<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 largestIsland(vector<vector<int>>& grid) {
        unordered_map<int, int> island;
        int area = 0;
        int maxArea = 0;
        int islandLabel = 2;
        for(int i = 0; i < grid.size(); i++)
        {
            for(int j = 0; j < grid[0].size(); j++)
            {
                if(grid[i][j] == 1)
                {
                    area = 0;
                    calculateArea(i, j, islandLabel, area, grid);
                    island[islandLabel] = area;
                    islandLabel++;
                }              
            }
        }
        
        if(island.size() == 0) return 1;
        maxArea = island.begin()->second;
        for(int i = 0; i < grid.size(); i++)
        {
            for(int j = 0; j < grid[0].size(); j++)
            {
                if(grid[i][j] == 0)
                {
                    vector<int> proccessed;
                    area = 1;
                    if(i > 0 && grid[i-1][j] > 1)
                    {
                        proccessed.push_back(grid[i-1][j]);
                        area += island[grid[i-1][j]];
                    }
                    if(j > 0 && grid[i][j-1] > 1 && find(proccessed.begin(), proccessed.end(), grid[i][j-1]) == proccessed.end())
                    {
                        proccessed.push_back(grid[i][j-1]);
                        area += island[grid[i][j-1]];
                    }
                    if(i < grid.size()-1 && grid[i+1][j] > 1 && find(proccessed.begin(), proccessed.end(), grid[i+1][j]) == proccessed.end())
                    {
                        proccessed.push_back(grid[i+1][j]);
                        area += island[grid[i+1][j]];
                    }
                    if(j < grid[0].size()-1 && grid[i][j+1] > 1 && find(proccessed.begin(), proccessed.end(), grid[i][j+1]) == proccessed.end())
                    {
                        area += island[grid[i][j+1]];
                    }
                    maxArea = max(maxArea, area);
                }              
            }
        }
        return maxArea;
    }

    void calculateArea(int i, int j, int label, int& area, vector<vector<int>>& grid)
    {
        if(i < 0 || j < 0 || i >= grid.size() || j >= grid[0].size())
        {
            return;
        }
        if(grid[i][j] != 1) return;
        grid[i][j] = label;
        area++;
        calculateArea(i-1, j, label, area, grid);
        calculateArea(i, j-1, label, area, grid);
        calculateArea(i+1, j, label, area, grid);
        calculateArea(i, j+1, label, area, grid);
    }
};
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