<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 DisjointSet {

public:
    vector<int> rank, parent, size;
    DisjointSet(int n) {
        rank.resize(n + 1, 0);
        parent.resize(n + 1);
        size.resize(n + 1);
        for (int i = 0; i <= n; i++) {
            parent[i] = i;
            size[i] = 1;
        }
    }

    int findUPar(int node) {
        if (node == parent[node])
            return node;
        return parent[node] = findUPar(parent[node]);
    }

    void unionByRank(int u, int v) {
        int ulp_u = findUPar(u);
        int ulp_v = findUPar(v);
        if (ulp_u == ulp_v) return;
        if (rank[ulp_u] < rank[ulp_v]) {
            parent[ulp_u] = ulp_v;
        }
        else if (rank[ulp_v] < rank[ulp_u]) {
            parent[ulp_v] = ulp_u;
        }
        else {
            parent[ulp_v] = ulp_u;
            rank[ulp_u]++;
        }
    }

    void unionBySize(int u, int v) {
        int ulp_u = findUPar(u);
        int ulp_v = findUPar(v);
        if (ulp_u == ulp_v) return;
        if (size[ulp_u] < size[ulp_v]) {
            parent[ulp_u] = ulp_v;
            size[ulp_v] += size[ulp_u];
        }
        else {
            parent[ulp_v] = ulp_u;
            size[ulp_u] += size[ulp_v];
        }
    }
};
class Solution {
public:
    int dx[4]={+1,-1,0,0};
    int dy[4]={0,0,1,-1};
    bool isValid(int nr,int nc,int n,int m){
        return (nr>=0 && nc>=0 && nr<n && nc<m);
    }
    int cnt(vector<vector<int>>&grid){
        int n=grid.size();
        int m=grid[0].size();
        int cnt=0;
        DisjointSet ds(n*m+1);
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==0) continue;
                for(int k=0;k<4;k++){
                    int nr=i+dx[k];
                    int nc=j+dy[k];
                    if(isValid(nr,nc,n,m)){
                        if(grid[nr][nc]==1){
                            int nodeno=i*m+j;
                            int adjnode=nr*m+nc;
                            ds.unionBySize(nodeno,adjnode);
                        }
                    }
                }
            }
        }

        //   int cnt = 0;
        set<int> uniqueIslands;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (grid[i][j] == 1) {
                    int node = i * m + j;
                    int root = ds.findUPar(node);
                    uniqueIslands.insert(root);
                }
            }
        }

        return uniqueIslands.size();

    }
    int minDays(vector<vector<int>>& grid) {
        int cntisland=cnt(grid);
        cout<<cntisland;
        if(cntisland!=1) return 0;

        int n=grid.size();
        int m=grid[0].size();
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if(grid[i][j]==0) continue;
                grid[i][j]=0;
                int cntisland=cnt(grid);
                if(cntisland!=1) return 1;
                grid[i][j]=1;
            }
        }
        return 2;
    }
};
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