Leetcode #417: Pacific Atlantic Water Flow
In this guide, we solve Leetcode #417 Pacific Atlantic Water Flow in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Depth-First Search, Breadth-First Search, Array, Matrix
Intuition
We need to explore a structure deeply before backing up, which suits DFS.
DFS keeps local context on the call stack and is easy to implement recursively.
Approach
Define a recursive DFS that carries the necessary state.
Combine child results as the recursion unwinds.
Steps:
- Define a recursive DFS with state.
- Visit children and combine results.
- Return the final aggregation.
Example
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.
Python Solution
class Solution:
def pacificAtlantic(self, heights: List[List[int]]) -> List[List[int]]:
def bfs(q: Deque[Tuple[int, int]], vis: List[List[bool]]) -> None:
while q:
x, y = q.popleft()
for dx, dy in pairwise(dirs):
nx, ny = x + dx, y + dy
if (
0 <= nx < m
and 0 <= ny < n
and not vis[nx][ny]
and heights[nx][ny] >= heights[x][y]
):
vis[nx][ny] = True
q.append((nx, ny))
m, n = len(heights), len(heights[0])
vis1 = [[False] * n for _ in range(m)]
vis2 = [[False] * n for _ in range(m)]
q1: Deque[Tuple[int, int]] = deque()
q2: Deque[Tuple[int, int]] = deque()
dirs = (-1, 0, 1, 0, -1)
for i in range(m):
q1.append((i, 0))
vis1[i][0] = True
q2.append((i, n - 1))
vis2[i][n - 1] = True
for j in range(n):
q1.append((0, j))
vis1[0][j] = True
q2.append((m - 1, j))
vis2[m - 1][j] = True
bfs(q1, vis1)
bfs(q2, vis2)
return [(i, j) for i in range(m) for j in range(n) if vis1[i][j] and vis2[i][j]]
Complexity
The time complexity is and the space complexity is , where and are the number of rows and columns in the matrix, respectively. The space complexity is , where and are the number of rows and columns in the matrix, respectively.
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.