<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:

    struct DisjointSet
    {
        vector<int> size, parent;

        DisjointSet(int v)
        {
            this->size.resize(v, 1);
            this->parent.resize(v);
            for (int i = 0; i < v; ++i)
                this->parent[i] = i;
        }

        int get_parent(int node)
        {
            if (node == this->parent[node])
                return node;
            return this->parent[node] = this->get_parent(this->parent[node]);
        }

        void union_by_size(int u, int v)
        {
            int ult_par_u = this->get_parent(u);
            int ult_par_v = this->get_parent(v);

            if (ult_par_u == ult_par_v)
                return;
            
            if(this->size[ult_par_u] > this->size[ult_par_v])
            {
                this->parent[ult_par_v] = ult_par_u;
                this->size[ult_par_u] += this->size[ult_par_v];
            }
            else
            {
                this->parent[ult_par_u] = ult_par_v;
                this->size[ult_par_v] += this->size[ult_par_u];
            }
        }
    };


    int maxAreaOfIsland(vector<vector<int>>& grid) {
        int max_area = 0, n = grid.size(), m = grid[0].size();

        DisjointSet ds = DisjointSet(n * m);

        for (int i = 0; i < grid.size(); ++i)
        {
            for (int j = 0; j < grid[0].size(); ++j)
            {
                if(grid[i][j])
                {
                    if(i + 1 < n and grid[i + 1][j])
                    {
                        ds.union_by_size((i * m) + j, (i + 1) * m + j);
                        max_area = max({max_area, ds.size[ds.get_parent((i * m) + j)], ds.size[ds.get_parent((i + 1) * m + j)]});
                    }
                    if(j + 1 < m and grid[i][j + 1])
                    {
                        ds.union_by_size((i * m) + j, (i) * m + j + 1);
                        max_area = max({max_area, ds.size[ds.get_parent((i * m) + j)], ds.size[ds.get_parent((i) * m + j + 1)]});
                    }
                    else
                        max_area = max(max_area, 1);
                }
            }
        }
        return max_area;
    }
};
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