<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>

from collections import defaultdict

class Solution:
    def largestIsland(self, grid: List[List[int]]) -> int:
        # flipping a 0 will either:
        # result in an island of size 1
        # or will be part of another island (adds 1)
        # or will connect 2-4 islands

        # maybe first figure out island sizes, then figure out combos?
        # dont flip the 1s to 0s on sizing pass
        # flip to -1 maybe
        # will need some way to know size of an island from any square the zero touches
        # maybe use entry point? then can use that entry point tuple both for visiting and map

        max_area = 0
        sizes = defaultdict(int)
        directions = [(-1,0),(1,0),(0,-1),(0,1)]
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                # go through every cell
                if grid[i][j] == 1:
                    # explore island
                    next_cells = [(i, j)]
                    area = 0
                    while next_cells:
                        row, col = next_cells.pop()
                        if grid[row][col] != 1:
                            continue
                        grid[row][col] = (i, j)
                        area += 1
                        for direction in directions:
                            next_row = row + direction[0]
                            next_col = col + direction[1]
                            if 0 <= next_row < len(grid) and 0 <= next_col < len(grid[0]):
                                if grid[next_row][next_col] == 1:
                                    next_cells.append((next_row, next_col))
                    sizes[(i, j)] = area
                    max_area = max(max_area, area)

        # now test flipping zeroes
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                 if grid[i][j] == 0:
                    curr_area = 1
                    islands_touched = set()
                    # check for islands in all 4 directions      
                    for direction in directions:
                        next_row = i + direction[0]
                        next_col = j + direction[1]
                        if 0 <= next_row < len(grid) and 0 <= next_col < len(grid[0]):
                            if grid[next_row][next_col] != 0:
                                islands_touched.add(grid[next_row][next_col])
                    for island in islands_touched:
                        curr_area += sizes[island]
                    max_area = max(max_area, curr_area)

        return max_area
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