<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 Node:
    def __init__(self):
        self.parent = self
        self.size = 1

    def find_root(self):
        if self.parent == self:
            return self
        self.parent = self.parent.find_root()
        return self.parent

    def union(self, other):
        root = self.find_root()
        other_root = other.find_root()

        if root == other_root:
            return

        if other_root.size > root.size:
            root, other_root = other_root, root

        root.parent = other_root
        other_root.size += root.size

class Solution:
    def largestIsland(self, grid: List[List[int]]) -> int:
        nodes = {}
        zero_coordinates = []
        for y in range(len(grid)):
            for x in range(len(grid[0])):
                if grid[y][x]:
                    nodes[(x, y)] = Node()
                else:
                    zero_coordinates.append((x, y))

        if len(zero_coordinates) == 0:
            return len(grid) * len(grid[0])
        elif len(zero_coordinates) == len(grid) * len(grid[0]):
            return 1


        
        for (x, y), node in nodes.items():
            neighbors = [(x-1, y), (x+1, y), (x, y-1), (x, y+1)]
            neighbors = [(x, y) for x, y in neighbors if x >= 0 and x < len(grid[0]) and y >= 0 and y < len(grid) and grid[y][x] == 1]

            for x_n, y_n in neighbors:
                neighbor = nodes[(x_n, y_n)]
                neighbor.union(node)

        max_island_size = 0

        for x, y in zero_coordinates:
            neighbors = [(x-1, y), (x+1, y), (x, y-1), (x, y+1)]
            neighbors = [(x, y) for x, y in neighbors if x >= 0 and x < len(grid[0]) and y >= 0 and y < len(grid) and grid[y][x] == 1]
            neighbor_nodes = [nodes[coord] for coord in neighbors]
            neighbor_roots = set([node.find_root() for node in neighbor_nodes])
            # print(y, x, len(neighbor_roots))
            max_island_size = max(max_island_size, 1+ sum([root.size for root in neighbor_roots]))
        
        return max_island_size


# [0,0,0,0,0,0,0]
# [0,1,1,1,1,0,0]
# [0,1,0,0,1,0,0]
# [1,0,1,0,1,0,0]
# [0,1,0,0,1,0,0]
# [0,1,0,0,1,0,0]
# [0,1,1,1,1,0,0]]
62443