<p>Given a 2D&nbsp;<code>grid</code> consists of <code>0s</code> (land)&nbsp;and <code>1s</code> (water).&nbsp; An <em>island</em> is a maximal 4-directionally connected group of <code><font face="monospace">0</font>s</code> and a <em>closed island</em>&nbsp;is an island <strong>totally</strong>&nbsp;(all left, top, right, bottom) surrounded by <code>1s.</code></p>

<p>Return the number of <em>closed islands</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/10/31/sample_3_1610.png" style="width: 240px; height: 120px;" /></p>

<pre>
<strong>Input:</strong> grid = [[1,1,1,1,1,1,1,0],[1,0,0,0,0,1,1,0],[1,0,1,0,1,1,1,0],[1,0,0,0,0,1,0,1],[1,1,1,1,1,1,1,0]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> 
Islands in gray are closed because they are completely surrounded by water (group of 1s).</pre>

<p><strong class="example">Example 2:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2019/10/31/sample_4_1610.png" style="width: 160px; height: 80px;" /></p>

<pre>
<strong>Input:</strong> grid = [[0,0,1,0,0],[0,1,0,1,0],[0,1,1,1,0]]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> grid = [[1,1,1,1,1,1,1],
&nbsp;              [1,0,0,0,0,0,1],
&nbsp;              [1,0,1,1,1,0,1],
&nbsp;              [1,0,1,0,1,0,1],
&nbsp;              [1,0,1,1,1,0,1],
&nbsp;              [1,0,0,0,0,0,1],
               [1,1,1,1,1,1,1]]
<strong>Output:</strong> 2
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= grid.length, grid[0].length &lt;= 100</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;=1</code></li>
</ul>

#include <bits/stdc++.h>
using namespace std;
class DisjointSet {
    vector<int> rank, parent, size; 
public: 
    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 closedIsland(vector<vector<int>>& a) {
        int n=a.size();
        int m=a[0].size();
        DisjointSet ds(n*m+1);
        unordered_set<int>s;   //boundary_island;
        unordered_set<int>total_island;
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                // explore all directions
                if(a[i][j]==1){continue;}

                if(i>0 && a[i-1][j]==0){
                    ds.unionBySize(i*m+j+1, (i-1)*m+j+1); // in connecting u and v by default ultimate parent if checking
                }
                if(i<n-1 && a[i+1][j]==0){
                    ds.unionBySize(i*m+j+1, (i+1)*m+j+1);
                }
                if(j>0 && a[i][j-1]==0){
                    ds.unionBySize(i*m+j+1, i*m+j);
                }
                if(j<m-1 && a[i][j+1]==0){
                    ds.unionBySize(i*m+j+1, i*m+j+2);
                }
                
            }

        }


        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                if( a[i][j]==0 &&(i==0 ||j==0||i==n-1||j==m-1)){
                   int x= ds.findUPar(i*m+j+1);
                    s.insert(x);
                }
                if( a[i][j]==0){
                int x= ds.findUPar(i*m+j+1);
                total_island.insert(x);
                }


            }
        }
        int ct=0;
        for(auto it:total_island){
            if(s.find(it)==s.end()){
                ct++;
            }
        }




        return ct;


        
    }
};
14666