<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 TTarjan {
public:
    TTarjan(const vector<vector<int>>& a)
        : adj(a)
        , disc(adj.size())
        , low(adj.size(), INT_MAX)
    {
    }

    vector<int> operator() () {
        for (int u = 0; u < disc.size(); ++u) {
            if (!disc[u]) {
                if (Find(u, -1) > 1) {
                    ap.push_back(u);
                }
            }
        }
        return std::move(ap);
    }

private:
    int Find(int u, int p) {
        int children = 0;
        disc[u] = time++;
        for (int v : adj[u]) {
            if (v == p) {
                continue;
            }
            if (!disc[v]) {
                ++children;
                Find(v, u);
                if (low[v] >= disc[u] && p != -1) {
                    ap.push_back(u);
                }
                low[u] = min(low[u], low[v]);
            } else { // ancestor
                low[u] = min(low[u], disc[v]);
            }
        }
        return children;
    }

private:
    const vector<vector<int>>& adj;
    vector<int> disc;
    vector<int> low;
    int time = 1;
    vector<int> ap;
};

class Solution {
public:
    void fill(vector<vector<int>>& grid, int row, int col) {
        if (row < 0 || col < 0 || row == grid.size() || col == grid[0].size()) {
            return;
        }
        if (grid[row][col] != 1) {
            return;
        }
        grid[row][col] = 2;
        fill(grid, row + 1, col);
        fill(grid, row - 1, col);
        fill(grid, row, col + 1);
        fill(grid, row, col - 1);
    }

    int minDays(vector<vector<int>>& grid) {
        int islandCount = 0;
        for (int row = 0; row < grid.size(); ++row) {
            for (int col = 0; col < grid[0].size(); ++col) {
                if (grid[row][col] == 1) {
                    ++islandCount;
                    fill(grid, row, col);
                }
            }
        }

        if (islandCount != 1) {
            return 0;
        }

        int cells = 0;
        for (int row = 0; row < grid.size(); ++row) {
            for (int col = 0; col < grid[0].size(); ++col) {
                if (grid[row][col]) {
                    grid[row][col] = ++cells;
                }
            }
        }

        if (cells <= 2) {
            return cells;
        }
        
        vector<vector<int>> adj(cells);
        const int cols = grid[0].size();
        for (int row = 0; row < grid.size(); ++row) {
            for (int col = 0; col < grid[0].size(); ++col) {
                if (!grid[row][col]) {
                    continue;
                }
                int i = grid[row][col];
                auto& a = adj[i - 1];
                if (row && grid[row - 1][col]) {
                    a.push_back(grid[row - 1][col] - 1);
                }
                if (col && grid[row][col - 1]) {
                    a.push_back(grid[row][col - 1] - 1);
                }
                if (row + 1 < grid.size() && grid[row + 1][col]) {
                    a.push_back(grid[row + 1][col] - 1);
                }
                if (col + 1 < cols && grid[row][col + 1]) {
                    a.push_back(grid[row][col + 1] - 1);
                }
            }
        }
        TTarjan t(adj);
        auto ap = t();
        return !ap.empty() ? 1 : 2;
    }
};
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