<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 {
public:

    int dfs(vector<vector<int>>& grid, int i, int j, int color)
    {
        if(i < 0 || i > grid.size() - 1 || j < 0 
                 || j > grid[0].size() - 1 ||
                  grid[i][j] != 1)
            return 0;

         grid[i][j] = color;

         return 1 + dfs(grid, i - 1, j, color)
                  + dfs(grid, i + 1, j, color)
                  + dfs(grid, i, j - 1, color)
                  + dfs(grid, i, j + 1, color);
    }

    int largestIsland(vector<vector<int>>& grid) 
    {
        int rows = grid.size();
        int cols = grid[0].size();
        unordered_map<int, int> color_to_size;
        int current_color = 2;
        for(int i = 0; i <rows; i++)
        {
            for(int j = 0; j <rows; j++)
            {
                if(grid[i][j] == 1)
                {
                    int size = dfs(grid,i,j,current_color);
                    color_to_size[current_color] = size;
                    current_color++;
                }
            }
        }

        
        if(color_to_size.size() == 1 && color_to_size[2] == rows*cols)
            return rows*cols;

        int max_iland = 0;
        for(int i = 0; i <rows; i++)
        {
            for(int j = 0; j <rows; j++)
            {
                if(grid[i][j] == 0)
                {
                    unordered_set<int> neigberhoods_ilands;
                    if(i>0)
                        neigberhoods_ilands.insert(grid[i-1][j]);
                    if(j>0)
                        neigberhoods_ilands.insert(grid[i][j - 1]);
                    if(i < rows - 1)
                        neigberhoods_ilands.insert(grid[i + 1][j]);
                    if(j < cols - 1)
                        neigberhoods_ilands.insert(grid[i][j + 1]);

                    int cur_size = 1;
                    for(int col : neigberhoods_ilands)
                        cur_size += color_to_size[col];

                    max_iland = max(max_iland,cur_size);
                }
            }
        }

        return max_iland;
    }
};
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