Pacific Atlantic Water Flow 解答

Posted 2020-11-13 ireneyanglan

Question

Given an m x n matrix of non-negative integers representing the height of each unit cell in a continent, the "Pacific ocean" touches the left and top edges of the matrix and the "Atlantic ocean" touches the right and bottom edges.

Water can only flow in four directions (up, down, left, or right) from a cell to another one with height equal or lower.

Find the list of grid coordinates where water can flow to both the Pacific and Atlantic ocean.

Note:

1. The order of returned grid coordinates does not matter.
2. Both m and n are less than 150.

Example:

Given the following 5x5 matrix:

  Pacific ~   ~   ~   ~   ~ 
       ~  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  *
          *   *   *   *   * Atlantic

Return:

[[0, 4], [1, 3], [1, 4], [2, 2], [3, 0], [3, 1], [4, 0]] (positions with parentheses in above matrix).

Solution

这道题的解题思路与Surrounded Regions类似。

已知在边缘上的点一定能到达Pacific或Atlantic，我们从边缘上的点开始遍历(BFS/DFS)，得到所有能到达Pacific或Atlantic的点，最后取交集就是答案。

DFS

 1 class Solution:
 2     def pacificAtlantic(self, matrix: List[List[int]]) -> List[List[int]]:
 3         if not matrix or not matrix[0]:
 4             return []
 5         m, n = len(matrix), len(matrix[0])
 6         result = []
 7         self.directions = [[0, -1], [0, 1], [-1, 0], [1, 0]]
 8         pacific = [[False for i in range(n)] for j in range(m)]
 9         atlantic = [[False for i in range(n)] for j in range(m)]
10         # DFS
11         for i in range(m):
12             self.dfs(matrix, pacific, matrix[i][0], i , 0)
13             self.dfs(matrix, atlantic, matrix[i][n - 1], i, n - 1)
14         for i in range(n):
15             self.dfs(matrix, pacific, matrix[0][i], 0, i)
16             self.dfs(matrix, atlantic, matrix[m - 1][i], m - 1, i)
17             
18         for i in range(m):
19             for j in range(n):
20                 if pacific[i][j] and atlantic[i][j]:
21                     result.append([i, j])
22         return result
23         
24     def dfs(self, matrix: List[List[int]], visited: List[List[bool]], pre: int, i: int, j: int) -> None:
25         m, n = len(matrix), len(matrix[0])
26         if i < 0 or i >= m or j < 0 or j >= n or visited[i][j] or matrix[i][j] < pre:
27             return
28         visited[i][j] = True
29         for direction in self.directions:
30             self.dfs(matrix, visited, matrix[i][j], i + direction[0], j + direction[1])

 

BFS

 1 from collections import deque
 2 class Solution:
 3     def pacificAtlantic(self, matrix: List[List[int]]) -> List[List[int]]:
 4         if not matrix or not matrix[0]:
 5             return []
 6         m, n = len(matrix), len(matrix[0])
 7         result = []
 8         self.directions = [[0, -1], [0, 1], [-1, 0], [1, 0]]
 9         pacific = [[False for i in range(n)] for j in range(m)]
10         atlantic = [[False for i in range(n)] for j in range(m)]
11         # BFS
12         for i in range(m):
13             self.bfs(matrix, pacific, i , 0)
14             self.bfs(matrix, atlantic, i, n - 1)
15         for i in range(n):
16             self.bfs(matrix, pacific, 0, i)
17             self.bfs(matrix, atlantic, m - 1, i)
18             
19         for i in range(m):
20             for j in range(n):
21                 if pacific[i][j] and atlantic[i][j]:
22                     result.append([i, j])
23         return result
24         
25     def bfs(self, matrix: List[List[int]], visited: List[List[bool]], i: int, j: int) -> None:
26         # Avoid duplicate calculation
27         if visited[i][j]:
28             return
29         m, n = len(matrix), len(matrix[0])
30         visited[i][j] = True
31         level = deque()
32         level.append((i, j))
33         while level:
34             L = len(level)
35             for _ in range(L):
36                 curr_i, curr_j = level.popleft()
37                 for direction in self.directions:
38                     next_i = curr_i + direction[0]
39                     next_j = curr_j + direction[1]
40                     if 0 <= next_i < m and 0 <= next_j < n and not visited[next_i][next_j] and matrix[next_i][next_j] >= matrix[curr_i][curr_j]:
41                         visited[next_i][next_j] = True
42                         level.append((next_i, next_j))