<p>An <code>n x n</code> grid is composed of <code>1 x 1</code> squares where each <code>1 x 1</code> square consists of a <code>&#39;/&#39;</code>, <code>&#39;\&#39;</code>, or blank space <code>&#39; &#39;</code>. These characters divide the square into contiguous regions.</p>

<p>Given the grid <code>grid</code> represented as a string array, return <em>the number of regions</em>.</p>

<p>Note that backslash characters are escaped, so a <code>&#39;\&#39;</code> is represented as <code>&#39;\\&#39;</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/15/1.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> grid = [&quot; /&quot;,&quot;/ &quot;]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/15/2.png" style="width: 200px; height: 198px;" />
<pre>
<strong>Input:</strong> grid = [&quot; /&quot;,&quot;  &quot;]
<strong>Output:</strong> 1
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2018/12/15/4.png" style="width: 200px; height: 200px;" />
<pre>
<strong>Input:</strong> grid = [&quot;/\\&quot;,&quot;\\/&quot;]
<strong>Output:</strong> 5
<strong>Explanation: </strong>Recall that because \ characters are escaped, &quot;\\/&quot; refers to \/, and &quot;/\\&quot; refers to /\.
</pre>

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

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 30</code></li>
	<li><code>grid[i][j]</code> is either <code>&#39;/&#39;</code>, <code>&#39;\&#39;</code>, or <code>&#39; &#39;</code>.</li>
</ul>

class Solution:
    def regionsBySlashes(self, grid: List[str]) -> int:  # O(n^2) time and space
        n = len(grid)
        m = 3*n
        mat = [[0] * m for _ in range(m)]  # need 3 rather than 2 because //
        for i, j in product(range(n), range(n)):
            r, c = 3 * i, 3 * j
            if grid[i][j] == "/":
                mat[r][c+2] = 1
                mat[r+1][c+1] = 1
                mat[r+2][c] = 1
            elif grid[i][j] == "\\":
                mat[r][c] = 1
                mat[r+1][c+1] = 1
                mat[r+2][c+2] = 1
        def dfs(mat, i, j):
            if not (0 <= i < m and 0 <= j < m) or mat[i][j] == 1:
                return
            mat[i][j] = 1
            for x, y in (i+1, j), (i-1, j), (i, j+1), (i, j-1):
                dfs(mat, x, y)
        count = 0  # count number of islands
        for i, j in product(range(m), range(m)):
            if mat[i][j] == 0:
                count += 1
                dfs(mat, i, j)
        return count
# https://leetcode.com/problems/regions-cut-by-slashes/solutions/5614788/simple-approach-using-expanded-grid-with-flood-fill-for-counting-regions/?envType=company&envId=facebook&favoriteSlug=facebook-three-months
        
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