*This is part of a series of Leetcode solution explanations (index). If you liked this solution or found it useful,* *please like**this post and/or* *upvote**my solution post on Leetcode’s forums.*

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Leetcode Problem #695 (*Medium*): Max Area of Island

####

*Description:*

*Description:*

(*Jump to*: *Solution Idea* || *Code*: *JavaScript* | *Python* | *Java* | *C++*)

You are given an

`m x n`

binary matrix grid. An island is a group of`1`

‘s (representing land) connected4-directionally(horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.The

areaof an island is the number of cells with a value`1`

in the island.Return

the maximum. If there is no island, returnareaof an island in grid`0`

.

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*Examples:*

*Examples:*

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. Visual:

Example 2: Input: grid = [[0,0,0,0,0,0,0,0]] Output: 0

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*Constraints:*

*Constraints:*

`m == grid.length`

`n == grid[i].length`

`1 <= m, n <= 50`

`grid[i][j]`

is either`0`

or`1`

.

####

*Idea:*

*Idea:*

(*Jump to*: *Problem Description* || *Code*: *JavaScript* | *Python* | *Java* | *C++*)

So we can just use a simple iteration through the **grid** and look for islands. When we find an island, we can use a **recursive** helper function (**trav**) to sum up all the connected pieces of land and **return** the total land mass of the island.

As we traverse over the island, we can replace the **1**s with **0**s to prevent “finding” the same land twice. We can also keep track of the largest island found so far (**ans**), and after the **grid** has been fully traversed, we can **return ans**.

**Time Complexity: O(N * M)**where**N**and**M**are the lengths of the sides of the**grid**-
**Space Complexity: O(L)**where**L**is the size of the largest island, representing the maximum**recursion stack***or***O(N * M + L)**if we create an**N * M**matrix in order to not modify the input

####

*Javascript Code:*

*Javascript Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

```
var maxAreaOfIsland = function(grid) {
let ans = 0, n = grid.length, m = grid[0].length
const trav = (i, j) => {
if (i < 0 || j < 0 || i >= n || j >= m || !grid[i][j]) return 0
grid[i][j] = 0
return 1 + trav(i-1, j) + trav(i, j-1) + trav(i+1, j) + trav(i, j+1)
}
for (let i = 0; i < n; i++)
for (let j = 0; j < m; j++)
if (grid[i][j]) ans = Math.max(ans, trav(i, j))
return ans
};
```

####

*Python Code:*

*Python Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

```
class Solution:
def maxAreaOfIsland(self, grid: List[List[int]]) -> int:
ans, n, m = 0, len(grid), len(grid[0])
def trav(i: int, j: int) -> int:
if i < 0 or j < 0 or i >= n or j >= m or grid[i][j] == 0: return 0
grid[i][j] = 0
return 1 + trav(i-1, j) + trav(i, j-1) + trav(i+1, j) + trav(i, j+1)
for i, j in product(range(n), range(m)):
if grid[i][j]: ans = max(ans, trav(i, j))
return ans
```

####

*Java Code:*

*Java Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

```
class Solution {
private int n, m;
public int maxAreaOfIsland(int[][] grid) {
int ans = 0;
n = grid.length;
m = grid[0].length;
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
if (grid[i][j] > 0) ans = Math.max(ans, trav(i, j, grid));
return ans;
}
private int trav(int i, int j, int[][] grid) {
if (i < 0 || j < 0 || i >= n || j >= m || grid[i][j] < 1) return 0;
grid[i][j] = 0;
return 1 + trav(i-1, j, grid) + trav(i, j-1, grid) + trav(i+1, j, grid) + trav(i, j+1, grid);
}
}
```

####

*C++ Code:*

*C++ Code:*

(*Jump to*: *Problem Description* || *Solution Idea*)

```
class Solution {
public:
int maxAreaOfIsland(vector<vector<int>>& grid) {
int ans = 0;
n = grid.size(), m = grid[0].size();
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++)
if (grid[i][j]) ans = max(ans, trav(i, j, grid));
return ans;
}
private:
int n, m;
int trav(int i, int j, vector<vector<int>>& grid) {
if (i < 0 || j < 0 || i >= n || j >= m || !grid[i][j]) return 0;
grid[i][j] = 0;
return 1 + trav(i-1, j, grid) + trav(i, j-1, grid) + trav(i+1, j, grid) + trav(i, j+1, grid);
}
};
```