<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 {
    vector<vector<int>> parent, size;
    int n;
public:
    DisjointSet(int n) 
    {
        this->n = n;
        parent.resize(n);
        size.resize(n);
        for (int i = 0; i < n; ++i) 
        {
            parent[i].resize(n);
            size[i].resize(n);
            for (int j = 0; j < n; j++) {
                parent[i][j] = i*n+j;
                size[i][j] = 1;
            }
        }
    }

    int findUPar(int node) {
        if (node == parent[node/n][node%n])
            return node;
        return parent[node/n][node%n] = findUPar(parent[node/n][node%n]);
    }

    void unionBySize(int u, int v) {
        int ulp_u = findUPar(u);
        int ulp_v = findUPar(v);
        if (ulp_u == ulp_v) return;
        if (size[ulp_u/n][ulp_u%n] < size[ulp_v/n][ulp_v%n]) {
            parent[ulp_u/n][ulp_u%n] = ulp_v;
            size[ulp_v/n][ulp_v%n] += size[ulp_u/n][ulp_u%n];
        }
        else {
            parent[ulp_v/n][ulp_v%n] = ulp_u;
            size[ulp_u/n][ulp_u%n] += size[ulp_v/n][ulp_v%n];
        }
    }
    void print()
    {
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n; j++)
            {
                cout<<parent[i][j]<<" ";
            }
            cout<<"\n";
        }

        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n; j++)
            {
                cout<<size[i][j]<<" ";
            }
            cout<<"\n";
        }
    }

    int get_size(int i)
    {
        return size[i/n][i%n];
    }
};
class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) 
    { 
        int n = grid.size(); 
        DisjointSet dsu(n);
        int final_answer = INT_MIN;
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n; j++)
            {
                if(grid[i][j] == 1)
                {
                    //up
                    if(i > 0)
                        if(grid[i-1][j] == 1)
                            dsu.unionBySize((i-1)*n+j , i*n+j);   
                    //left
                    if(j > 0)
                        if(grid[i][j-1] == 1)
                            dsu.unionBySize(i*n+(j-1) , i*n+j);
                }
            }
        }
        
        // dsu.print();

        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n; j++)
            {
                unordered_map<int, int>um;
                if(grid[i][j] == 0)
                {
                    //up
                    if(i > 0)
                    {
                        if(grid[i-1][j] == 1)
                        {
                            int val = (i-1) * n + j;
                            int par = dsu.findUPar(val);
                            if(um.find(par) == um.end())
                            {
                                um[par] = dsu.get_size(par);
                            }
                        }
                    }

                    //down
                    if(i < n-1)
                    {
                        if(grid[i+1][j] == 1)
                        {
                            int val = (i+1) * n + j;
                            int par = dsu.findUPar(val);
                            if(um.find(par) == um.end())
                            {
                                um[par] = dsu.get_size(par);
                            }
                        }
                    }
                      
                    //left
                    if(j > 0)
                    {
                        if(grid[i][j-1] == 1)
                        {
                            int val = i * n + (j-1);
                            int par = dsu.findUPar(val);
                            if(um.find(par) == um.end())
                            {
                                um[par] = dsu.get_size(par);
                            }
                        }
                    }

                    //right
                    if(j < n-1)
                    {
                        if(grid[i][j+1] == 1)
                        {
                            int val = i * n + (j+1);
                            int par = dsu.findUPar(val);
                            if(um.find(par) == um.end())
                            {
                                um[par] = dsu.get_size(par);
                            }
                        }
                    }   
                
                int sum = 1;
                for(auto it : um)
                {
                    // cout<<it.first<<"-"<<it.second<<"\n";
                    sum += it.second;
                }
                final_answer = max(final_answer, sum);
                }
            }
        }


        if(final_answer == INT_MIN)
            return n*n;
        return final_answer;
    }
};
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