<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{
public:
    vector<int>rank, parent, size;
    DisjointSet(int n)
    {
        rank.resize(n+1, 0);
        parent.resize(n+1);
        size.resize(n+1);
        for(int i =0; i<=n; i++)
        {
            parent[i] = i;
            size[i] = 1;
        }
    }
    
    int findUPar(int node)
    {
        if(node == parent[node]) return node;
        return parent[node] = findUPar(parent[node]);
    }
    
    void unionbyRank(int u, int v)
    {
        int ulp_u = findUPar(u);
        int ulp_v = findUPar(v);
        if(ulp_u==ulp_v) return; //already connected
        if(rank[ulp_u] < rank[ulp_v])  parent[ulp_u] = ulp_v;
        else if(rank[ulp_v] < rank[ulp_u]) parent[ulp_v] = ulp_u;
        else 
        {
            parent[ulp_v] = ulp_u;
            rank[ulp_u]++;
        }
    }
    
    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] < 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:
    bool chk(int r, int c, int n)
    {
        return r>=0 && r<n && c<n && c>=0;
    }
    int largestIsland(vector<vector<int>>& grid) 
    {
        int n = grid.size();
        int maxArea = 1;
        DisjointSet ds(n* n);
        for(int i =0; i<n; i++)
        {
            for(int j =0; j <n; j++)
            {
                int cell = i * n + j;
                if(grid[i][j] == 0) continue;
                vector<int>dr ={-1, 0, 1, 0};
                vector<int>dc ={0, 1, 0, -1};
                for(int ind = 0; ind < 4; ind++)
                {
                    int nr = i + dr[ind];
                    int nc = j + dc[ind];
                    if(chk(nr, nc, n) && grid[nr][nc])
                    {
                        int adjcell = nr * n + nc;
                        if(ds.findUPar(cell) != ds.findUPar(adjcell))
                        {
                            ds.unionbySize(cell, adjcell);
                        }
                    }
                }
            }
        }

        for(int i =0;i<n; i++)
        {
            for(int j =0; j <n; j++)
            {
                int cell = i * n + j;
                if(grid[i][j] == 1) continue;
                vector<int>dr ={-1, 0, 1, 0};
                vector<int>dc ={0, 1, 0, -1};
                set<int>adjcoor;
                for(int ind = 0; ind < 4; ind++)
                {
                    int nr = i + dr[ind];
                    int nc = j + dc[ind];
                    if(chk(nr, nc, n) && grid[nr][nc])
                    {
                        int adjcell = nr * n + nc;
                        if(ds.findUPar(cell) != ds.findUPar(adjcell))
                        {
                            adjcoor.insert(ds.findUPar(adjcell));
                        }
                    }
                }
                int tempsz = 1;
                for(auto it : adjcoor) tempsz += ds.size[it];
                maxArea = max(maxArea, tempsz);
            }
        }

        maxArea = max(maxArea, ds.size[ds.findUPar(0)]);
        return maxArea;
    }
};
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