<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 DSU{
public:
    vector<int> size,parent;
    DSU(int n){
        size.resize(n+1,1);
        parent.resize(n+1);
        for(int i=0;i<n;i++){
            parent[i]=i;
        }
    }
    int findUltimateParent(int node){
        if(node==parent[node]) return node;
        return parent[node]=findUltimateParent(parent[node]);
    }
    void unionByRank(int u,int v){
        int ulp_u=findUltimateParent(u);
        int ulp_v=findUltimateParent(v);
        if(ulp_u==ulp_v) return;
        if(size[ulp_u]<size[ulp_v]){
            parent[ulp_u]=ulp_v;
            size[ulp_v]+=size[ulp_u];
        }else{
            parent[ulp_v]=ulp_u;
            size[ulp_u]+=size[ulp_v];
        }
    }
};
class Solution {
public:
    int isValid(int i,int j,vector<vector<int>>& grid){
       int n=grid.size();
       if(i>=0 && i<n && j>=0 && j<n){
        return 1;
       }
       return 0; 
    }
    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        vector<vector<int>> vis(n,vector<int> (n,0));
        DSU 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]==0){
                    int r=i;
                    int c=j;
                    int node=i*n+j;
                    int dr[]={-1,0,1,0};
                    int dc[]={0,-1,0,1};
                    for(int ind=0;ind<4;ind++){
                        int ar=r+dr[ind];
                        int ac=c+dc[ind];
                        int aNode=ar*n+ac;
                        if(isValid(ar,ac,grid) && grid[ar][ac]==1){
                            if(!vis[ar][ac]){
                                ds.unionByRank(node,aNode);
                            }
                        }
                    }
                }
            }
        }
        int ans=INT_MIN;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                int r=i;
                int c=j;
                int node=i*n+j;
                ans=max(ans,ds.size[node]);
            }
        }
        cout<<ans<<endl;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==0){
                    int r=i;
                    int c=j;
                    int node=i*n+j;
                    int dr[]={-1,0,1,0};
                    int dc[]={0,-1,0,1};
                    int cnt=1;
                    set<int> st;
                    for(int ind=0;ind<4;ind++){
                        int ar=r+dr[ind];
                        int ac=c+dc[ind];
                        int aNode=ar*n+ac;
                        if(isValid(ar,ac,grid) && grid[ar][ac]==1){
                            int ulp_an=ds.findUltimateParent(aNode);
                            st.insert(ulp_an);
                        }
                    }
                    for(auto it:st){
                        cnt+=ds.size[it];
                    }
                    ans=max(ans,cnt);
                }
            }
        }
        return ans;
    }
};
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