<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 {
public:
    int time;
    vector<vector<int>> vis;
    vector<vector<int>> low;
    int d[5] = {0, 1, 0, -1, 0};
    bool arti;
    
    int minDays(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        arti = false;
        vis = vector<vector<int>>(n, vector<int>(m, 0));
        low = vector<vector<int>>(n, vector<int>(m, 0));
        time = 1;
        bool hasArt = false;
        bool found = false;
        
        for(int i = 0; i < n; ++i) {
            for(int j = 0; j < m; ++j) {
                if(grid[i][j] == 1) {
                    if(found)
                        return 0;
                    found = true;
                    art(i, j, grid, -100, -100);
                }
            }
        }

        if(time == 1)
            return 0;

        if(time == 2)
            return 1;
        if(arti)
            return 1;
        else
            return 2;
    }

    void art(int row, int col, vector<vector<int>>& grid, int parRow, int parCol) {
        grid[row][col] = 0;
        vis[row][col] = time;
        low[row][col] = time;
        time++;
        int child = 0;
        for(int i = 0; i < 4; ++i) {
            int x = d[i] + row;
            int y = d[i+1] + col;

            if(x < 0 || y < 0 || x >= grid.size() || y >= grid[0].size() || (x == parRow && y == parCol) || (vis[x][y] == 0 && grid[x][y] == 0))
                continue;
            if(vis[x][y] == 0) {
                child++;
                art(x, y, grid, row, col);
                low[row][col] = min(low[row][col], low[x][y]);
                if(low[x][y] >= vis[row][col] && (parRow != -100 && parCol != -100))
                    arti = true;
            } else {
                low[row][col] = min(low[row][col], vis[x][y]);
            }
        }

        if(parRow == -100 && parCol == -100 && child > 1)
            arti = true;
    }
};
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