<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> rank, size, parent;

    disjointSet(int n){
        rank.resize(n);
        for(int i = 0;i < n+1;i++){
            size.push_back(1);
            parent.push_back(i);
        }
    }

    int findParent(int u){
        if(u == parent[u]) return u;

        parent[u] = findParent(parent[u]);
        return parent[u];
    }

    void unionBySize(int u, int v){
        int pu = findParent(u);
        int pv = findParent(v);

        if(pu == pv) return;
        else if(size[pu] >= size[pv]){
            parent[pv] = pu;
            size[pu] += size[pv];
        }
        else{
            parent[pu] = pv;
            size[pv] += size[pu];
        }
        return;
    }
};

class Solution {
public:
    bool isValid(int nr, int nc, int n){
        return (nr >= 0 && nc >= 0 && nr < n && nc < n);
    }
    int largestIsland(vector<vector<int>>& grid) {
        int r = grid.size(), c = r;
        disjointSet ds(r*c);

        for(int i = 0;i < r;i++){
            for(int j = 0;j < c;j++){
                if(grid[i][j] == 1){
                    int curIndex = (c * i) + j;
                    int aboveIndex = (i-1 >= 0) ? (c * (i - 1)) + j : -1;
                    int leftIndex = (j - 1 >= 0) ? (c * i) + (j-1) : -1;

                    if(aboveIndex != -1 && grid[i-1][j] != 0){
                        int p1 = ds.findParent(aboveIndex);
                        int p2 = ds.findParent(curIndex);
                        if(p1 != p2) ds.unionBySize(p1, p2);
                    }
                    if(leftIndex != -1 && grid[i][j-1] != 0){
                        int p1 = ds.findParent(leftIndex);
                        int p2 = ds.findParent(curIndex);
                        if(p1 != p2) ds.unionBySize(p1, p2);
                    }
                }
            }
        }

        int ans = 0;
        for(int i = 0;i < r;i++){
            for(int j = 0;j < c;j++){

                if(grid[i][j] == 0){
                    // cout<<i<<", "<<j<<endl;
                    int area = 0;

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

                    unordered_set<int> uSet;

                    for(int k = 0;k < 4;k++){
                        int nr = i + dr[k];
                        int nc = j + dc[k];
                        
                        if(isValid(nr, nc, r)){
                            if(grid[nr][nc] == 1){
                                int curIndex = (c * nr) + nc;
                                int p = ds.findParent(curIndex);
                                
                                if(uSet.count(p) == 0){
                                    area += ds.size[p];
                                    uSet.insert(p);
                                }
                            }
                        }
                    }

                    ans = max(ans, area + 1);
                }
            }
        }
        
        for(int x : ds.size) ans = max(ans, x);
        return ans;
    }
};
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