<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:
    int* parent; int* size;

    DSU(int n){
        parent = new int[n];
        size = new int[n];
        for(int i=0; i<n; i++){
            parent[i] = i;
            size[i] = 1;
        }
    } 

    int find(int node){
        if(parent[node] == node){
            return node;
        }
        return parent[node] = find(parent[node]);
    }

    void unite(int x, int y){
        int x_rep = find(x);
        int y_rep = find(y);

        if(x_rep == y_rep){
            return; 
        }
        else if(size[x_rep] > size[y_rep]){
            parent[y_rep] = x_rep;
            size[x_rep] += size[y_rep];
        }
        else if(size[x_rep] < size[y_rep]){
            parent[x_rep] = y_rep;
            size[y_rep] += size[x_rep];
        }
        else{
            parent[y_rep] = x_rep;
            size[x_rep] += size[y_rep];
        }
    }
};

class Solution {
public:
    bool isValid(int r, int c, vector<vector<int>>& grid, int n){
        return (r >=0 && r < n && c >= 0 && c < n && grid[r][c] == 1);
    }

    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        DSU ds(n*n);
        
        vector<pair<int, int>> zeros;

        for(int row=0; row<n; row++){
            for(int col=0; col<n; col++){

                if(grid[row][col] == 1){
                    int node = (row*n)+col;

                    int dr[] = {0, -1, 0, +1};
                    int dc[] = {+1, 0, -1, 0};

                    for(int i=0; i<4; i++){

                        int adjRow = row + dr[i];
                        int adjCol = col + dc[i];

                        if(isValid(adjRow, adjCol, grid, n)){
                            int adjNode = (adjRow*n) + adjCol;
                            if(ds.find(node) != ds.find(adjNode)){
                                ds.unite(node, adjNode);
                            }
                        }
                    }
                }
                else{
                    zeros.push_back({row, col});
                }
            }
        }
        
        if(zeros.size() == 0 || zeros.size() == 1){
            return n*n;
        }

        int ans = 1;
        for(auto zero:zeros){
            int row = zero.first;
            int col = zero.second;

            int dr[] = {0, -1, 0, +1};
            int dc[] = {+1, 0, -1, 0};
            
            int cur = 0;
            unordered_set<int> st;
            for(int i=0; i<4; i++){
                int adjRow = row + dr[i];
                int adjCol = col + dc[i];

                if(isValid(adjRow, adjCol, grid, n)){
                    int adjNode = (adjRow*n) + adjCol;
                    st.insert(ds.find(adjNode));
                }
            }

            for(auto node:st){
                cur += ds.size[node];
            }

            ans = max(ans, 1+cur);   
        }

        return ans;
    }
};
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