<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 Solution {
public:
    int dx[4]={0,0,1,-1};
    int dy[4]={1,-1,0,0};

    bool check(int x, int y, int n, int m){
        if(x>=0 && x<n && y>=0 && y<m)return true;
        return false;
    }

    int getParent(int p, vector<int>&parent){
        if(p==parent[p])return p;
        return parent[p]=getParent(parent[p],parent);
    }

    void Union(int a, int b, vector<int>&parent, vector<int>&rank){
        a=getParent(a,parent);
        b=getParent(b,parent);

        if(a!=b){
            if(rank[a]>rank[b])parent[b]=a;
            else if(rank[a]<rank[b])parent[a]=b;
            else{
                parent[b]=a;
                rank[a]++;
            }
        }
        return ;
    }

    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size(),ans=0;
        vector<vector<bool>>visited(n,vector<bool>(n,false));
        vector<int>parent(n*n+1),rank(n*n+1,1),size(n*n+1,0);
        for(int i=0;i<n*n;i++)parent[i]=i;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1 && visited[i][j]==false){
                    queue<pair<int,int>>q;
                    q.push({i,j});
                    visited[i][j]=true;
                    while(q.size()){
                        pair<int,int>p=q.front();
                        q.pop();
                        for(int k=0;k<4;k++){
                            int x=p.first+dx[k];
                            int y=p.second+dy[k];
                            if(check(x,y,n,n) && grid[x][y]==1){
                                Union(p.first*n+p.second, x*n+y, parent,rank);
                                if(visited[x][y]==false)q.push({x,y});
                                visited[x][y]=true;
                            }
                        }
                    }
                }
            }
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                size[getParent(i*n+j,parent)]++;
            }
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                ans=max(ans,size[i*n+j]);
                if(grid[i][j]==0){
                    int a=0;
                    set<int>s;
                    for(int k=0;k<4;k++){
                        int x=i+dx[k];
                        int y=j+dy[k];
                        if(check(x,y,n,n) && grid[x][y]==1){
                            if(s.find(getParent(x*n+y,parent))==s.end()){
                                s.insert(getParent(x*n+y,parent));
                                a+=size[getParent(x*n+y,parent)];
                            }
                        }
                    }
                    ans=max(ans,a+1);
                }
            }
        }
        return ans;
    }
};
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