<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 Solution:
    def largestIsland(self, grid: List[List[int]]) -> int:
        self.max_island = 0
        num_islands = 0
        # id of island coord is associated with
        self.islands_history = {}
        self.island_size = {}

        num_rows = len(grid)
        num_columns = len(grid[0])

        directions = [(0, 1), (1, 0), (-1, 0), (0, -1)]

        def island_mapper(x, y, island_key):
            if (
                x < 0
                or y < 0
                or x >= num_rows
                or y >= num_columns
                or grid[x][y] == 0
                or (x, y) in self.islands_history
            ):
                return
            else:
                self.islands_history[(x, y)] = island_key
                if island_key in self.island_size:
                    self.island_size[island_key] += 1
                else:
                    self.island_size[island_key] = 1
                for new_x, new_y in directions:
                    island_mapper(x + new_x, y + new_y, island_key)

        def island_checker(x, y):
            current_islands = set()
            total_area = 1
            for new_x, new_y in directions:
                next_coords = (x + new_x, y + new_y)
                if (
                    x + new_x,
                    y + new_y,
                ) in self.islands_history and self.islands_history[
                    next_coords
                ] not in current_islands:
                    current_islands.add(self.islands_history[next_coords])
                    total_area += self.island_size[self.islands_history[next_coords]]

            if total_area > self.max_island:
                self.max_island = total_area

        for i in range(num_rows):
            for j in range(num_columns):
                if (i, j) in self.islands_history:
                    continue
                else:
                    if grid[i][j] == 1 and (i, j) not in self.islands_history:
                        island_mapper(i, j, num_islands + 1)
                        num_islands += 1
                        if self.island_size[num_islands] > self.max_island:
                            self.max_island = self.island_size[num_islands]

        for i in range(num_rows):
            for j in range(num_columns):
                if grid[i][j] == 0:
                    island_checker(i, j)

        return self.max_island

73843