<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 UnionFind:

    def __init__(self, nodes):
        self.par = [i for i in range(nodes)]
        self.size = [1]*nodes
    
    def find(self, node):
        if self.par[node] != node:
            self.par[node] = self.find(self.par[node])
        return self.par[node]
    
    def union(self, node1, node2):
        p1, p2 = self.find(node1), self.find(node2)
        if p1 != p2:
            if self.size[p1] > self.size[p2]:
                self.par[p2] = p1
                self.size[p1] += self.size[p2]
            else:
                self.par[p1] = p2
                self.size[p2] += self.size[p1]


class Solution:
    def largestIsland(self, grid: List[List[int]]) -> int:
        n = len(grid)
        uf = UnionFind(n*n)
        directions = [[1, 0], [-1, 0], [0, 1], [0, -1]]
        vis = set()
        for r in range(n):
            for c in range(n):
                if grid[r][c]:
                    vis.add((r, c))  
                    for dx, dy in directions:
                        newR, newC = r+dx, c+dy
                        if 0 <= newR < n and 0 <= newC < n and grid[newR][newC] and (newR, newC) not in vis:
                            uf.union((r*n + c), (newR*n + newC))

        res = max(uf.size)

        for r in range(n):
            for c in range(n):
                if grid[r][c] == 0:
                    par = set()
                    for dx, dy in directions:
                        newR, newC = r+dx, c+dy
                        if 0 <= newR < n and 0 <= newC < n and grid[newR][newC]:
                            par.add(uf.find(newR*n + newC))
                    
                    total = 0
                    for p in par:
                        total += uf.size[p]
                    res = max(res, total + 1)
        
        return res

48193