<p>You are given an <code>m x n</code> binary matrix <code>grid</code>. An island is a group of <code>1</code>&#39;s (representing land) connected <strong>4-directionally</strong> (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.</p>

<p>The <strong>area</strong> of an island is the number of cells with a value <code>1</code> in the island.</p>

<p>Return <em>the maximum <strong>area</strong> of an island in </em><code>grid</code>. If there is no island, return <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/05/01/maxarea1-grid.jpg" style="width: 500px; height: 310px;" />
<pre>
<strong>Input:</strong> 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]]
<strong>Output:</strong> 6
<strong>Explanation:</strong> The answer is not 11, because the island must be connected 4-directionally.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[0,0,0,0,0,0,0,0]]
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
public:
    // Helper function to perform DFS on the grid and calculate the area of the island
    int helper(vector<vector<int>>& grid, int i, int j){
        // Base case: check for invalid indices or if the current cell is water ('0')
        if(i<0 || j<0 || i>=grid.size() || j>=grid[0].size() || grid[i][j] == 0)
            return 0;

        // Mark the current cell as visited by setting it to '0'
        grid[i][j] = 0;

        // Initialize the area of this island to 1 (current cell)
        int area = 1;

        // Recursively calculate the area of the island by exploring all adjacent cells
        area += helper(grid, i+1, j); // Down
        area += helper(grid, i, j+1); // Right
        area += helper(grid, i-1, j); // Up
        area += helper(grid, i, j-1); // Left

        return area;
    }

    // Main function to find the maximum area of an island
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        int maxArea = 0; // Initialize the maximum area to 0

        // Iterate over each cell in the grid
        for(int i = 0; i < grid.size(); i++){
            for(int j = 0; j < grid[0].size(); j++){
                // If the cell contains '1' (land), calculate the area of the island
                if(grid[i][j] == 1){
                    // Use DFS to find the area of the island and update the maximum area
                    maxArea = max(maxArea, helper(grid, i, j));
                }
            }
        }
        return maxArea; // Return the maximum area of any island found
    }
};

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