<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>

import copy
class DisJointSet:
    def __init__(self,n):
        self.arr=[i for i in range(n)]
        self.parent=[i for i in range(n)]
        self.size=[1]*n

    def findParent(self, node):
        if node == self.parent[node]:
            return node
        self.parent[node] = self.findParent(self.parent[node])
        return self.parent[node]

    def unionBySize(self, node1, node2):
        p_node1 = self.findParent(node1)
        p_node2 = self.findParent(node2)
        if p_node1 == p_node2:
            return 
        if self.size[p_node1] < self.size[p_node2]:
            self.parent[p_node1] = p_node2
            self.size[p_node2] += self.size[p_node1]
        else:
            self.parent[p_node2] = p_node1
            self.size[p_node1] += self.size[p_node2]

class Solution:
    def getNode(self, r, c, cols):
        return r * cols + c

    def getCell(self, node, cols):
        r = node // cols
        c = node % cols
        return r, c

    def largestIsland(self, grid: List[List[int]]) -> int:
        n = len(grid)
        ds = DisJointSet(n*n)
        for node in range(n*n):
            r, c = self.getCell(node, n)
            if grid[r][c] == 0:
                continue
            else:
                for neighbour in [(-1,0),(-1,0),(1,0),(0,1)]:
                    nr, nc = neighbour
                    nr , nc = nr + r, nc + c
                    if 0 <= nr < n and 0 <= nc < n and grid[nr][nc] == 1:
                        n_node = self.getNode(nr,nc,n)
                        if ds.findParent(node) != ds.findParent(n_node):
                            ds.unionBySize(node, n_node)
        ma = max(ds.size)
        for node in range(n*n):
            r, c = self.getCell(node, n)
            if grid[r][c] == 0:
                size = 1
                s = set()
                for neighbour in [(-1,0),(0,-1),(0,1),(1,0)]:
                    nr, nc = neighbour
                    nr , nc = nr + r, nc + c
                    if 0 <= nr < n and 0 <= nc < n and grid[nr][nc] == 1:
                        n_node = self.getNode(nr, nc, n)
                        ulp = ds.findParent(n_node)
                        s.add(ulp)
                for i in s:
                    size += ds.size[i]
                ma = max(ma, size)
        return ma



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