<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:
        visited = set()
        sz = dict()
        parent = dict()
        def dfs(i,j, strti, strtj):
            visited.add((i,j))
            parent[(i,j)] = (strti, strtj)
            size = 1
            for x,y in [[0,1],[1,0],[0,-1],[-1,0]]:
                if i+x>=0 and i+x<len(grid) and j+y>=0 and j+y<len(grid[0])\
                 and (i+x,j+y) not in visited and grid[i+x][j+y]==1:
                    size+=dfs(i+x,j+y,strti,strtj)
            return size
        res = 0
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j]==1 and (i,j) not in visited:
                    size = dfs(i,j, i,j)
                    sz[(i,j)] = size
                    res = max(res, size)
        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j]==0:
                    curr = 1
                    grp_parents = set()
                    for x,y in [[0,1],[1,0],[0,-1],[-1,0]]:
                        if i+x>=0 and i+x<len(grid) and j+y>=0 and j+y<len(grid[0])\
                        and grid[i+x][j+y]==1:
                            grp_parents.add(parent[(i+x,j+y)])
                    for pi,pj in grp_parents:
                        curr+=sz[(pi,pj)]
                    res = max(res, curr)
        return res
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