<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:
        d = defaultdict(list)
        maxVal = 0
        def dfs(i,j, identification):
            nonlocal d, maxVal
            stack = [(i,j)]
            visited = set()
            visited.add((i,j))
            # print(visited)
            directions = [(1,0),(-1,0), (0, 1), (0, -1)]
            while len(stack) > 0:
                x,y = stack.pop()
                # print(x,y)
                for xDiff,yDiff in directions:
                    newX = x + xDiff
                    newY = y + yDiff
                    # print("inside ", newX, newY, stack)
                    if 0 <= newX < len(grid) and 0<= newY <len(grid[0]) and grid[newX][newY] == 1 and (newX,newY) not in visited:
                        stack.append((newX,newY))
                        visited.add((newX,newY))
            for x,y in visited:
                d[(x,y)] = (len(visited), identification)
            maxVal = max(maxVal, len(visited))
            # print(d)

        identification = 0
        for i in range(len(grid)):
            for j in range(len(grid[i])):
                if grid[i][j] == 1 and (i,j) not in d:
                    dfs(i,j, identification)
                    identification += 1
        # print(d)
        
        for i in range(len(grid)):
            for j in range(len(grid[i])):
                if grid[i][j] == 0:
                    visited = set()
                    values = [(i-1,j) , (i+1,j) ,(i, j-1) ,(i, j+1)]
                    maxCurr = 0
                    for x, y in values:
                        if (x,y) in d and d[(x,y)][1] not in visited:
                            visited.add(d[(x,y)][1])
                            maxCurr += d[(x,y)][0]
                    maxVal = max(maxVal, maxCurr + 1)
        return maxVal
51756