<p>You are given an <code>n x n</code> binary matrix <code>grid</code>. You are allowed to change <strong>at most one</strong> <code>0</code> to be <code>1</code>.</p>

<p>Return <em>the size of the largest <strong>island</strong> in</em> <code>grid</code> <em>after applying this operation</em>.</p>

<p>An <strong>island</strong> is a 4-directionally connected group of <code>1</code>s.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,0],[0,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> Change one 0 to 1 and connect two 1s, then we get an island with area = 3.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1],[1,0]]
<strong>Output:</strong> 4
<strong>Explanation: </strong>Change the 0 to 1 and make the island bigger, only one island with area = 4.</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1],[1,1]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> Can&#39;t change any 0 to 1, only one island with area = 4.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
public:
    class Ds {
        

    public:
    vector<int> rank, parent, size;
        Ds(int n) {
            rank.resize(n + 1, 0);
            size.resize(n + 1, 1);
            parent.resize(n + 1, 0);
            for (int i = 0; i <= n; i++) {
                parent[i] = i;
            }
        }
        int find(int node) {
            if (node == parent[node]) {
                return node;
            }
            return parent[node] = find(parent[node]);
        }
   void unionn(int node1, int node2) {
    int par1 = find(node1);
    int par2 = find(node2);
    if (par1 == par2) {
        return;
    }
    
    if (size[par1] >= size[par2]) {
        parent[par2] = par1;
        size[par1] += size[par2];
    } else {
        parent[par1] = par2;
        size[par2] += size[par1];
    }
}


    }; int largestIsland(vector<vector<int>>& grid) {  int n = grid.size();
        vector<vector<int>> vis(n, vector<int>(n, 0));
      
        Ds ds(n * n);
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 1 && !vis[i][j]) {
                     vis[i][j] = 1; 
                    int node = n * i + j;
                    vector<int> dr = {-1, 0, 0, 1};
                    vector<int> dc = {0, 1, -1, 0};
                    for (int k = 0; k < 4; k++) {
                        int nr = i + dr[k];
                        int nc = j + dc[k];
                        if (nr >= 0 && nc >= 0 && nr < n && nc < n &&
                            vis[nr][nc] && grid[nr][nc] == 1) {
                            int nodeval = nr * n + nc;
                            if (ds.find(node) != ds.find(nodeval)) {
                                ds.unionn(node, nodeval);
                            }
                        }
                    }
                }
            }
     }
     int maxsize=0;
      int flag=0;
      for(int i=0;i<n;i++)
      {
        for(int j=0;j<n;j++)
        {
             if (grid[i][j] == 0)
             {   
                   flag=1;
                    int node = n * i + j;
                    unordered_set<int>unique;
                    vector<int> dr = {-1, 0, 0, 1};
                    vector<int> dc = {0, 1, -1, 0};
                    int size=1;

                    for (int k = 0; k < 4; k++) {
                        int nr = i + dr[k];
                        int nc = j + dc[k];
                        if (nr >= 0 && nc >= 0 && nr < n && nc < n &&
                             grid[nr][nc] == 1) {
                            int nodeval = nr * n + nc;
                            int parent=ds.find(nodeval);
                            if(unique.find(parent)==unique.end())
                            {int nodesize=ds.size[parent];
                            size+=nodesize;
                             unique.insert(parent);
                            }
                        }
                    }
                    maxsize=max(maxsize,size);
             }
        }
      }
      if(flag)
  {    return maxsize;}
  return n*n;
    }
};
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