<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:
    vector<vector<int>> directions = {{0, 1}, {1, 0}, {0, -1}, {-1, 0}};  // right, down, left, up
    vector<vector<bool>> visited;
    vector<vector<int>> grid;
    
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        this->grid = grid;

        int m = grid.size();
        int n = grid[0].size();
        
        visited = vector(m, vector<bool>(n, false));
        int maxSize = 0;
        
        for (int row = 0; row < m; row++) {
            for (int col = 0; col < n; col++) {
                // run dfs if valid square
                if (isValid(row, col) && visited[row][col] == false) {
                    maxSize = max(maxSize, dfs(row, col));   
                }
            }
        }
        
        return maxSize;
    }
    
    int dfs(int row, int col) {
        int sizeComp = 1;
        visited[row][col] = true;
        
        // iterate through valid neighbors and recursively run DFS from each
        for (auto& dir : directions) {
            int newRow = row + dir[0];
            int newCol = col + dir[1];
            if (isValid(newRow, newCol) && visited[newRow][newCol] == false) {
                sizeComp += dfs(newRow, newCol);
            }
        }
        
        return sizeComp;
    }
    
    bool isValid(int row, int col) {
        return row >= 0 && row < grid.size() && col >= 0 && col < grid[0].size() && grid[row][col] == 1;
    }
};
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