<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:
    int par[250001];
    int rnk[250001];
    
    void ini_set(int& V){
        for(int i=0;i<V;i++){
            par[i]=i;
            rnk[i]=1;
        }
    }
    
    int rep_set(int &V){
        if(par[V]==V) return V;
        par[V]=rep_set(par[V]);
        return par[V];
    }
    
    void merge_set(int &V1, int &V2){
        int repV1 = rep_set(V1);
        int repV2 = rep_set(V2);
        if(repV1==repV2) return;
        
        if(rnk[repV1]>=rnk[repV2]){
            par[repV2]=repV1;
            rnk[repV1]+=rnk[repV2];
        }
        else{
            par[repV1]=repV2;
            rnk[repV2]+=rnk[repV1];
        }
    }
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        int sz=n*n;
        ini_set(sz);
        vector<pair<int,int>>dir={{0,1},{0,-1},{1,0},{-1,0}};


        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==0) continue;
                int node = (i*n)+j;
                for(int k=0;k<4;k++){
                    auto d=dir[k];
                    int newi=i+d.first;
                    int newj=j+d.second;
                    if(newi>=0 && newi<n && newj>=0 && newj<n && grid[newi][newj]==1){
                        int newnode = (newi*n)+newj;
                        if(rep_set(node)==rep_set(newnode)) continue;
                        merge_set(node,newnode);
                    }
                }
            }
        }
        
        int ans=0;
        for(int i=0;i<(n*n);i++){
            if(par[i]==i) ans=max(ans,rnk[i]);
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1) continue;
                set<int>storepar;
                for(int k=0;k<4;k++){
                    auto d=dir[k];
                    int newi=i+d.first;
                    int newj=j+d.second;
                    if(newi>=0 && newi<n && newj>=0 && newj<n && grid[newi][newj]==1){
                        int newnode = (newi*n)+newj;
                        storepar.insert(rep_set(newnode));
                    }
                }
                int count=1;
                for(auto &p:storepar){
                    count+=rnk[p];
                }
                ans=max(ans,count);
            }
        }

        return ans;


    }
};
100096