<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 dir[5] = {1, 0, -1, 0, 1};

    class UnionFold {
        public:
            vector<int> parent;
            UnionFold(int n) {
                parent.resize(n);

                for(int i=0;i<n;i++) {
                    parent[i] = i;
                }
            }
    
            int find(int x) {
                if(parent[x] != x) {
                    return parent[x] = find(parent[x]);
                }

                return x;
            }

            void _union(int x, int y) {
                int px = find(x);
                int py = find(y);
                if(px != py) {
                    for(auto &p: parent) {
                        if(p==px) {
                            p = py;
                        }
                    }
                }
            }

            int count(vector<vector<int>>& grid) {
                int n = parent.size();
                int y = grid[0].size();
                unordered_set<int> rec;
                for(int i=0;i<n;i++) {
                    if (grid[i/y][i%y] == 1) {
                        rec.insert(parent[i]);
                    }
                }

                return rec.size();
            }
    };

    int countIsland(vector<vector<int>>& grid) {
        int m = grid.size();
        int n = grid[0].size();
        UnionFold u(m*n);

        for(int i=0;i<m;i++) {
            for(int j=0;j<n;j++) {
                if(grid[i][j]==0) continue;
                for(int k=0;k<4;k++) {
                    int new_i = i + dir[k];
                    int new_j = j + dir[k+1];

                    if(new_i >=0 && new_i < m && new_j >= 0 && new_j < n && grid[new_i][new_j]==1) {
                        u._union(i*n+j, new_i*n+new_j);
                    }
                }
            }
        }
        return u.count(grid);
    }

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

        int islandNum = countIsland(grid);
        if(islandNum>1 || islandNum==0) {
            return 0;
        } else {
            for(int i=0;i<m;i++) {
                for(int j=0;j<n;j++) {
                    if(grid[i][j]==1) {
                        grid[i][j] = 0;
                        islandNum = countIsland(grid);
                        grid[i][j] = 1;

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

    }
};
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