<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> rank,parent,size;
     dsu(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 findparent(int node){
        if(node==parent[node]){
            return node;}
        return parent[node]=findparent(parent[node]);
     }
     void uniter(int u,int v){
        int up=findparent(u),vp=findparent(v);
        if(up==vp){return;}
        if(rank[up]<rank[vp]){parent[up]=vp;}
        else if(rank[vp]<rank[up]){parent[vp]=up;}
        else{parent[vp]=up;rank[up]++;}
     }
     void unites(int u, int v){
        int up=findparent(u),vp=findparent(v);
        if(up==vp){return;}
        if(rank[up]<rank[vp]){parent[up]=vp;size[vp]+=size[up];}
        else{parent[vp]=up;size[up]+=size[vp];}
     }
};


class Solution {
public:
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size(), mx = 0;

        int m = n*n + 1;

        dsu d(m);

        for(int i=0;i<n;i++){
            int k = (i+1)*n;
            for(int j=0;j<n;j++){
                int u = k-n+j;
                if(grid[i][j]==1){
                    vector<pair<int,int>> dir = {{0,1},{1,0},{-1,0},{0,-1}};
                    for(auto it : dir){
                        int r = i+it.first, c = j+it.second;
                        if(r>=0&&r<n&&c>=0&&c<n&&grid[r][c]==1){
                            int v = (r+1)*n - n + c;
                            d.unites(u,v);
                        }
                    }
                }
            }
        }

        for(int i=0;i<m;i++) mx = max(mx,d.size[i]);

        for(int i=0;i<n;i++){
            int k = (i+1)*n;
            for(int j=0;j<n;j++){
                int u = k-n+j;
                if(grid[i][j]==0){
                    vector<pair<int,int>> dir = {{0,1},{1,0},{-1,0},{0,-1}};
                    set<int> st;
                    for(auto it : dir){
                        int r = i+it.first, c = j+it.second;
                        if(r>=0&&r<n&&c>=0&&c<n&&grid[r][c]==1){
                            int v = (r+1)*n - n + c;
                            st.insert(d.findparent(v));
                        }
                    }
                    int ct = 1;
                    for(auto it : st) ct += d.size[it];
                    mx = max(mx,ct);
                }
            }
        }
        return mx;
    }
};
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