Problem Description
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 rainwater 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 where result[i] = [r_i, c_i] denotes that rainwater can flow from cell (r_i, c_i) to both the Pacific and Atlantic oceans.
Key Insights
- Each cell can potentially flow water to adjacent cells if their height is less than or equal to its own.
- Cells on the edges can flow directly into the oceans.
- A cell can reach both oceans if it can flow to cells that can reach each ocean.
- The problem can be approached using Depth-First Search (DFS) or Breadth-First Search (BFS) from the borders of the matrix.
Space and Time Complexity
Time Complexity: O(m * n)
Space Complexity: O(m * n)
Solution
To solve this problem, we can use a Depth-First Search (DFS) approach starting from the cells adjacent to both the Pacific and Atlantic oceans. We will maintain two boolean matrices to track which cells can reach the Pacific and Atlantic oceans. We will start our DFS from the borders of the matrix (the first row and first column for the Pacific, and the last row and last column for the Atlantic). For each cell we visit, we will check its neighbors and continue the DFS if the neighbor is lower or equal in height. If a cell can reach both oceans, we will add it to our result list.