cpp-flashcards/org/study_deck_02/dsa/graphs/0417-pacific-atlantic-water-flow.org

#+PROPERTY: STUDY_DECK_02
* TODO 0417. Pacific Atlantic Water Flow :medium:
:PROPERTIES:
:NEETCODE: [[file:../../roadmap.org::*0417. Pacific Atlantic Water Flow][0417. Pacific Atlantic Water Flow]]
:END:

There is an ~m x n~ rectangular island that borders both the *Pacific Ocean* and *Atlantic Ocean*. The *Pacific Ocean* touches the island's left and top edges, and the *Atlantic Ocean* touches the island's right and bottom edges.

The island is partitioned into a grid of square cells. You are given an ~m x n~ integer matrix ~heights~ where ~heights[r][c]~ represents the *height above sea level* of the cell at coordinate ~(r, c)~.

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's height is *less than or equal to* the current cell's height. Water can flow from any cell adjacent to an ocean into the ocean.

Return /a *2D list* of grid coordinates /~result~/ where /~result[i] = [r_{i}, c_{i}]~/ denotes that rain water can flow from cell /~(r_{i}, c_{i})~/ to *both* the Pacific and Atlantic oceans/.

*Example 1:*


#+begin_src
Input: 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]]
Output: [[0,4],[1,3],[1,4],[2,2],[3,0],[3,1],[4,0]]
Explanation: The following cells can flow to the Pacific and Atlantic oceans, as shown below:
[0,4]: [0,4] -> Pacific Ocean 
       [0,4] -> Atlantic Ocean
[1,3]: [1,3] -> [0,3] -> Pacific Ocean 
       [1,3] -> [1,4] -> Atlantic Ocean
[1,4]: [1,4] -> [1,3] -> [0,3] -> Pacific Ocean 
       [1,4] -> Atlantic Ocean
[2,2]: [2,2] -> [1,2] -> [0,2] -> Pacific Ocean 
       [2,2] -> [2,3] -> [2,4] -> Atlantic Ocean
[3,0]: [3,0] -> Pacific Ocean 
       [3,0] -> [4,0] -> Atlantic Ocean
[3,1]: [3,1] -> [3,0] -> Pacific Ocean 
       [3,1] -> [4,1] -> Atlantic Ocean
[4,0]: [4,0] -> Pacific Ocean 
       [4,0] -> Atlantic Ocean
Note that there are other possible paths for these cells to flow to the Pacific and Atlantic oceans.
#+end_src


*Example 2:*


#+begin_src
Input: heights = [[1]]
Output: [[0,0]]
Explanation: The water can flow from the only cell to the Pacific and Atlantic oceans.
#+end_src


*Constraints:*

 - ~m == heights.length~

 - ~n == heights[r].length~

 - ~1 <= m, n <= 200~

 - ~0 <= heights[r][c] <= 10^{5}~

** TODO Approach
Write your approach here.

** TODO Python
#+begin_src python
class Solution:
    def pacificAtlantic(self, heights: List[List[int]]) -> List[List[int]]:
#+end_src

** TODO C++
#+begin_src cpp
class Solution {
public:
    vector<vector<int>> pacificAtlantic(vector<vector<int>>& heights) {
        
    }
};
#+end_src