<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:
        h = w = len(grid)
        
        seen = set()
        def dfs(r, c):
            seen.add((r, c))
            res = [(r, c)]
            for x, y in ((0, 1), (1, 0), (0, -1), (-1, 0)):
                nr = r+x
                nc = c+y
                if nr in range(h) and nc in range(w) and grid[nr][nc] == 1 and (nr, nc) not in seen:
                    res += dfs(nr, nc)
            return res

        islands = {}
        lengs = {}
        island = 0
        ans = 0
        for r in range(h):
            for c in range(w):
                if grid[r][c] == 1 and (r, c) not in seen:
                    curr = dfs(r, c)
                    for cord in curr:
                        islands[cord] = island
                    lengs[island] = len(curr)
                    ans = max(ans, len(curr))
                    island += 1
        
        for r in range(h):
            for c in range(w):
                if grid[r][c] == 0:
                    neis = set()
                    for x, y in ((0, 1), (1, 0), (0, -1), (-1, 0)):
                        nr = r+x
                        nc = c+y
                        if nr in range(h) and nc in range(w) and grid[nr][nc] == 1:
                            neis.add(islands[(nr, nc)])
                    res = 1
                    for n in neis:
                        res += lengs[n]
                    ans = max(ans, res)
        
        return ans


        return ans


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