_visit_atl.push_back({n - 1, i});
        }

        processHeights(to_visit_pac, can_pac, heights, n, m, visited_pac);
        processHeights(to_visit_atl, can_atl, heights, n, m, visited_atl);

        std::set<std::pair<int, int>> result_set;
        std::set_intersection(can_pac.begin(), can_pac.end(), can_atl.begin(),
                              can_atl.end(),
                              std::inserter(result_set, result_set.begin()));

        for (const auto& p : result_set) {
            result.push_back({p.first, p.second});
        }

        return result;
    }
};
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