<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:
    map<int, int> par;
    map<int, int> sz;

    int find(int a)
    {
        if (a == par[a])
        {
            return a;
        }
        return par[a] = find(par[a]);
    }
    void unite(int a, int b)
    {
        int par_a = find(a);
        int par_b = find(b);
        if (par_a != par_b)
        {
            if (sz[par_a] > sz[par_b])
            {
                par[par_b] = par_a;
                sz[par_a] += sz[par_b];
            }
            else
            {
                par[par_a] = par_b;
                sz[par_b] += sz[par_a];
            }
        }
    }
    int maxAreaOfIsland(vector<vector<int>> &grid)
    {
        int dx[4] = {-1, 1, 0, 0};
        int dy[4] = {0, 0, 1, -1};
        int n = grid.size();
        int m = grid[0].size();
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {

                int k =  i*m + j;
                par[k] = k;
              
                if (grid[i][j]==1)
                {
                    sz[k] = 1;
                }
            }
         
        }
     
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
                int k =  i*m + j; 
      
    if(grid[i][j]){

                for (int x = 0; x < 4; x++)
                {
                    int di = dx[x] + i;
                    int dj = dy[x] + j;
                    if (di >= 0 && di < n && dj >= 0 && dj < m && grid[di][dj]==1)
                    {
                        int r = di * m + dj;
                        unite(r, k);
                    }
                }}
            }
        }
        int mx = 0;
        for (int i = 0; i < n; i++)
        {
            for (int j = 0; j < m; j++)
            {
                int k = i * m + j;
                int par = find(k);
                mx = max(sz[par], mx);
            }
        }
        return mx;
    }
};
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