<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 dirr[4] = {0,0,-1,1};
    int dirc[4] = {1,-1,0,0};
    bool valid(int r, int c, vector<vector<int>>& grid){
        int n = grid.size(), m = grid[0].size();
        return r >= 0 && r < n && c >=0 && c < m && grid[r][c];
    }
    int bfs(vector<vector<int> >&grid){
        int sz = 0;
        int n = grid.size(), m = grid[0].size();
        vector<vector<bool > >seen(n, vector<bool>(m, 0));
        for(int i = 0 ; i < n; i++){
            for(int j = 0 ; j < m ; j++){
                if(grid[i][j] && !seen[i][j]){
                    queue<pair<int, int> > q;
                    q.push({i, j});
                    while(!q.empty()){
                        auto [ur, uc] = q.front();
                        q.pop();
                        if(seen[ur][uc])
                            continue;
                        sz++;
                        seen[ur][uc] = 1;
                        for(int k = 0 ; k < 4; k++){
                            int vr = ur + dirr[k], vc = uc + dirc[k];
                            if(valid(vr, vc, grid)){
                                if(!seen[vr][vc])
                                    q.push({vr, vc});
                            }
                        }
                    }
                    return sz;
                }
            }
        }
        return sz;
    }

    int minDays(vector<vector<int>>& grid) {
        int numOfComponents = 0;
        int n = grid.size(), m = grid[0].size();
        vector<vector<bool > >seen(n, vector<bool>(m, 0));

        int sz = 0;
        for(int i = 0 ; i < n ; i++){
            for(int j = 0 ; j < m ; j++){
                if(grid[i][j] && !seen[i][j]){
                    numOfComponents ++;
                    queue<pair<int, int> > q;
                    q.push({i, j});
                    while(!q.empty()){
                        auto [ur, uc] = q.front();
                        q.pop();
                        if(seen[ur][uc])
                            continue;
                        sz++;
                        seen[ur][uc] = 1;
                        for(int k = 0 ; k < 4; k++){
                            int vr = ur + dirr[k], vc = uc + dirc[k];
                            if(valid(vr, vc, grid)){
                                if(!seen[vr][vc])
                                    q.push({vr, vc});
                            }
                        }
                    }
                }
            }
        }
        if(numOfComponents != 1)
            return 0;
        if(sz <= 2)
            return sz;
        if(sz == 3)
            return 1;
        int ans = n*m;
        for(int i = 0 ; i < n ; i++){
            for(int j = 0; j < m ; j++){
                if(grid[i][j]){
                    grid[i][j] = 0;
                    int nw = bfs(grid);
                    if(nw != sz-1 )
                        return 1;
                    grid[i][j] = 1;
                }
            }
        }
        return 2;
    }
};
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