<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 DisjointSet{
    vector<int> rank, parent;
    int count;
    public:
    DisjointSet(int n){
        rank.resize(n,0);
        parent.resize(n);
        count=0;
        for(int i=0; i<n; i++){
            parent[i] = i;
        }
    }

    int findPar(int node){
        if(parent[node] == node) return node;
        return parent[node] = findPar(parent[node]);
    }

    void Union(int u, int v){
        int rootU = findPar(u);
        int rootV = findPar(v);

        if(rootU != rootV){
            if(rank[rootU] > rank[rootV]){
                parent[rootV] = rootU;
            }else if(rank[rootV] > rank[rootU]){
                parent[rootU] = rootV;
            }else{
                parent[rootV] = rootU;
                rank[rootU]++;
            }
        }
    }
};
class Solution {
public:
    int maxAreaOfIsland(vector<vector<int>>& grid) {
        int rows = grid.size();
        int cols = grid[0].size();
        DisjointSet ds(rows*cols);

        int directions[4][2] = {{-1,0}, {1,0}, {0,-1}, {0,1}};
        for(int i=0; i<rows; i++){
            for(int j=0; j<cols; j++){
                if(grid[i][j] == 1){
                    int currId = i*cols + j;
                    for(auto dir:directions){
                        int u = i + dir[0];
                        int v = j + dir[1];

                        if(u>=0 && v>=0 && u<rows && v<cols && grid[u][v] == 1){
                            int neighbourId = u*cols + v;
                            ds.Union(currId, neighbourId);
                        }
                    }

                }
            }
        }

        vector<int> area(rows*cols,0);
        int maxArea = 0;
        for(int i=0; i<rows; i++){
            for(int j=0; j<cols; j++){
                if(grid[i][j] == 1){
                    int id = i*cols + j;
                    int root = ds.findPar(id);
                    area[root]++;
                    maxArea = max(maxArea,area[root]);
                }
            }
        }

        return maxArea;
    }
};
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