<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<int> par, size;
public:
    Disjointset(int n)
    {
        par.resize(n+1);
        size.resize(n+1);
        for(int i = 0; i <= n; i++)
        {
            par[i] = i;
            size[i] = 1;
        }
    }
    int findParent(int node)
    {
        if(par[node] == node) return node;
        par[node] = findParent(par[node]);
        return par[node];
    }
    void unionBySize(int u, int v)
    {
        int u_p = findParent(u);
        int v_p = findParent(v);
        if(u_p == v_p) return;
        if(size[u_p] > size[v_p])
        {
            par[v_p] = u_p;
            size[u_p] += size[v_p];
        }
        else
        {
            par[u_p] = v_p;
            size[v_p] += size[u_p];
        }
    }
    int findMaxSize()
    {
        return *(max_element(size.begin(), size.end()));
    }
    int findSize(int node)
    {
        int p = findParent(node);
        return size[p];
    }
};

class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        Disjointset ds(n*n-1);
        vector<vector<int>> v;
        for(int i = 0; i < n; i++)
        {
            for(int j = 0; j < n; j++)
            {
                if(grid[i][j] == 0)
                {
                    v.push_back({i, j});
                    continue;
                }
                vector<int> dx = {-1,1,0,0};
                vector<int> dy = {0,0,1,-1};
                for(int k = 0; k < 4; k++)
                {
                    int r = i+dx[k];
                    int c = j+dy[k];
                    if(r >= 0 && c >= 0 && r < n && c < n && grid[r][c] == 1)
                    {
                        if(ds.findParent(r*n+c) != ds.findParent(i*n+j))
                        {
                            ds.unionBySize(r*n+c, i*n+j);
                        }
                    }
                }
            }
        }
        int maxi = ds.findMaxSize();
        for(int p = 0; p < v.size(); p++)
        {
            set<int> comps;
            int i = v[p][0];
            int j = v[p][1];
            vector<int> dx = {-1,1,0,0};
            vector<int> dy = {0,0,1,-1};
            for(int k = 0; k < 4; k++)
            {
                int r = i+dx[k];
                int c = j+dy[k];
                if(r >= 0 && c >= 0 && r < n && c < n && grid[r][c] == 1)
                {
                    comps.insert(ds.findParent(r*n+c));
                }
            }
            int total = 1;
            for(auto it : comps) total += ds.findSize(it);
            maxi = max(maxi, total);
        }
        return maxi;
    }
};
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