<p>You are given two <code>m x n</code> binary matrices <code>grid1</code> and <code>grid2</code> containing only <code>0</code>&#39;s (representing water) and <code>1</code>&#39;s (representing land). An <strong>island</strong> is a group of <code>1</code>&#39;s connected <strong>4-directionally</strong> (horizontal or vertical). Any cells outside of the grid are considered water cells.</p>

<p>An island in <code>grid2</code> is considered a <strong>sub-island </strong>if there is an island in <code>grid1</code> that contains <strong>all</strong> the cells that make up <strong>this</strong> island in <code>grid2</code>.</p>

<p>Return the <em><strong>number</strong> of islands in </em><code>grid2</code> <em>that are considered <strong>sub-islands</strong></em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/10/test1.png" style="width: 493px; height: 205px;" />
<pre>
<strong>Input:</strong> grid1 = [[1,1,1,0,0],[0,1,1,1,1],[0,0,0,0,0],[1,0,0,0,0],[1,1,0,1,1]], grid2 = [[1,1,1,0,0],[0,0,1,1,1],[0,1,0,0,0],[1,0,1,1,0],[0,1,0,1,0]]
<strong>Output:</strong> 3
<strong>Explanation: </strong>In the picture above, the grid on the left is grid1 and the grid on the right is grid2.
The 1s colored red in grid2 are those considered to be part of a sub-island. There are three sub-islands.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/03/testcasex2.png" style="width: 491px; height: 201px;" />
<pre>
<strong>Input:</strong> grid1 = [[1,0,1,0,1],[1,1,1,1,1],[0,0,0,0,0],[1,1,1,1,1],[1,0,1,0,1]], grid2 = [[0,0,0,0,0],[1,1,1,1,1],[0,1,0,1,0],[0,1,0,1,0],[1,0,0,0,1]]
<strong>Output:</strong> 2 
<strong>Explanation: </strong>In the picture above, the grid on the left is grid1 and the grid on the right is grid2.
The 1s colored red in grid2 are those considered to be part of a sub-island. There are two sub-islands.
</pre>

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

<ul>
	<li><code>m == grid1.length == grid2.length</code></li>
	<li><code>n == grid1[i].length == grid2[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 500</code></li>
	<li><code>grid1[i][j]</code> and <code>grid2[i][j]</code> are either <code>0</code> or <code>1</code>.</li>
</ul>

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

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

    void unionbysize(int u, int v){
        int ulp_u=findUparent(u);
        int ulp_v=findUparent(v);
        if(ulp_u==ulp_v){
            return;
        }
        else{
            if(size[ulp_u]<size[ulp_v]){
                parent[ulp_u]=ulp_v;
                size[ulp_v]=size[ulp_v]+size[ulp_u];
            }
            else{
                parent[ulp_v]=ulp_u;
                size[ulp_u]=size[ulp_u]+size[ulp_v];
            }
            return;
        }
        return;
    }
};

class Solution {
public:
    int findsubisland(int i, int j, int m, int n, vector<vector<int>>& visited, vector<vector<int>>& grid1, vector<vector<int>>& grid2){
        queue<pair<int,int>> q;
        visited[i][j]=1;
        q.push({i,j});
        bool isconnected=true;
        while(!q.empty()){
            int a=q.front().first;
            int b=q.front().second;
            // cout<<a<<" "<<b<<endl;
            q.pop();
            if(a<m-1&&grid2[a+1][b]==1&&visited[a+1][b]==0){
                visited[a+1][b]=1;
                q.push({a+1,b});
                if(grid1[a+1][b]==0){
                    isconnected=false;
                }
            }
            if(b<n-1&&grid2[a][b+1]==1&&visited[a][b+1]==0){
                visited[a][b+1]=1;
                q.push({a,b+1});
                if(grid1[a][b+1]==0){
                    isconnected=false;
                }
            }
            if(a>0&&grid2[a-1][b]==1&&visited[a-1][b]==0){
                visited[a-1][b]=1;
                q.push({a-1,b});
                if(grid1[a-1][b]==0){
                    isconnected=false;
                }
            }
            if(b>0&&grid2[a][b-1]==1&&visited[a][b-1]==0){
                visited[a][b-1]=1;
                q.push({a,b-1});
                if(grid1[a][b-1]==0){
                    isconnected=false;
                }
            }
        }
        if(isconnected){
            return 1;
        }
        return 0;
    }

    void markvisited(int i, int j, int m, int n, vector<vector<int>>& grid2, vector<vector<int>>& visited){
        visited[i][j]=1;
        if(i<m-1&&grid2[i+1][j]==1&&visited[i+1][j]==0){
            markvisited(i+1,j,m,n,grid2,visited);
        }
        if(j<n-1&&grid2[i][j+1]==1&&visited[i][j+1]==0){
            markvisited(i,j+1,m,n,grid2,visited);
        }
        if(i>0&&grid2[i-1][j]==1&&visited[i-1][j]==0){
            markvisited(i-1,j,m,n,grid2,visited);
        }
        if(j>0&&grid2[i][j-1]==1&&visited[i][j-1]==0){
            markvisited(i,j-1,m,n,grid2,visited);
        }
        return;
    }

    int countSubIslands(vector<vector<int>>& grid1, vector<vector<int>>& grid2) {
        int m=grid1.size();
        int n=grid1[0].size();
        // DisjointSet ds1(m*n);
        // DisjointSet ds2(m*n);
        // for(int i=0;i<m;i++){
        //     for(int j=0;j<n;j++){
        //         if(j<n-1&&grid2[i][j+1]==1){
        //             ds1.unionbysize(i*n+j,i*n+j+1);
        //         }
        //         if(i<m-1&&grid2[i+1][j]==1){
        //             ds1.unionbysize(i*n+j,(i+1)*n+j);
        //         }
        //     }
        // }
        // for(int i=0;i<m;i++){
        //     for(int j=0;j<n;j++){
        //         if(j<n-1&&grid1[i][j+1]==1&&grid2[i][j+1]){
        //             ds2.unionbysize(i*n+j,i*n+j+1);
        //         }
        //         if(i<m-1&&grid1[i+1][j]==1&&grid2[i][j+1]){
        //             ds2.unionbysize(i*n+j,(i+1)*n+j);
        //         }
        //     }
        // }
        // int count=0;
        // for(int k=0;k<m*n;k++){
        //     int i=k/n;
        //     int j=k%n;
        //     if(grid2[i][j]==1){
        //         if(ds2.parent[k]==k){
        //             if(ds2.size[k]==ds1.size[k]){
        //                 count++;
        //             }
        //         }
        //     }
        // }
        // return count;
        int count=0;
        vector<vector<int>> visited(m,vector<int>(n));
        for(int i=0;i<m;i++){
            for(int j=0;j<n;j++){
                if(grid1[i][j]==1&&grid2[i][j]==1&&visited[i][j]==0){
                    // cout<<"sjhbvecwsvh "<<i<<" "<<j<<endl;
                    count=count+findsubisland(i,j,m,n,visited,grid1,grid2);
                }
                else if(grid1[i][j]==0&&grid2[i][j]==1&&visited[i][j]==0){
                    markvisited(i,j,m,n,grid2,visited);
                }
            }
        }
        return count;
    }
};
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