# 695. Max Area of Island

### Description

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`.

### Constraints

* `m == grid.length`
* `n == grid[i].length`
* `1 <= m, n <= 50`
* `grid[i][j]` is either `0` or `1`.

### Approach

### Links

* Binarysearch
* GeeksforGeeks
* [Leetcode](https://leetcode.com/problems/max-area-of-island/)
* ProgramCreek
* YouTube

### **Examples**

{% tabs %}
{% tab title="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.

<div align="left"><img src="/files/-Mb7cYHAkPt-2px_3hx_" alt=""></div>
{% endtab %}

{% tab title="Example 2" %}
**Input:** grid = \[\[0,0,0,0,0,0,0,0]]

**Output:** 0
{% endtab %}
{% endtabs %}

### **Solutions**

{% tabs %}
{% tab title="Solution 1" %}

```java
/**
 * Time complexity : O(R*C), where R is the number of rows in the given grid, 
 *    and C is the number of columns. We visit every square once.
 * Space complexity : O(R*C), the space used by seen to keep track of 
 *    visited squares, and the space used by stack.
 */

class Solution {
    public int maxAreaOfIsland(int[][] grid) {
        int maxArea = 0;
        if(grid != null && grid.length != 0) {
            int rows = grid.length, cols = grid[0].length;
            for(int i = 0; i < rows; i++) {
                for(int j = 0; j < cols; j++) {
                    if(grid[i][j] == 1) {
                        maxArea = Math.max(maxArea, calcArea(grid, i, j));
                    }
                }
            }
        }
        return maxArea;
    }
    
    private int calcArea(int[][] grid, int x, int y) {
        if(x < 0 || x >= grid.length || 
            y < 0 || y >= grid[0].length || grid[x][y] != 1) {
            return 0;
        }
        grid[x][y] = 2;
        return 1 + calcArea(grid, x-1, y) + calcArea(grid, x, y+1) + 
                calcArea(grid, x+1, y) + calcArea(grid, x, y-1);
    }
}
```

{% endtab %}
{% endtabs %}

### **Follow up**

*


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