<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 m;
    int n;
    
    vector<vector<int>> mGrid;

    
    
    vector<vector<int>> seen;
    vector<vector<int>> directions = {{0,1},{1,0},{0,-1},{-1,0}};
    
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        
        int maxSizeSoFar = 0;
        mGrid = grid;
        m = grid.size();
        n = grid[0].size();
        seen = vector(m, vector<int>(n, 0));
        
        for (int i=0; i<m; i++)
        {
            for (int j=0; j<n; j++)
            {
                int size = 0;               
                if (grid[i][j] == 1 && (!seen[i][j]))
                {
                    seen[i][j] = 1;
                    size++;
                    dfs(i,j,size);
                    
                    // ok we are done growing the island, compare its size to max so far
                    if (size > maxSizeSoFar)
                    {
                        maxSizeSoFar = size;
                    }
                }
            }
        }
        return maxSizeSoFar;         
    }
    
    void dfs(int row, int col, int& size)
    {
        for (vector<int>& direction : directions)
        {
            int nextRow = row + direction[0];
            int nextCol = col + direction[1];
            
            if (valid(nextRow, nextCol) && !seen[nextRow][nextCol])
            {
                seen[nextRow][nextCol] = 1;
                size++;
                
                dfs(nextRow, nextCol, size);
            }
        }
    }
    
    
    bool valid(int row, int col)
    {
        if (0 <= row && row < m && 0 <= col && col < n && mGrid[row][col] == 1)
            return true;
            
        return false;
    }
    
};


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