<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:
        data = {}
        directions = [[0,1], [0,-1], [1,0], [-1,0]]
        color_index = 2
        visited = set()
        def dfs(r,c,color):
            nonlocal visited      
            nonlocal directions
            if r >= len(grid)  or r< 0 or c >= len(grid[0]) or c<0 or (r,c) in visited or grid[r][c] == 0:
                return 0      
            visited.add((r,c))
            grid[r][c] = color
            size = 1
            for dr, dc in directions:
                size += dfs(r+dr, c+dc, color)
            return size

        for i in range(len(grid)):
            for j in range(len(grid[0])):
                if grid[i][j] == 1 and (i,j) not in visited:
                    total = dfs(i,j, color_index)
                    data[color_index] = total
                    color_index += 1
        
        maxResult = max(data.values(), default=0)
        for r in range(len(grid)):
            for c in range(len(grid[0])):
                if grid[r][c] == 0:
                    connected = set()
                    for dr,dc in directions:
                        nr, nc = r+dr, c+dc
                        if 0 <= nr < len(grid) and 0 <= nc < len(grid[0]) and grid[nr][nc] > 1:
                            connected.add(grid[nr][nc])
                    total = 1
                    for i in connected:
                        total += data[i]
                    maxResult = max(maxResult, total)
        return maxResult



        
    
    # 10
    #  1

    # 1 + dfs()
70281