> ## Documentation Index
> Fetch the complete documentation index at: https://leetcode-py.wisl.dev/llms.txt
> Use this file to discover all available pages before exploring further.

> ## Agent Instructions
> leetcode-py is a Python LeetCode practice environment generator with one CLI: lcpy. It is not a service or platform.
> Each problem is a directory under leetcode/ with README.md, solution.py, test_solution.py, helpers.py, and playground.ipynb. lcpy gen creates them from JSON templates bundled with the package.
> Examples are backed by tests; copy them verbatim.

# Pacific Atlantic Water Flow Python Solution

> Tested Python solution for LeetCode 417 with 12 pytest cases. Generate a practice environment with lcpy.

LeetCode 417, Medium. Topics: Array, Depth-First Search, Breadth-First Search, Matrix. [View on LeetCode](https://leetcode.com/problems/pacific-atlantic-water-flow/description/).

Generate this problem as a practice environment: tested reference solution, 12 [parametrized pytest cases](/practice/testing), and a playground notebook:

```bash theme={"theme":{"light":"github-light","dark":"github-dark"}}
lcpy gen -n 417   # by problem number
lcpy gen -s pacific_atlantic_water_flow   # by problem name
```

## Problem

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] = [ri, ci]` *denotes that rain water can flow from cell* `(ri, ci)` *to **both** the Pacific and Atlantic oceans*.

### Examples

![Example 1](https://assets.leetcode.com/uploads/2021/06/08/waterflow-grid.jpg)

```
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.
```

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

### Constraints

* `m == heights.length`
* `n == heights[r].length`
* `1 <= m, n <= 200`
* `0 <= heights[r][c] <= 10^5`

## Solution

Reference implementation from [solution.py on GitHub](https://github.com/wislertt/leetcode-py/blob/main/leetcode/pacific_atlantic_water_flow/solution.py), full suite in [test\_solution.py](https://github.com/wislertt/leetcode-py/blob/main/leetcode/pacific_atlantic_water_flow/test_solution.py):

```python theme={"theme":{"light":"github-light","dark":"github-dark"}}
class Solution:
    # Time: O(m * n)
    # Space: O(m * n)
    def pacific_atlantic(self, heights: list[list[int]]) -> list[list[int]]:
        if not heights or not heights[0]:
            return []

        m, n = len(heights), len(heights[0])
        pacific: set[tuple[int, int]] = set()
        atlantic: set[tuple[int, int]] = set()

        def dfs(r: int, c: int, visited: set) -> None:
            visited.add((r, c))
            for dr, dc in [(0, 1), (0, -1), (1, 0), (-1, 0)]:
                nr, nc = r + dr, c + dc
                if (
                    0 <= nr < m
                    and 0 <= nc < n
                    and (nr, nc) not in visited
                    and heights[nr][nc] >= heights[r][c]
                ):
                    dfs(nr, nc, visited)

        # DFS from Pacific borders (top and left)
        for i in range(m):
            dfs(i, 0, pacific)
        for j in range(n):
            dfs(0, j, pacific)

        # DFS from Atlantic borders (bottom and right)
        for i in range(m):
            dfs(i, n - 1, atlantic)
        for j in range(n):
            dfs(m - 1, j, atlantic)

        return [[r, c] for r, c in pacific & atlantic]
```

## Complexity

| Time      | Space     |
| --------- | --------- |
| O(m \* n) | O(m \* n) |

## Tags

[Grind](/catalog/grind), [Blind 75](/catalog/blind-75), [NeetCode 150](/catalog/neetcode-150), [NeetCode 250](/catalog/neetcode-250), [NeetCode All](/catalog/neetcode).