<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:
    vector<vector<int>> dir{{-1, 0}, {0, -1}, {1, 0}, {0, 1}};
    vector<bool> visited;
    vector<int> ids;
    vector<int> low_links;

    int flag = 2;

    void articulationPointsUtil(vector<vector<int>>& adj, int id, int parent, int u) {
        visited[u] = true;
        ids[u] = low_links[u] = id++;
        int out = 0;

        for (auto v : adj[u]) {
            if (v == parent) continue;
            if (!visited[v]) {
                out++;
                articulationPointsUtil(adj, id, u, v);
                low_links[u] = min(low_links[u], low_links[v]);

                if (parent == -1 && out > 1) {
                    flag = 1;
                }

                if (parent != -1 && ids[u] <= low_links[v]) {
                    flag = 1;
                }
            } else {
                low_links[u] = min(low_links[u], ids[v]);
            }
        }
    }

    int articulationPoints(vector<vector<int>>& adj, int n) {
        visited.resize(n, false);
        ids.resize(n);
        low_links.resize(n);

        flag = 2; // Reset flag before each new test
        int islands = 0;
        for (int i = 0; i < n; i++) {
            if (!visited[i]) {
                islands++;
                articulationPointsUtil(adj, 0, -1, i);
            }
        }

        return (islands == 1) ? flag : 0;
    }

    int minDays(vector<vector<int>>& grid) {
        map<pair<int, int>, int> map;
        int id = 0;
        int m = grid.size(), n = grid[0].size();
        vector<vector<int>> adj(m * n);
        
        if (m * n == 1 && grid[0][0] == 0) return 0;
        if (m * n == 1 && grid[0][0] == 1) return 1;
        
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == 1) {
                    if (map.find({i, j}) == map.end()) {
                        map[{i, j}] = id++;
                    }
                    int u = map[{i, j}];

                    for (int k = 0; k < 4; k++) {
                        int nx = i + dir[k][0];
                        int ny = j + dir[k][1];
                        if (nx >= 0 && nx < m && ny >= 0 && ny < n && grid[nx][ny] == 1) {
                            if (map.find({nx, ny}) == map.end()) {
                                map[{nx, ny}] = id++;
                            }
                            int v = map[{nx, ny}];
                            adj[u].push_back(v);
                            adj[v].push_back(u);
                        }
                    }
                }
            }
        }
        if(id==1 && adj[id-1].size()==0) return 1;
        return articulationPoints(adj, id);
    }
};

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