<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 dsu {
public:
    vector<int> parent;
    vector<int> rank;

    dsu(int n) : rank(n, 0), parent(n, 0) {
        for (int i = 0; i < n; i++) {
            parent[i] = i;
        }
    }

    int find(int x) {
        return parent[x] = (parent[x] == x) ? x : find(parent[x]);
    }

    void unite(int x, int y) {
        int x_parent = find(x);
        int y_parent = find(y);

        if (x_parent == y_parent) return;
        if (rank[x_parent] < rank[y_parent]) {
            parent[x_parent] = y_parent;
        } else if (rank[x_parent] > rank[y_parent]) {
            parent[y_parent] = x_parent;
        } else {
            parent[x_parent] = y_parent;
            rank[y_parent]++;
        }
    }
};
class Solution {
public:
    int min_days = INT_MAX;
    vector<vector<int>> matrix;
    int m,n;
    vector<int>dir = {1,0,-1,0,1};
    bool checkValid() {
        dsu ds(m * n);
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (matrix[i][j] == 1) {
                    for (int k = 0; k < 4; k++) {
                        int new_i = i + dir[k];
                        int new_j = j + dir[k + 1];
                        if (new_i < m && new_i >= 0 && new_j < n && new_j >= 0 && matrix[new_i][new_j] == 1) {
                            ds.unite(i * n + j, new_i * n + new_j);
                        }
                    }
                }
            }
        }
        unordered_set<int> s;
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (matrix[i][j] == 1) {
                    s.insert(ds.find(i * n + j));
                }
            }
        }
        return s.size() != 1;
    }
    int solve() {
        if(checkValid())return 0;
        for(int i=0;i<m;i++){
            for(int j=0;j<n;j++){
                if(matrix[i][j]==1){
                    matrix[i][j]=0;
                    if(checkValid())return 1;
                    matrix[i][j]=1;
                }
            }
        }
        return 2;
    }
    int minDays(vector<vector<int>>& grid) {
        matrix=grid;
        m=grid.size(),n=grid[0].size();
        return solve();
    }
};
29500