<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>> directions;
    vector<vector<bool>> seen;
    vector<vector<int>> grid;

    int maxAreaOfIsland(vector<vector<int>>& grid) {
        int maxArea=0;
        this->m = grid.size();
        this->n = grid[0].size();
        this->directions = {{0,1}, {1,0}, {0,-1}, {-1,0}};
        seen = vector(m, vector(n, false));
        this->grid = grid;
        for(int i=0; i<m; i++) {
            for(int j=0; j<n; j++) {
                if(grid[i][j]== 0 || seen[i][j]) {
                    continue;
                }
                int area = dfs(i,j);
                maxArea = max(maxArea, area);
            }
        }
        return maxArea;
    }

    int dfs(int x, int y) {
        int ans=0;
        if(seen[x][y] || grid[x][y]==0) {
            return 0;
        }

        if(grid[x][y] == 1) {
            seen[x][y] = true;
            ans++;
        }

        for(auto dir : directions) {
            int nextX = x + dir[0];
            int nextY = y + dir[1];
            if(!inBound(nextX, nextY)) { continue;}
            ans += dfs(nextX, nextY);
        }

        return ans;
    }

    bool inBound(int x, int y) {
        return (x>=0 && x<m && y>=0 && y<n);
    }


};
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