# Time:  O(m * n)
# Space: O(1)

# Given a non-empty 2D array grid of 0's and 1's,
# an island is a group of 1's (representing land) connected 4-directionally (horizontal or vertical.)
# You may assume all four edges of the grid are surrounded by water.
#
# Find the maximum area of an island in the given 2D array. (If there is no island, the maximum area is 0.)
#
# Example 1:
# [[0,0,1,0,0,0,0,1,0,0,0,0,0],
#  [0,0,0,0,0,0,0,1,1,1,0,0,0],
#  [0,1,1,0,1,0,0,0,0,0,0,0,0],
#  [0,1,0,0,1,1,0,0,1,0,1,0,0],
#  [0,1,0,0,1,1,0,0,1,1,1,0,0],
#  [0,0,0,0,0,0,0,0,0,0,1,0,0],
#  [0,0,0,0,0,0,0,1,1,1,0,0,0],
#  [0,0,0,0,0,0,0,1,1,0,0,0,0]]
#
# Given the above grid, return 6. Note the answer is not 11,
# because the island must be connected 4-directionally.
#
# Example 2:
# [[0,0,0,0,0,0,0,0]]
#
# Given the above grid, return 0.
#
# Note: The length of each dimension in the given grid does not exceed 50.

class Solution(object):
    def maxAreaOfIsland(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        directions = [[-1,  0], [ 1,  0], [ 0,  1], [ 0, -1]]

        def dfs(i, j, grid, area):
            if not (0 <= i < len(grid) and \
                    0 <= j < len(grid[0]) and \
                    grid[i][j] > 0):
                return False
            grid[i][j] *= -1
            area[0] += 1
            for d in directions:
                dfs(i+d[0], j+d[1], grid, area)
            return True

        result = 0
        for i in xrange(len(grid)):
            for j in xrange(len(grid[0])):
                area = [0]
                if dfs(i, j, grid, area):
                    result = max(result, area[0])
        return result

Create max-area-of-island.py