417. Pacific Atlantic Water Flow

Author: sbk1014

pacific-atlantic-water-flow/bhyun-kim.py

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+"""
+417. Pacific Atlantic Water Flow
+https://leetcode.com/problems/pacific-atlantic-water-flow/
+
+Solution:
+    To solve this problem, we can use depth-first search (DFS) to explore all possible paths starting from each cell.
+    We can create a helper function that takes the current cell and marks it as reachable.
+
+    - We can create two sets to store the cells that are reachable from the Pacific and Atlantic oceans.
+    - We can start DFS from the cells on the borders of the Pacific and Atlantic oceans.
+    - We can find the intersection of the two sets to get the cells that are reachable from both oceans.
+
+
+Time complexity: O(m x n)
+    - m and n are the dimensions of the grid.
+    - We explore all cells in the grid once.
+
+Space complexity: O(m x n)
+    - We use two sets to store the reachable cells from the Pacific and Atlantic oceans.
+    - The maximum size of the sets is the number of cells in the grid.
+"""
+
+
+from typing import List
+
+class Solution:
+    def pacificAtlantic(self, heights: List[List[int]]) -> List[List[int]]:
+        
+        if not heights or not heights[0]:
+            return []
+
+        def dfs(matrix, reachable, x, y):
+            directions = [(1, 0), (-1, 0), (0, 1), (0, -1)]
+            reachable.add((x, y))
+            for dx, dy in directions:
+                nx, ny = x + dx, y + dy
+                if 0 <= nx < m and 0 <= ny < n and (nx, ny) not in reachable and matrix[nx][ny] >= matrix[x][y]:
+                    dfs(matrix, reachable, nx, ny)
+
+        m, n = len(heights), len(heights[0])
+        pacific_reachable = set()
+        atlantic_reachable = set()
+
+        for i in range(m):
+            dfs(heights, pacific_reachable, i, 0)
+            dfs(heights, atlantic_reachable, i, n - 1)
+
+        for j in range(n):
+            dfs(heights, pacific_reachable, 0, j)
+            dfs(heights, atlantic_reachable, m - 1, j)
+
+        return list(pacific_reachable & atlantic_reachable)