<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 {
vector<int>d1={1,-1,0,0};
vector<int>d2={0,0,1,-1};
vector<vector<int>>vis;
vector<vector<int>>timer;
vector<vector<int>>low;
int counter;
int child;
bool articulation_pt;
void dfs(int i, int j, vector<vector<int>>&grid, vector<vector<vector<pair<int,int>>>>&graph){
    vis[i][j]=1;
    for(auto e: graph[i][j]){
        if(!vis[e.first][e.second]){
            dfs(e.first,e.second,grid,graph);
        }
    }
}
void artPt(int i, int j, int pi, int pj, vector<vector<int>>&grid, vector<vector<vector<pair<int,int>>>>&graph){

    vis[i][j]=1;
    timer[i][j] = low[i][j] = counter++;

    for(auto e:graph[i][j]){
        if(e.first==pi && e.second==pj){continue;}
        if(!vis[e.first][e.second]){
            if(pi==-1 && pj == -1){
                child++;
            }
            artPt(e.first,e.second,i,j,grid,graph);
            if(low[e.first][e.second]>=timer[i][j] && pi!=-1 && pj!=-1){
                articulation_pt=true;
            }
            low[i][j]=min(low[i][j],low[e.first][e.second]);
        }
        else{
            low[i][j] = min(timer[e.first][e.second], low[i][j]);
        }
    }
}
public:
    int minDays(vector<vector<int>>& grid) {
        int n=grid.size();
        int m=grid[0].size();
        int num_nodes=0;
        vector<vector<vector<pair<int,int>>>>graph(n,vector<vector<pair<int,int>>>(m));
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1){
                    num_nodes++;
                    for(int k=0;k<4;k++){
                        int x=i+d1[k];
                        int y=j+d2[k];
                        if(x>=0 && y>=0 && x<n && y<m && grid[x][y]==1){
                            graph[i][j].push_back({x,y});
                        }
                    }
                }
            }
        }
        if(num_nodes==1){return 1;}
        vis.assign(n,vector<int>(m,0));
        int num_islands=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1 && !vis[i][j]){
                    dfs(i,j,grid,graph);
                    num_islands++;
                }
            }
        }
        if(num_islands==0 || num_islands>1){
            return 0;
        }

        vis.assign(n,vector<int>(m,0));
        counter=1;
        timer.assign(n,vector<int>(m,0));
        low.assign(n,vector<int>(m,0));
        child=0;
        articulation_pt=false;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1 && !vis[i][j]){
                    artPt(i,j,-1,-1,grid,graph);
                }
            }
        }
        
        if(child>1){
            return 1;
        }
        if(articulation_pt){
            return 1;
        }
        return 2;
    }
};
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