<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 Disjoint{
    public :
    vector<int> parent,size;
    Disjoint(int n){
      parent.resize(n+1);
      size.resize(n+1,1);
      for(int i=0;i<n+1;i++){
        parent[i] = i;
      }
    }
    int findUp(int n){
        if(parent[n]==n) return n;
        return parent[n] = findUp(parent[n]);
    }
    void join(int u,int v){
        int pu = findUp(u);
        int pv = findUp(v);
        if(pu==pv) return;
        else if(size[pu]<size[pv]){
            parent[pu] = pv;
            size[pv]+=size[pu];
        }
        else{
            parent[pv] = pu;
            size[pu]+=size[pv];
        }
    }
};
class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        Disjoint ds(n*n);
        queue<pair<int,int>> q;
        int ax[4] = {1,-1,0,0};
        int ay[4] = {0,0,-1,1};
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
               if(grid[i][j]==0) q.push({i,j});
               else{
               for(int k=0;k<4;k++){
                int x = i + ax[k];
                int y = j + ay[k];
                if(x>=0 && x<n && y>=0 && y<n && grid[x][y]!=0){
                    
                    ds.join(i*n+j,x*n+y);
                }
               }
               }
            }
        }
        int m = 0;
         while(!q.empty()){
               int i=q.front().first;;
               int j = q.front().second;
               q.pop();
               if(grid[i][j]==1) continue;
               set<int> tmp;
               for(int k=0;k<4;k++){
                int x = i + ax[k];
                int y = j + ay[k];
                if(x>=0 && x<n && y>=0 && y<n && grid[x][y]!=0){
                    
                    tmp.insert(ds.findUp(x*n+y));
                }
               }
               int t=0;
               for(auto x : tmp){
                 t+=ds.size[x];
                }
                m=max(m,t+1);
            
        }

        return m==0 ? n*n : m;
    }
};
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