<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>parent;
    vector<int>size;
    DisjointSet(int n){
        for(int i=0;i<n;i++){
            parent.push_back(i);
            size.push_back(1);
        }
    }
    int findParent(int n){
        if(parent[n]==n)return n;
        return parent[n]=findParent(parent[n]);
    }
    bool unionbysize(int u,int v){
        int pu=findParent(u);
        int pv=findParent(v);
        if(pu==pv)return false;
        if(size[pu]<size[pv]){
            parent[pu]=pv;
            size[pv]+=size[pu];
        }else{
            parent[pv]=pu;
            size[pu]+=size[pv];
        }
        return true;
    }
};
class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        vector<vector<int>>vis(n,vector<int>(n));
        int dr[]={-1,0,1,0};
        int dc[]={0,1,0,-1};
        DisjointSet d(n*n);
        for(int r=0;r<n;r++){
            for(int c=0;c<n;c++){
                if(grid[r][c]==1){
                    for(int i=0;i<4;i++){
                        int nr=r+dr[i];
                        int nc=c+dc[i];
                        if(nr>=0 && nc>=0 && nr<n && nc<n && grid[nr][nc]==1){
                            int node=r*n+c;
                            int adjnode=nr*n+nc;
                            if(d.findParent(node)!=d.findParent(adjnode)){
                                d.unionbysize(node,adjnode);
                            }
                        }
                    }
                }
            }
        }
        int maxi=0,ans=0;
        for(int r=0;r<n;r++){
            for(int c=0;c<n;c++){
                if(grid[r][c]==0){
                    set<int>st;
                    for(int i=0;i<4;i++){
                        int nr=r+dr[i];
                        int nc=c+dc[i];
                        if(nr>=0 && nc>=0 && nr<n && nc<n && grid[nr][nc]==1){
                            int adjnode=nr*n+nc;
                            int p=d.findParent(adjnode);
                            st.insert(p);
                        }
                    }
                    int size=0;
                    for(auto it:st){
                        size+=d.size[it];
                    }
                    ans=max(ans,size+1);
                }
            }
        }
        for(int i=0;i<n*n;i++){
            ans=max(ans,d.size[i]);
        }
        return ans;
    }
};
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