<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:
    bool vis[55][55];
    int n, m;
    int ans;
    int mx;
    vector<pair<int, int>> d = {{0, 1}, {0, -1}, {-1, 0}, {1, 0}};
    bool valid(int si, int sj) {
        if (si < 0 || si >= n || sj < 0 || sj >= m)
            return false;
        return true;
    }
    void dfs(int si, int sj, vector<vector<int>>& grid) {
        vis[si][sj] = true;
        ans++;
        for (int i = 0; i < 4; i++) {
            int ci = si + d[i].first;
            int cj = sj + d[i].second;
            if (valid(ci, cj) && vis[ci][cj] == false && grid[ci][cj] == 1) {
                dfs(ci, cj,grid);
            }
        }
    }
    
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        n = grid.size();
        m = grid[0].size();

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (grid[i][j] == 1) {
                    ans = 0;
                    dfs(i, j, grid);
                    mx = max(mx,ans);
                }
            }
        }
        return mx;
    }
};
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