Given an m x n matrix of nonnegative 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: 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. :type matrix: ListListint :rtype: ListListint
# 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:

# 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).

def pacific_atlantic(matrix):
    """
    :type matrix: List[List[int]]
    :rtype: List[List[int]]
    """
    n = len(matrix)
    if not n: return []
    m = len(matrix[0])
    if not m: return []
    res = []
    atlantic = [[False for _ in range (n)] for _ in range(m)]
    pacific =  [[False for _ in range (n)] for _ in range(m)]
    for i in range(n):
        dfs(pacific, matrix, float("-inf"), i, 0)
        dfs(atlantic, matrix, float("-inf"), i, m-1)
    for i in range(m):
        dfs(pacific, matrix, float("-inf"), 0, i)
        dfs(atlantic, matrix, float("-inf"), n-1, i)
    for i in range(n):
        for j in range(m):
            if pacific[i][j] and atlantic[i][j]:
                res.append([i, j])
    return res

def dfs(grid, matrix, height, i, j):
    if i < 0 or i >= len(matrix) or j < 0 or  j >= len(matrix[0]):
        return
    if grid[i][j] or matrix[i][j] < height:
        return
    grid[i][j] = True
    dfs(grid, matrix, matrix[i][j], i-1, j)
    dfs(grid, matrix, matrix[i][j], i+1, j)
    dfs(grid, matrix, matrix[i][j], i, j-1)
    dfs(grid, matrix, matrix[i][j], i, j+1)
