### View *Max Area of Island* on LeetCode

## Statistics

**Time Spent Coding**

10 minutes

**Time Complexity**

O(n * m) - Every cell in the matrix must be visited at least once, resulting in the O(n * m) time complexity.

**Space Complexity**

O(n * m) - Assuming every cell in the matrix is `1`

, there could be n * m recursive calls active simultaneously, resulting in the O(n * m) space complexity.

**Runtime Beats**

98.32% of other submissions

## Explanation

The algorithm explores all non-diagonal directions from every found island and returns the sum of its area. During the exploration of an island, it is “sunk” by being changed to 0 to eliminate repetition of the island.

The algorithm uses depth-first search by fully exploring all directions from the first island until no further islands can be explored. When this condition is met, the sum of islands is sent backward through all the recursive calls to be compared to the current `max_area`

finally.

## Algorithm Used

**Depth-First Search -** An algorithm for traversing a tree/matrix data structure. The algorithm begins at the root and searches until it can not continue any deeper. Once at the deepest point, the algorithm works backward until all the nodes/cells have been visited.

## Solution

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37

class Solution:
def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
max_r = len(grid)
max_c = len(grid[0])
max_area = 0
directions = ((1,0),(-1,0),(0,1),(0,-1))
def explore(r,c):
# Sink the island
grid[r][c] = 0
cur_area = 0
for x,y in directions:
new_c = c + x
new_r = r + y
# Ensure the next island is valid
if new_c < 0 or new_c >= max_c: continue
if new_r < 0 or new_r >= max_r: continue
if grid[new_r][new_c] == 0: continue
# Increase the area and explore another connected island
cur_area += explore(new_r,new_c) + 1
return cur_area
for i in range(max_r):
for j in range(max_c):
if grid[i][j] == 1:
# Explore all attached islands and update max_area
max_area = max(max_area,explore(i,j)+1)
return max_area