<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:
    directions = [(0,1),(1,0),(-1,0),(0,-1)]
    def dfs(self,grid,x,y,visited,row,col,visited_island,idx):
        ans = 0
        for d in self.directions:
            x_next = x + d[0]
            y_next = y + d[1]
            if 0 <= x_next < row and 0 <= y_next < col and grid[x_next][y_next] == 1 and visited[x_next][y_next] == False:
                visited_island[(x_next,y_next)] = idx
                visited[x_next][y_next] = True
                ans += self.dfs(grid, x_next, y_next, visited, row, col,visited_island,idx)
        return ans + 1
        
    def largestIsland(self, grid: List[List[int]]) -> int:
        row = len(grid)
        col = len(grid[0])
        visited = [[False] * col for _ in range(row)]
        max_value = 0
        visited_island = {}
        area_island = {}
        idx = 0
        for i in range(row):
            for j in range(col):
                if grid[i][j] == 1 and visited[i][j] == False:
                    visited[i][j] = True
                    visited_island[(i,j)] = idx
                    area = self.dfs(grid,i,j,visited,row,col,visited_island,idx)
                    max_value = max(max_value,area)
                    area_island[idx] = area
                    idx += 1
        print(visited_island)
        print(area_island)
        for i in range(row):
            for j in range(col):
                if grid[i][j] == 0:
                    idx_travel = []
                    ans = 1
                    for d in self.directions:
                        x_next = i + d[0]
                        y_next = j + d[1]
                        if (x_next,y_next) in visited_island:
                            island_idx = visited_island[(x_next,y_next)]
                            if island_idx not in idx_travel:
                                idx_travel.append(island_idx)
                                ans += area_island[island_idx]
                    max_value = max(max_value,ans)
        return max_value


        

        
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