<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> rank, parent, size;

    disjoint(int n)
    {
        rank.resize(n + 1, 0);
        parent.resize(n + 1);
        size.resize(n + 1, 1);
        for (int i = 0; i <= n; i++)
        {
            parent[i] = i;
        }
    }
    int findPar(int node)
    {
        if (node == parent[node])
        {
            return node;
        }
        return parent[node] = findPar(parent[node]);
    }
    void unionByRank(int u, int v)
    {
        int pu = findPar(u);
        int pv = findPar(v);

        if (pu == pv)
        {
            return;
        }
        if (rank[pu] < rank[pv])
        {
            parent[pu] = pv;
        }
        else if (rank[pu] > rank[pv])
        {
            parent[pv] = pu;
        }
        else
        {
            parent[pu] = pv;
            rank[pv]++;
        }
        return;
    }
    void unionBySize(int u, int v)
    {
        int pu = findPar(u);
        int pv = findPar(v);

        if (pu == pv)
        {
            return;
        }
        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);
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                vector<int> coor ={1,0,-1,0,1};
                if(grid[i][j]==1){
                    for(int k=0;k<4;k++){
                        int nr = i+coor[k];
                        int nc = j+coor[k+1];
                        if(nr>=0 && nc>=0 && nr<n && nc<n){
                            if(grid[nr][nc]==1){
                                ds.unionBySize((i*n)+j,(nr*n) + nc);
                            }
                        }
                    }
                }
            }
        }
        int ans=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                vector<int> coor ={1,0,-1,0,1};
                if(grid[i][j]==0){
                    int x=1;
                    set<int> up;
                    for(int k=0;k<4;k++){
                        int nr = i+coor[k];
                        int nc = j+coor[k+1];
                        if(nr>=0 && nc>=0 && nr<n && nc<n){
                            if(grid[nr][nc]==1){
                                int node = ds.findPar(nr*n +nc);
                                if(up.find(node)==up.end()){
                                    x+=ds.size[node];
                                }
                                up.insert(node);
                            }
                        }
                    }
                    ans=max(ans,x);
                    
                }
            }
        }
        if(ans==0){
            return *max_element(ds.size.begin(),ds.size.end());
        }
        return ans;
    }
};
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