<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){
        for(int i=0;i<=n;i++){
            size.push_back(1);
            parent.push_back(i);
        }
    }
    int find(int node){
        if(parent[node]==node)return node;
        return parent[node]=find(parent[node]);
    }
    void unionSet(int x,int y){
        int upx = find(x);
        int upy = find(y);
        if(size[upx]>size[upy]){
            parent[upy]=upx;
            size[upx]+=size[upy];
        }else{
            parent[upx]=upy;
            size[upy]+=size[upx];
        }
    }
};
class Solution {
public:
    vector<pair<int,int>>plus={{1,0},{-1,0},{0,1},{0,-1}};
    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        DisjointSet ds(n*m);
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                int r = i;
                int c = j;
                if(grid[i][j]==1){
                    int num = r*m+c;
                    for(int t=0;t<4;t++){
                        int row = r+plus[t].first;
                        int col = c+plus[t].second;
                        if(row>=0 && row<n && col>=0 && col<m && grid[row][col]==1){
                            int num2 = row*m+col;
                            if(ds.find(num)!=ds.find(num2)){
                                ds.unionSet(num,num2);
                            }
                        }
                    }
                }
            }
        }
        int ans = INT_MIN;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==0){
                    set<int>s;
                    for(int t=0;t<4;t++){
                        int r = i+plus[t].first;
                        int c = j+plus[t].second;
                        if(r>=0 && r<n && c>=0 && c<m && grid[r][c]==1){
                            int num = r*m+c;
                            int upx = ds.find(num);
                            s.insert(upx);
                        }
                    }
                    int temp = 0;
                    for(auto it:s){
                        // cout<<it<<endl;
                        temp+=ds.size[it];
                    }
                    temp++;
                    ans=max(ans,temp);
                }
            }
        }
        if(ans==INT_MIN)return n*m;
        return ans;
    }
};
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