<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:
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        if (grid.empty()) {
            return 0;
        }

        int area = 0;
        int rows = grid.size();
        int cols = grid[0].size();
        vector<vector<bool>> visited(rows, vector<bool>(cols, false));  // Keep track of all the visited "1"s

        // Lambda function for DFS traversal
        auto dfs = [&](int r, int c, auto& dfs_ref) -> int {
            if (r < 0 || r >= rows || c < 0 || c >= cols || grid[r][c] == 0 || visited[r][c]) {
                return 0;
            }

            visited[r][c] = true;

            // Check the neighbors (up, down, left, right)
            return 1 + dfs_ref(r + 1, c, dfs_ref) + dfs_ref(r - 1, c, dfs_ref) +
                        dfs_ref(r, c + 1, dfs_ref) + dfs_ref(r, c - 1, dfs_ref);
        };

        for (int r = 0; r < rows; ++r) {
            for (int c = 0; c < cols; ++c) {
                if (grid[r][c] == 1 && !visited[r][c]) {
                    area = max(area, dfs(r, c, dfs));
                }
            }
        }

        return area;
    }
};
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