<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> parent;
    vector<int> size;
    
    dsu(int n)
    {
        for(int i=0;i<n;i++)
        {
            parent.push_back(i);
            size.push_back(1);
        }
    }
    
    int getparent(int u)
    {
        if(parent[u] == u)
        {
            return u;
        }
        
        int pu = getparent(parent[u]);
        
        parent[u] = pu;
        
        return pu;
    }
    
    void unio_n(int u,int v)
    {
        int pu = getparent(u);
        int pv = getparent(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];
        }
    }
    
    bool isConnected(int u,int v)
    {
        int pu = getparent(u);
        int pv = getparent(v);
        
        return pu == pv;
    }
    
};

class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        
        //intintilze dsu

        int n = grid.size();
        dsu d(n*n);

        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(grid[i][j] == 1)
                {
                    int nodenum = i*n + j;

                    if(i-1 >= 0 && grid[i-1][j] == 1)
                    {
                        d.unio_n(nodenum,nodenum-n);
                    }
                    if(i+1 < n && grid[i+1][j] == 1)
                    {
                        d.unio_n(nodenum,nodenum+n);
                    }
                    if(j-1 >= 0 && grid[i][j-1] == 1)
                    {
                        d.unio_n(nodenum,nodenum-1);
                    }
                    if(j+1 < n && grid[i][j+1] == 1)
                    {
                        d.unio_n(nodenum,nodenum+1);
                    }
                }
            }
        }

        //after doing set up

        int ret = 0;

        for(int i=0;i<n;i++)
        {
            for(int j=0;j<n;j++)
            {
                if(grid[i][j] == 0)
                {
                    int tempret = 0;

                    set<int> vec;
                    int nodenum = i*n + j;

                    if(i-1 >= 0 && grid[i-1][j] == 1) vec.insert(d.getparent(nodenum-n));
                    if(i+1 < n && grid[i+1][j] == 1) vec.insert(d.getparent(nodenum+n));
                    if(j-1 >= 0 && grid[i][j-1] == 1) vec.insert(d.getparent(nodenum-1));
                    if(j+1 < n && grid[i][j+1] == 1) vec.insert(d.getparent(nodenum+1));

                    for(auto it : vec) tempret += d.size[it];

                    ret = max(ret,tempret+1);
                    
                }
                else
                {
                    ret = max(ret,d.size[d.getparent(i*n+j)]);
                }
            }
        }

        return ret;
    }
};
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