<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>size,parent;
    DisjointSet(int n){
        size.resize(n+1,1);
        parent.resize(n+1);
        for(int i=0;i<=n;i++){
            parent[i]=i;
        }
    }
    int findUpar(int node){
        if(parent[node]==node)
            return parent[node];
        return parent[node]=findUpar(parent[node]);
    }
    void unionBySize(int u,int v){
        int pu=findUpar(u);
        int pv=findUpar(v);
        if(pu==pv)return;
        if(size[pu]>size[pv]){
            size[pu]+=size[pv];
            parent[pv]=parent[pu];
        }else{
            size[pv]+=size[pu];
            parent[pu]=parent[pv];
        }
        return;
    }
    int getSize(int node){
        return size[findUpar(node)];
    }
};
class Solution {
public:
    int n,m;
    bool isValid(int i,int j){
        return (i>=0 && i<n && j>=0 && j<m);
    }
    int largestIsland(vector<vector<int>>& grid) {
        int ans=INT_MIN;
        n=grid.size();
        m=grid[0].size();
        unordered_map<int,unordered_map<int,int>> mp;
        DisjointSet ds(n*m+1);
        int c=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                mp[i][j]=c++;
            }
        }
        queue<pair<int,int>> q;
        vector<vector<int>> vis(n,vector<int>(m,0));
        int dx[4]={1,-1,0,0};
        int dy[4]={0,0,1,-1};
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1 && vis[i][j]==0){
                    vis[i][j]=1;
                    q.push({i,j});
                    while(!q.empty()){
                        int row=q.front().first;
                        int col=q.front().second;
                        q.pop();
                        for(int k=0;k<4;k++){
                            int nr=dx[k]+row;
                            int nc=dy[k]+col;
                            if(isValid(nr,nc) && !vis[nr][nc] && grid[nr][nc]==1){
                                vis[nr][nc]=1;
                                q.push({nr,nc});
                                ds.unionBySize(mp[nr][nc],mp[row][col]);
                            }
                        }
                    }
                }
            }
        }

        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==0){
                    set<int> temp;
                    int cnt=0;
                    for(int k=0;k<4;k++){
                        int nr=i+dx[k],nc=j+dy[k];
                        if(isValid(nr,nc) && grid[nr][nc]==1)
                        {
                            temp.insert(ds.findUpar(mp[nr][nc]));
                        }
                    }
                    for(auto it:temp)cnt+=ds.getSize(it);
                    ans=max(ans,cnt+1);
                }   
            }
        }
        if(ans==INT_MIN )
            return (grid[0][0]==1)?n*m:1;
        return ans;
    }
};
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