<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<int> dx{-1,1,0,0};
    vector<int> dy{0,0,-1,1};
    int timer = 1;

    bool isSafe(int x, int y, vector<vector<int>> &grid){
        int n = grid.size();
        int m = grid[0].size();

        bool ans = (x>=0 && x<n && y>=0 && y<m && grid[x][y]==1);
        //cout<<"answer for x = "<<x<<" y = "<<y<<" is "<<ans<<endl;
        return ans;
    }

    void dfs(int x, int y, int px, int py,  vector<vector<int>> &grid ,vector<vector<int>> &low, vector<vector<int>> &timeIn,  bool &isArtPoint , vector<vector<int>> &visited){

        //cout<<x<<" "<<y<<endl;
        timeIn[x][y] = low[x][y] = timer++;
        visited[x][y] = 1;
        int childCount = 0;
        for(int i=0;i<4;i++){
            int newX = x+dx[i];
            int newY = y+dy[i];
            //cout<<"Child = "<<newX<<" "<<newY<<endl;
            if(isSafe(newX, newY, grid)){
                if(visited[newX][newY]==0){
                    childCount++;
                    dfs(newX, newY, x, y, grid, low, timeIn, isArtPoint, visited);
                    low[x][y] = min(low[x][y], low[newX][newY]);
                    if(low[newX][newY]>=timeIn[x][y] && px!=-1 && py!=-1){
                        isArtPoint = true;
                    }
                }else{
                    low[x][y] = min(low[x][y], timeIn[newX][newY]);
                }
            } 
        }

        if((childCount>1 && px==-1 && py==-1) || (childCount==0 && px==-1 && py==-1)){
            isArtPoint = true;
        }
       
    }


    int minDays(vector<vector<int>>& grid) {
        int n = grid.size();
        int m = grid[0].size();
        vector<vector<int>> low(n, vector<int>(m,-1));
        vector<vector<int>> timeIn(n, vector<int>(m,-1));
        vector<vector<int>> visited(n, vector<int>(m,0));
        bool isArtPoint = false;
        int countIsland = 0;

        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==1 && timeIn[i][j]==-1){
                    //cout<<"checking for i = "<<i<<" j = "<<j<<endl;
                    dfs(i, j,-1, -1, grid, low, timeIn, isArtPoint, visited);
                    countIsland++;
                }
            }
        }

        if(countIsland==0 || countIsland>=2){
            return 0;
        }
        if(isArtPoint){
            return 1;
        }

        return 2;


    }
};

/*

1 1 1
1 0 1
0 1 1


*/
12700