题目
You are given an m x n
binary matrix grid
. 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.
The area of an island is the number of cells with a value 1
in the island.
Return the maximum area of an island in grid
. If there is no island, return 0
.
Example 1:
Input: grid = [[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]]
Output: 6
Explanation: The answer is not 11, because the island must be connected 4-directionally.
Example 2:
Input: grid = [[0,0,0,0,0,0,0,0]]
Output: 0
Constraints:
m == grid.length
n == grid[i].length
1 <= m, n <= 50
grid[i][j]
is either0
or1
.
思路
dfs,自上而下将问题分解为求当前位置与上下左右位置面积的子问题,然后相加这些求得的面积。
代码
python版本:
class Solution:
def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
def dfs(i, j):
if i < 0 or i >= len(grid) or j < 0 or j >= len(grid[0]) or grid[i][j] == 0:
return 0
grid[i][j] = 0
return dfs(i-1, j)+dfs(i+1, j)+dfs(i, j-1)+dfs(i, j+1)+1
res = [dfs(i, j) for i in range(len(grid)) for j in range(len(grid[0]))]
return max(res)