Pacific Atlantic Water Flow

LeetCode

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.

Initial attempt

Time spent: 1h 16m | Runtime: 10.58% | Memory: 0.01%

• I tested every point for water flow while keeping track of two sets on what paths were taken along the way. If the recursion ever reached a coast, the entire path was added to that coast. This was pretty costly memory-wise and the code was more complicated than it needed to be.

Solution

• Write a function that recurses based on reverse flow while tracking a single visited set.
• Run every coast point through that function while adding to a the appropriate set.
• Intersect the two sets for the results.

Cleaned up code

Time spent: 17m | Runtime: 16.39% | Memory: 53.17%

class Solution:
    directions = [(1, 0), (0, 1), (-1, 0), (0, -1)]

    def pacificAtlantic(self, heights: List[List[int]]) -> List[List[int]]:
        rows = len(heights)
        cols = len(heights[0])

        reaches_pacific = set()
        for j in range(cols):
            self.reverse_flow(heights, 0, j, reaches_pacific)

        for i in range(rows):
            self.reverse_flow(heights, i, 0, reaches_pacific)

        reaches_atlantic = set()
        for j in range(cols):
            self.reverse_flow(heights, rows - 1, j, reaches_atlantic)

        for i in range(rows):
            self.reverse_flow(heights, i, cols - 1, reaches_atlantic)

        return [[i, j] for i, j in (reaches_pacific & reaches_atlantic)]

    def reverse_flow(self, heights, i, j, visited):
        visited.add((i, j))
        for di, dj in self.directions:
            if (
                0 <= i + di < len(heights)
                and 0 <= j + dj < len(heights[0])
                and (i + di, j + dj) not in visited
            ):
                if heights[i][j] <= heights[i + di][j + dj]:
                    self.reverse_flow(heights, i + di, j + dj, visited)