<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 DisjointSet{
    public:
	vector<int> size,parent;
	DisjointSet(int n ){
		size.resize(n+1,1);
		parent.resize(n+1,0);
		for(int i=0;i<=n;i++)parent[i]=i;
	}
	int findUpar(int node){
		if(node==parent[node])return node;
		return parent[node]=findUpar(parent[node]);
	}
	void unionbysize(int u,int v){
		int upu=findUpar(u);
		int upv=findUpar(v);
		if(upu==upv)return;
		if(size[upu]<size[upv]){
			parent[upu]=upv;
			size[upv]+=size[upu];
		}
		else {
			parent[upv]=upu;
			size[upu]+=size[upv];
		}
	}

};
class Solution {
public:
    bool isValid(int adjr,int adjc,int n){
        return (adjr<n && adjc<n && adjr>=0 && adjc>=0);
    }
    int largestIsland(vector<vector<int>>& grid) {
        int mx=0;
        int n= grid.size();
        DisjointSet ds(n*n);

        int dr[]={-1,0,1,0};
        int dc[]={0,1,0,-1};
        vector<vector<int>>vis(n,vector<int>(n,0));
        vector<vector<int>> sz(n,vector<int>(n,0));
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                int node= i*n+j;
                vis[i][j]=1;
                for(int ind=0;ind<4;ind++){
                    int adjr=dr[ind]+i;
                    int adjc=dc[ind]+j;
                    int adjnode= adjr*n+adjc;
                    if(isValid(adjr,adjc,n)){
                        if(grid[adjr][adjc]==1 && grid[i][j]==1 && vis[adjr][adjc]==0){
                            ds.unionbysize(adjnode,node);
                        }
                    }
                }
            }
        }
        mx=*max_element (ds.size.begin(), ds.size.end());
        // return mx;
        vector<int> vs(n*n,0);
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                int node= i*n+j;
                if(grid[i][j]==1)continue;
                int temp=1;

                for(int ind=0;ind<4;ind++){
                    int adjr=dr[ind]+i;
                    int adjc=dc[ind]+j;
                    int adjnode= adjr*n+adjc;
                    if(isValid(adjr,adjc,n)){
                        int par= ds.findUpar(adjnode);
                      if(vs[par]==0 && grid[adjr][adjc]==1)  temp=temp+ds.size[par];
                        vs[par]=1;
                    }
                }
                for(int ind=0;ind<4;ind++){
                    int adjr=dr[ind]+i;
                    int adjc=dc[ind]+j;
                    int adjnode= adjr*n+adjc;
                    if(isValid(adjr,adjc,n)){
                        int par= ds.findUpar(adjnode);
                        vs[par]=0;
                    }
                }
                mx=max(mx,temp);
            }
        }
         
         return mx;
    }
};
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