<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:
        ROWS, COLS = len(grid), len(grid[0])
        islandArea = {} #will hold islandId : area, also islandId will replace grid values 
        # islandArea[0] = 0
        islandId = -1 
        visit = set()
        
        # will write grid squares w/ id and write area to islandArea 
        def dfs(r, c):

            if r < 0 or r >= ROWS or c <0 or c >= COLS or (r,c) in visit or grid[r][c] != 1:
                return 0
            
            visit.add((r,c))
            grid[r][c] = islandId
            result = dfs(r-1,c) + dfs(r+1,c) + dfs(r, c+1) + dfs(r, c-1)
            return 1 + result
        
        for r in range(ROWS):
            for c in range(COLS):
                if grid[r][c] == 1:
                    area = dfs(r,c)
                    islandArea[islandId] = area
                    islandId -= 1
        
        maxArea = 0
        directions = [(1,0), (-1,0), (0,1), (0,-1)]
        for r in range(ROWS):
            for c in range(COLS):
                if grid[r][c] == 0:
                    area = 1
                    surroundingIslands = set()

                    for dr, dc in directions:
                        if r + dr >= 0 and r + dr < ROWS and \
                            c + dc >= 0 and c + dc < COLS and grid[r+dr][c+dc] != 0:
                            surroundingIslands.add(grid[r+dr][c+dc])
                    
                    for idIsl in surroundingIslands:
                        area += islandArea[idIsl]
                    maxArea = max(maxArea, area)
        
        return maxArea if maxArea else ROWS*COLS
66006