<p>You are given an <code>m x n</code> binary grid <code>grid</code> where <code>1</code> represents land and <code>0</code> represents water. An <strong>island</strong> is a maximal <strong>4-directionally</strong> (horizontal or vertical) connected group of <code>1</code>&#39;s.</p>

<p>The grid is said to be <strong>connected</strong> if we have <strong>exactly one island</strong>, otherwise is said <strong>disconnected</strong>.</p>

<p>In one day, we are allowed to change <strong>any </strong>single land cell <code>(1)</code> into a water cell <code>(0)</code>.</p>

<p>Return <em>the minimum number of days to disconnect the grid</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land1.jpg" style="width: 500px; height: 169px;" />
<pre>
<strong>Input:</strong> grid = [[0,1,1,0],[0,1,1,0],[0,0,0,0]]

<strong>Output:</strong> 2
<strong>Explanation:</strong> We need at least 2 days to get a disconnected grid.
Change land grid[1][1] and grid[0][2] to water and get 2 disconnected island.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/24/land2.jpg" style="width: 404px; height: 85px;" />
<pre>
<strong>Input:</strong> grid = [[1,1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> Grid of full water is also disconnected ([[1,1]] -&gt; [[0,0]]), 0 islands.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
private:
    bool isDisconnected(vector<vector<int>>& grid, int islands, int startI, int startJ)
    {
        if (islands == 1)
            return false;
        
        int count = 0;
        std::queue<std::pair<int, int>> q;
        std::vector<std::vector<bool>> visited(grid.size(), std::vector<bool>(grid[0].size()));

        q.push({startI, startJ});
        while(!q.empty())
        {
            auto [i, j] = q.front();
            q.pop();
            if (visited[i][j])
                continue;
            visited[i][j] = true;

            count++;

            if (i > 0 && !visited[i - 1][j] && grid[i - 1][j] == 1)
                q.push({i - 1, j});
            if (i < grid.size() - 1 && !visited[i + 1][j] && grid[i + 1][j] == 1)
                q.push({i + 1, j});
            if (j > 0 && !visited[i][j - 1] && grid[i][j - 1] == 1)
                q.push({i, j - 1});
            if (j < grid[0].size() - 1 && !visited[i][j + 1] && grid[i][j + 1] == 1)
                q.push({i, j + 1});
        }
        return count != islands;
    }   

public:
    int minDays(vector<vector<int>>& grid) {
        int islands = std::accumulate(grid.begin(), grid.end(), 0,
        [](int acc, vector<int>& x)
        {
            return acc + std::accumulate(x.begin(), x.end(), 0, std::plus<int>());
        });

        if (islands == 0)
            return 0;
        if (islands == 1)
            return 1;

        int startI = -1;
        int startJ = -1;
        int nextI = -1;
        int nextJ = -1;

        for (int i = 0; i < grid.size(); i++)
        {
            for (int j = 0; j < grid[0].size(); j++)
            {
                if (grid[i][j] == 1)
                {
                    if (startI == -1)
                    {
                        startI = i;
                        startJ = j;
                    }
                    else
                    {
                        nextI = i;
                        nextJ = j;
                        break;
                    }
                }
            }
            if (nextI != -1)
                break;
        }

        if (isDisconnected(grid, islands, startI, startJ))
            return 0;

        for (int i = 0; i < grid.size(); i++)
        {
            for (int j = 0; j < grid[0].size(); j++)
            {
                if (grid[i][j] == 1)
                {
                    grid[i][j] = 0;
                    if ((i == startI && j == startJ && isDisconnected(grid, islands - 1, nextI, nextJ)) || 
                        ((i != startI || j != startJ) && isDisconnected(grid, islands - 1, startI, startJ))) 
                        return 1;
                    grid[i][j] = 1;
                }
            }
        }
        return 2;
    }
};
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