<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 findNeighbors(self, grid, i, j, visited):
        indices = []
        queue = deque()
        queue.append([i,j])
        visited[i][j]=1

        horiz = [0,0,-1,1]
        vert = [1,-1,0,0]

        while queue:
            item = queue.popleft()
            indices.append((item[0], item[1]))
            x,y = item[0], item[1]

            for i in range(len(horiz)):
                newx = horiz[i] + x
                newy = vert[i] + y

                if newx>=0 and newy>=0 and newx<len(grid) and newy < len(grid[0]) and grid[newx][newy] == 1 and visited[newx][newy] == 0:
                    visited[newx][newy] = 1
                    queue.append([newx, newy])
        
        return indices

    def countSubIslands(self, grid1: List[List[int]], grid2: List[List[int]]) -> int:
        '''
        get num of islands in grid 2
        for each island, store the indices in a set
        then traverse through these islands, and indices in each island to check if they are set as 1 in grid 1
        
        how to count islands:
        start traversing through the grid from 0,0. whenever encounter a 1, do a bfs to look for neighboring 1's.
        each time we encounter a 1, save the index in a set.
        '''
        visited = [[0 for _ in range(len(grid2[0]))] for _ in range(len(grid2))]
        indices = []
        for i in range(len(grid2)):
            for j in range(len(grid2[0])):
                if grid2[i][j]==0 or visited[i][j]==1:
                    continue
                
                indices.append(self.findNeighbors(grid2, i, j, visited))
                
        out = 0
        for i in indices:
            found = True
            for idx in i:
                x, y = idx[0], idx[1]
                if grid1[x][y] == 1:
                    continue
                else:
                    found = False
                    break
            
            if found:
                out+=1
        
        return out


41030