<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 <stack>
#include <iostream>

using namespace std;

class Node {
public:
    int i;
    int j;

    bool pacific;
    bool atlantic;

    vector<Node*> heights;

    Node() :
        pacific(false),
        atlantic(false)
        {}
};

class Solution {
public:
    vector<vector<int>> pacificAtlantic(vector<vector<int>>& heights) {
        int m = heights.size();
        int n = heights[0].size();

        vector<vector<Node>> nodes(m, vector<Node>(n, Node()));
        vector<vector<int>> answer;
        
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                int height = heights[i][j];

                bool hasTop = true;
                bool hasBot = true;
                bool hasLeft = true;
                bool hasRight = true;

                nodes[i][j].i = i;
                nodes[i][j].j = j;

                if (i == 0) {
                    nodes[i][j].pacific = true;
                    hasTop = false;
                }
                if (i == m - 1) {
                    nodes[i][j].atlantic = true;
                    hasBot = false;
                }
                if (j == 0) {
                    nodes[i][j].pacific = true;
                    hasLeft = false;
                }
                if (j == n - 1) {
                    nodes[i][j].atlantic = true;
                    hasRight = false;
                }

                if (hasTop   && heights[i - 1][j + 0] >= height) {
                    nodes[i][j].heights.push_back(&nodes[i - 1][j + 0]);
                }
                if (hasBot   && heights[i + 1][j + 0] >= height) {
                    nodes[i][j].heights.push_back(&nodes[i + 1][j + 0]);
                }
                if (hasLeft  && heights[i + 0][j - 1] >= height) {
                    nodes[i][j].heights.push_back(&nodes[i + 0][j - 1]);
                }
                if (hasRight && heights[i + 0][j + 1] >= height) {
                    nodes[i][j].heights.push_back(&nodes[i + 0][j + 1]);
                }
            }
        }

        stack<Node*> pacificStack, atlanticStack;
        int i = 0;
        for (int j = 0; j < n; j++) {
            pacificStack.push(&nodes[i][j]);
        }
        int j = 0;
        for (int i = 1; i < m; i++) {
            int idx = j + i * m;
            pacificStack.push(&nodes[i][j]);
        }

        i = m - 1;
        for (int j = 0; j < n; j++) {
            int idx = j + i * m;
            atlanticStack.push(&nodes[i][j]);
        }
        j = n - 1;
        for (int i = 0; i < m - 1; i++) {
            int idx = j + i * m;
            atlanticStack.push(&nodes[i][j]);
        }

        while (!pacificStack.empty()) {
            Node* n = pacificStack.top();
            pacificStack.pop();

            for (Node* h : n->heights) {
                if (!h->pacific) {
                    h->pacific = true;
                    pacificStack.push(h);
                }
            }
        }

        while (!atlanticStack.empty()) {
            Node* n = atlanticStack.top();
            atlanticStack.pop();
            
            if (n->pacific) {
                answer.push_back({n->i, n->j});
            }
            
            for (Node* h : n->heights) {
                if (!h->atlantic) {
                    h->atlantic = true;
                    atlanticStack.push(h);
                }
            }
        }

        return answer;
    }
};
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