<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:
    def __init__(self,length):
        self.par = {}
        self.size = {}
        for i in range(length):
            self.par[i] = i 
            self.size[i] = 1
        
        
    def find(self,node):
        if node == self.par[node]:
            return node
        par = self.find(self.par[node])
        self.par[node] = par 
        return par 
    
    def union(self,node1,node2):
        par1 = self.find(node1)
        par2 = self.find(node2)
        if par1 == par2:
            return False 
        if self.size[par1]  > self.size[par2]:
            self.par[par2] = par1
            self.size[par1] += self.size[par2]
        else:
            self.par[par1] = par2 
            self.size[par2] += self.size[par1]
        return True 
            

class Solution:
    def largestIsland(self, grid: List[List[int]]) -> int:
        rows = len(grid)
        cols = len(grid[0])
        length = rows * cols
        disjoint_set = DisjointSet(length)
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 0:
                    continue 
                top =  (i-1) * cols + j 
                left = i * cols + j - 1
                node = i * cols + j
                if i == 0 and j == 0:
                    continue 
                if i != 0 and grid[i-1][j] == 1:
                    disjoint_set.union(node,top)
                if j != 0 and grid[i][j-1]:
                    disjoint_set.union(node,left)
        directions = [[0,1],[1,0],[-1,0],[0,-1]] 
        result = float('-inf')
        for i in range(rows):
            for j in range(cols):
                if grid[i][j] == 1:
                    continue 
                temp = 1
                visited = {}
                for dx,dy in directions:
                    new_x = i + dx 
                    new_y = j + dy
                    node = new_x * cols + new_y
                    calculated = False 
                    if new_x >= 0 and new_x < rows and new_y >= 0 and new_y < cols and grid[new_x][new_y] == 1:
                        for c in visited:
                            if disjoint_set.find(c) == disjoint_set.find(node):
                                calculated = True 
                        if calculated:
                            continue 
                        visited[node] = disjoint_set.size[disjoint_set.find(node)]
                        temp += disjoint_set.size[disjoint_set.find(node)]
                result = max(temp,result)
        return result if result != float('-inf') else length 
                    
                    
    
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