Pacific-Atlantic water flow#

Levels: level-4

Data structures: graph

Algorithms: dfs, bfs

Practice Link#

LeetCode

Description#

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:

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

Example#

 1Input:
 2  Pacific ~   ~   ~   ~   ~
 3       ~  1   2   2   3  (5) *
 4       ~  3   2   3  (4) (4) *
 5       ~  2   4  (5)  3   1  *
 6       ~ (6) (7)  1   4   5  *
 7       ~ (5)  1   1   2   4  *
 8          *   *   *   *   * Atlantic
 9Output:
10[[0, 4], [1, 3], [1, 4], [2, 2], [3, 0], [3, 1], [4, 0]]
11(positions with parentheses in above matrix).

Python Solution#

 1class Solution(object):
 2    def pacificAtlantic(self, matrix):
 3        """
 4        :type matrix: List[List[int]]
 5        :rtype: List[List[int]]
 6        """
 7        if not matrix: return []
 8        self.directions = [(1, 0), (-1, 0), (0, 1), (0, -1)]
 9        m = len(matrix)
10        n = len(matrix[0])
11        p_visited = [[False for _ in range(n)] for _ in range(m)]
12
13        a_visited = [[False for _ in range(n)] for _ in range(m)]
14        result = []
15
16        for i in range(m):
17            # p_visited[i][0] = True
18            # a_visited[i][n-1] = True
19            self.dfs(matrix, i, 0, p_visited, m, n)
20            self.dfs(matrix, i, n - 1, a_visited, m, n)
21        for j in range(n):
22            # p_visited[0][j] = True
23            # a_visited[m-1][j] = True
24            self.dfs(matrix, 0, j, p_visited, m, n)
25            self.dfs(matrix, m - 1, j, a_visited, m, n)
26
27        for i in range(m):
28            for j in range(n):
29                if p_visited[i][j] and a_visited[i][j]:
30                    result.append([i, j])
31        return result
32
33    def dfs(self, matrix, i, j, visited, m, n):
34        # when dfs called, meaning its caller already verified this point
35        visited[i][j] = True
36        for dir in self.directions:
37            x, y = i + dir[0], j + dir[1]
38            if x < 0 or x >= m or y < 0 or y >= n or visited[x][
39                    y] or matrix[x][y] < matrix[i][j]:
40                continue
41            self.dfs(matrix, x, y, visited, m, n)