<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 Solution {
public:
    vector<int> dx = {-1, 1, 0, 0};
    vector<int> dy = {0, 0, 1, -1};
    void dfs2(vector<vector<int>>& grid2, int row, int col, int n, int m, vector<vector<int>>& vis2) {
        vis2[row][col] = 1;
        for (int i = 0; i < 4; i++) {
            int newrow = row + dx[i];
            int newcol = col + dy[i];
            if (newrow >= 0 && newrow < n && newcol >= 0 && newcol < m && !vis2[newrow][newcol] && grid2[newrow][newcol] == 1) {
                dfs2(grid2, newrow, newcol, n, m, vis2);
            }
        }
    }
    bool dfs1(vector<vector<int>>& grid1, vector<vector<int>>& grid2, int row, int col, int n, int m, vector<vector<int>>& vis1) {
        vis1[row][col] = 1;
        bool isSubIsland = true;
        if (grid1[row][col] == 0) {
            isSubIsland = false;
        }
        for (int i = 0; i < 4; i++) {
            int newrow = row + dx[i];
            int newcol = col + dy[i];
            if (newrow >= 0 && newrow < n && newcol >= 0 && newcol < m && !vis1[newrow][newcol] && grid2[newrow][newcol] == 1) {
                if (!dfs1(grid1, grid2, newrow, newcol, n, m, vis1)) {
                    isSubIsland = false;
                }
            }
        }
        return isSubIsland;
    }

    int countSubIslands(vector<vector<int>>& grid1, vector<vector<int>>& grid2) {
        int n = grid1.size();
        int m = grid1[0].size();
        vector<vector<int>> vis2(n, vector<int>(m, 0));
        vector<vector<int>> vis1(n, vector<int>(m, 0));
        int ans = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                if (!vis2[i][j] && grid2[i][j] == 1) {
                    dfs2(grid2, i, j, n, m, vis2);
                    if (dfs1(grid1, grid2, i, j, n, m, vis1)) {
                        ans++;
                    }
                }
            }
        }

        return ans;
    }
};

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