<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>

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

class Solution:
    def udpateIslandHelper(self, grid: List[List[int]], index: int, visited, curr, islandSizeByIndex):
        if curr[0] < 0 or curr[1] < 0 or curr[0] >= len(grid) or curr[1] >= len(grid):
            return

        if grid[curr[0]][curr[1]] == 0 or curr in visited:
            return

        visited.add(curr)
        grid[curr[0]][curr[1]] = index
        islandSizeByIndex[index] += 1
        for direction in DIRECTION:
            self.udpateIslandHelper(
                grid,
                index,
                visited,
                (curr[0] + direction[0], curr[1] + direction[1]),
                islandSizeByIndex
            )


    def udpateIsland(self, grid: List[List[int]]) -> int:
        islandCount = 1
        visited = set()

        islandSizeByIndex = defaultdict(int)
        
        for row in range(len(grid)):
            for col in range(len(grid[row])):
                curr = (row, col)
                if grid[curr[0]][curr[1]] == 1 and curr not in visited:
                    self.udpateIslandHelper(grid, islandCount, visited, curr, islandSizeByIndex)
                    islandCount += 1


        return islandSizeByIndex

    def largestIsland(self, grid: List[List[int]]) -> int:
        islandSizeByIndex = self.udpateIsland(grid)
        result = 0
        hasZero = False
        print(grid)
        for row in range(len(grid)):
            for col in range(len(grid[row])):
                if grid[row][col] == 0:
                    hasZero = True
                    connectedIslandSize = 1
                    connectedIslandIndex = set()
                    for direction in DIRECTION:
                        nextIslandPos = (row + direction[0], col + direction[1])
                        if nextIslandPos[0] < 0 or nextIslandPos[1] < 0 or nextIslandPos[0] >= len(grid) or nextIslandPos[1] >= len(grid):
                            continue
                        index = grid[row + direction[0]][col + direction[1]]
                        if index in connectedIslandIndex:
                            continue

                        connectedIslandSize += islandSizeByIndex[index]
                        connectedIslandIndex.add(index)
                    result = max(result, connectedIslandSize)
        
        if not hasZero:
            return len(grid) * len(grid)
        return result
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