Pacific Atlantic Water Flow
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[r][c] represents the height above sea level of the cell at coordinate
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[i] = [ri, ci] denotes that rain water can flow from cell
(ri, ci) to both the Pacific and Atlantic oceans.
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]]
Explanation: The following cells can flow to the Pacific and Atlantic oceans, as shown below:\
1[0,4]: [0,4] -> Pacific Ocean 2 [0,4] -> Atlantic Ocean 3[1,3]: [1,3] -> [0,3] -> Pacific Ocean 4 [1,3] -> [1,4] -> Atlantic Ocean 5[1,4]: [1,4] -> [1,3] -> [0,3] -> Pacific Ocean 6 [1,4] -> Atlantic Ocean 7[2,2]: [2,2] -> [1,2] -> [0,2] -> Pacific Ocean 8 [2,2] -> [2,3] -> [2,4] -> Atlantic Ocean 9[3,0]: [3,0] -> Pacific Ocean 10 [3,0] -> [4,0] -> Atlantic Ocean 11[3,1]: [3,1] -> [3,0] -> Pacific Ocean 12 [3,1] -> [4,1] -> Atlantic Ocean 13[4,0]: [4,0] -> Pacific Ocean 14 [4,0] -> Atlantic Ocean
Note that there are other possible paths for these cells to flow to the Pacific and Atlantic oceans.
heights = []
Explanation: The water can flow from the only cell to the Pacific and Atlantic oceans.
m == heights.length
n == heights[r].length
1 <= m, n <= 200
0 <= heights[r][c] <= 105
The best way to approach this question is to traverse from the outside cells into the inner cells. Both BFS and DFS will produce an efficient implementation. Below, we will to show a recusive dfs approach to this problem. To find the cells that will flow to both oceans, we will recursively find the cells that can be reached by the Pacific Ocean, and the cells reached by the Atlantic Ocean. Finally, we find the overlapping cells that can be reached by both oceans.
1def pacificAtlantic(self, heights: List[List[int]]) -> List[List[int]]: 2 m = len(heights) 3 n = len(heights) 4 pacific = [[False for _ in range(n)] for _ in range(m)] 5 atlantic = [[False for _ in range(n)] for _ in range(m)] 6 res =  7 8 dirs = [(0,1), (0,-1), (1,0), (-1,0)] 9 def get_neighbours(x, y): 10 neighbours =  11 for dirx, diry in dirs: 12 newx, newy = x+dirx, y+diry 13 if 0 <= newx < m and 0 <= newy < n: 14 neighbours.append((newx, newy)) 15 return neighbours 16 17 def dfs(x, y, ocean): 18 if ocean[x][y]: return 19 ocean[x][y] = True 20 for newx, newy in get_neighbours(x,y): 21 if heights[newx][newy] >= heights[x][y]: 22 dfs(newx, newy, ocean) 23 24 for x in range(m): 25 dfs(x, 0, pacific) 26 dfs(x, n-1, atlantic) 27 for y in range(n): 28 dfs(0, y, pacific) 29 dfs(m-1, y, atlantic) 30 31 for x in range(m): 32 for y in range(n): 33 if pacific[x][y] and atlantic[x][y]: 34 res.append([x,y]) 35 return res
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