<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 {
    int m, n;
    std::vector<std::vector<bool>> seen;

    bool isValid(const vector<vector<int>>& grid, int row, int col) {
        return (0 <= row && row < m && 0 <= col && col < n && grid[row][col] == 1 && !seen[row][col]);
    }

    int dfs(const vector<vector<int>>& grid, int row, int col) {
        vector<pair<int, int>> directions = {{0,1}, {1,0}, {0,-1}, {-1, 0}};

        int subIslandArea = 0;

        for(auto& dir: directions) {
            int neighbor_row = row + dir.first;
            int neighbor_col = col + dir.second;
            if(isValid(grid, neighbor_row, neighbor_col)) {
                seen[neighbor_row][neighbor_col] = true;
                subIslandArea += dfs(grid, neighbor_row, neighbor_col);
            }
        }

        return subIslandArea + 1;
    }

public:
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        m = grid.size();
        n = grid[0].size();
        seen = vector(m, vector(n, false));

        int ans = 0;
        for(int row = 0; row < m; row++) {
            for(int col = 0; col < n; col++) {
                if(isValid(grid, row, col)) {
                    seen[row][col] = true;
                    int islandArea = dfs(grid, row, col);
                    ans = std::max(ans, islandArea);
                }
            }
        }

        return ans;
    }
};
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