<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 count_islands(int i, int j, vector<vector<int>>& v, vector<vector<int>>& grid, int n, int color)
    {

        v[i][j] = color;
        int islands = 1;
        // look left
        if (j-1>=0 && grid[i][j-1]==1 && v[i][j-1]!=color ) islands+= count_islands(i, j-1, v, grid, n, color);
        // look right
        if (j+1<n && grid[i][j+1]==1 && v[i][j+1]!=color) islands+= count_islands(i, j+1, v, grid, n, color);
        // look up
        if (i-1>=0 && grid[i-1][j]==1 && v[i-1][j]!=color) islands+= count_islands(i-1, j, v, grid, n, color);
        // look down
        if (i+1<n && grid[i+1][j]==1 && v[i+1][j]!=color) islands+= count_islands(i+1, j, v, grid, n, color);
        
        //v[i][j] = 0;
        return islands;
    }

    int largestIsland(vector<vector<int>>& grid) {
        int n = grid.size();
        if (n==1) return 1;
        vector<vector<int>> visited(n, vector<int>(n,0));
        bool is_zero_present = false;
        int max_islands = INT_MIN;
        int color = 2;
        for (int i=0;i<n;i++)
        {
            for (int j=0;j<n;j++)
            {
                int islands;
                if(grid[i][j]==0)
                {
                    //cout<< visited[i][j];
                    visited[i][j] = color;
                    is_zero_present = true;
                    islands = count_islands(i,j, visited, grid, n,   color);
                    cout<< i<<j<<islands;
                    max_islands = max(max_islands, islands);
                    color++;
                }
            }
        }

        if(!is_zero_present) return n*n;
        return max_islands;
    }
};
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