<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:
    def countSubIslands(self, grid1: List[List[int]], grid2: List[List[int]]) -> int:

        #this is easy
        #do a breadth first search on grid 2 with seen to get the islands 
        #then go through each island and see if it matches in grid 1 
        #increment the number 
        islands = []
        seen = set()

        def traverse_grid_2(j, k):
            island.append((j,k))
            if j-1 >=0 and grid2[j-1][k] == 1 and (j-1, k) not in seen:
                    # island.append((j-1, k))
                    seen.add((j-1,k))
                    traverse_grid_2(j-1,k)
            if j+1 < len(grid2) and grid2[j+1][k] == 1 and (j+1, k) not in seen:
                    # island.append((j+1, k))
                    seen.add((j+1,k))
                    traverse_grid_2(j+1,k)
            if k-1 >= 0 and grid2[j][k-1] == 1 and (j, k-1) not in seen:
                    # island.append((j, k-1))
                    seen.add((j,k-1))
                    traverse_grid_2(j,k-1)
            if k+1 < len(grid2[0]) and grid2[j][k+1] == 1 and (j, k+1) not in seen:
                    # island.append((j, k+1))
                    seen.add((j,k+1))
                    traverse_grid_2(j,k+1)



        for i in range(len(grid2)):
            for j in range(len(grid2[i])):
                if grid2[i][j] == 1 and (i,j) not in seen:
                    island = []
                    traverse_grid_2(i, j)
                    if island:
                        islands.append(island)
        
        cnt = 0
        for island in islands:
            f = True
            for i,j in island:
                if grid1[i][j] != 1:
                    f = False
                    break
            if f:
                cnt+=1
        
        return cnt





        
60750