<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:
        # label each island in grid1
        # for each island in grid2, check that each square in that island is in the same grid1 island
        ROWS, COLS = len(grid1), len(grid1[0])

        visit = set()
        def labelIsland(i, j, islandNum):
            if ((i, j) in visit or
                i not in range(0, ROWS) or
                j not in range(0, COLS) or
                grid1[i][j] == 0):
                return False

            visit.add((i, j))
            grid1[i][j] = islandNum
            if grid2[i][j] == 1:
                grid2[i][j] = islandNum

            transforms = [(0, 1), (0, -1), (1, 0), (-1, 0)]

            for di, dj in transforms:
                labelIsland(i + di, j + dj, islandNum)

            return True

        islandNum = 2
        for i in range(ROWS):
            for j in range(COLS):
                if grid1[i][j] == 1:
                    if labelIsland(i, j, islandNum):
                        islandNum += 1

        visit = set()

        def checkSubIsland(i, j, islandNum):
            if (i, j) in visit or i not in range(0, ROWS) or j not in range(0, COLS) or grid2[i][j] == 0:
                return True

            visit.add((i, j))

            transforms = [(0, 1), (0, -1), (1, 0), (-1, 0)]

            out = islandNum == grid1[i][j]
            for di, dj in transforms:
                out = checkSubIsland(i + di, j + dj, islandNum) and out

            return out

        count = 0
        for i in range(ROWS):
            for j in range(COLS):
                if grid2[i][j] != 0 and (i, j) not in visit and grid1[i][j] != 0:
                    if checkSubIsland(i, j, grid1[i][j]):
                        count += 1

        return count
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