<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 find(int x, vector<int>& parent) {
        if (parent[x] != x) {
            parent[x] = find(parent[x], parent);
        }
        return parent[x];
    }

    void unionSet(int x, int y ,vector<int>& parent, vector<int>& sizes) {
        x = find(x,parent); 
        y = find(y,parent); 
        if(x==y){
            return;
        }
        if (sizes[x] < sizes[y]) {
            parent[x] = y;
            sizes[y]=sizes[x]+sizes[y];
        } 
        else {
            parent[y] = x; 
            sizes[x]=sizes[x]+sizes[y];
        }
    }

    int largestIsland(vector<vector<int>>& grid) {
        int n=grid.size();
        vector<int> parent(n*n),sizes(n*n,1);
        for(int i=0;i<parent.size();i++){
            parent[i]=i;
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==1){
                    vector<int> x{-1,0,1,0};
                    vector<int> y{0,-1,0,1};
                    for(int k=0;k<4;k++){
                        int nr=i+x[k];
                        int nc=j+y[k];
                        if(nr>=0&&nr<n&&nc>=0&&nc<n&&grid[nr][nc]==1){
                            unionSet(n*i+j,n*nr+nc,parent,sizes);
                        }
                    }
                }
            }
        }
        int ans=1;
        for(int i:sizes){
            ans=max(ans,i);
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]==0){
                    unordered_set<int> s;
                    vector<int> x{-1,0,1,0};
                    vector<int> y{0,-1,0,1};
                    for(int k=0;k<4;k++){
                        int nr=i+x[k];
                        int nc=j+y[k];
                        if(nr>=0&&nr<n&&nc>=0&&nc<n&&grid[nr][nc]==1){
                            s.insert(find(n*nr+nc,parent));
                        }
                    }
                    int temps = 1;
                    for(auto it:s){
                        temps += sizes[it];
                    }
                    ans = max(ans,temps);
                }
            }
        }
        return ans;
    }
};
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