<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:
    def __init__(self):
        self.dirs = [(1, 0), (-1, 0), (0, 1), (0, -1)]

    def printDebug(self, title, twoDArray):
        print('Title:', title)
        for i, row in enumerate(twoDArray):
            arr = []
            for ele in row:
                if type(ele) == int:
                    arr.append(str(ele).rjust(2))
                elif type(ele) == bool:
                    arr.append(str(+ele).rjust(2))
                elif ele == None:
                    arr.append(str(-1).rjust(2))
            print(str(i).rjust(2), ':', ', '.join(arr))
        print()

    def pacificAtlantic(self, heights: List[List[int]]) -> List[List[int]]:
        # self.printDebug('heights', heights)
        pacific = [[None] * len(row) for row in heights]
        visited = [[False] * len(row) for row in heights]
        for i in range(len(heights)):
            for j in range(len(heights[i])):
                self.findPacific(heights, pacific, visited, i, j)
        # self.printDebug('pacific', pacific)
        atlantic = [[None] * len(row) for row in heights]
        visited = [[False] * len(row) for row in heights]
        for i in range(len(heights) - 1, -1, -1):
            for j in range(len(heights[i]) - 1, -1, -1):
                # print('i, j:', i, j)
                self.findAtlantic(heights, atlantic, visited, i, j)
        # self.printDebug('atlantic', atlantic)
        ans = [[i, j] for i in range(len(heights)) for j in range(len(heights[i])) if pacific[i][j] and atlantic[i][j]]
        return ans

    def findPacific(self, heights, pacific, visited, i, j):
        hit = False
        visited[i][j] = True
        for (di, dj) in self.dirs:
            ni, nj = i + di, j + dj
            if ni < 0 or nj < 0:
                hit |= True
            elif ni >= len(heights) or nj >= len(heights[0]):
                hit |= False
            elif heights[i][j] < heights[ni][nj]:
                hit |= False
            elif pacific[ni][nj] != None:
                hit |= pacific[ni][nj]
            elif visited[ni][nj]:
                hit |= False
            else:
                hit |= self.findPacific(heights, pacific, visited, ni, nj)
        visited[i][j] = False
        if hit == True:
            pacific[i][j] = hit
        return hit

    def findAtlantic(self, heights, atlantic, visited, i, j):
        # if i == 11 and j == 3:
        #     self.printDebug('atlantic', atlantic)
        #     self.printDebug('visited', visited)
        hit = False
        visited[i][j] = True
        for (di, dj) in self.dirs:
            ni, nj = i + di, j + dj
            if ni < 0 or nj < 0:
                hit |= False
            elif ni >= len(heights) or nj >= len(heights[0]):
                hit |= True
            elif heights[i][j] < heights[ni][nj]:
                hit |= False
            elif atlantic[ni][nj] != None:
                hit |= atlantic[ni][nj]
            elif visited[ni][nj]:
                hit |= False
            else:
                hit |= self.findAtlantic(heights, atlantic, visited, ni, nj)
        visited[i][j] = False
        if hit == True:
            atlantic[i][j] = hit
        return hit

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