<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:
        n = len(grid)
        matrix = [[0] * 2 * n for _ in range(2 * n)]
        diagonals = set()
        for i in range(n):
            j = 0
            while j < n:
                if grid[i][j] == '/':
                    matrix[2 * i][2 * j + 1] = 1
                    matrix[2 * i + 1][2 * j] = 1
                    diagonals.add((2 * i, 2 * j + 1, 2 * i + 1, 2 * j))
                    if i >= 1 and j < n - 1:
                        if (2 * (i - 1), 2 * (j + 1) + 1, 2 * (i - 1) + 1, 2 * (j + 1)) in diagonals:
                            diagonals.add((2 * (i - 1) + 1, 2 * (j + 1), 2 * i, 2 * j + 1))
                    j += 1
                elif grid[i][j] == '\\':
                    matrix[2 * i][2 * j] = 1
                    matrix[2 * i + 1][2 * j + 1] = 1
                    diagonals.add((2 * i, 2 * j, 2 * i + 1, 2 * j + 1))
                    if i >= 1 and j >= 1:
                        if ((2 * (i - 1), 2 * (j - 1), 2 * (i - 1) + 1, 2 * (j - 1) + 1)) in diagonals:
                            diagonals.add((2 * (i - 1) + 1, 2 * (j - 1) + 1, 2 * i, 2 * j))
                    j += 1
                else:
                    j += 1


        visited = set()
        def dfs(start_row: int, start_col: int):
            visited.add((start_row, start_col))
            
            # vertical & horizontal moving
            if start_col + 1 < 2 * n:
                if matrix[start_row][start_col + 1] == 0 and \
                    (start_row, start_col + 1) not in visited:
                    dfs(start_row, start_col + 1)
            if start_row + 1 < 2 * n:
                if matrix[start_row + 1][start_col] == 0 and \
                    (start_row + 1, start_col) not in visited:
                    dfs(start_row + 1, start_col)

            if start_col - 1 >= 0:
                if matrix[start_row][start_col - 1] == 0 and \
                    (start_row, start_col - 1) not in visited:
                    dfs(start_row, start_col - 1)
            if start_row - 1 >= 0:
                if matrix[start_row - 1][start_col] == 0 and \
                    (start_row - 1, start_col) not in visited:
                    dfs(start_row - 1, start_col)

            # diagonal moving
            # left & down
            if start_col - 1 >= 0 and start_row + 1 < 2 * n and (start_row, start_col - 1, start_row + 1, start_col) not in diagonals:
                if matrix[start_row + 1][start_col - 1] == 0 and \
                    (start_row + 1, start_col - 1) not in visited:
                    dfs(start_row + 1, start_col - 1)

            # right & down
            if start_col + 1 < 2 * n and start_row + 1 < 2 * n and (start_row, start_col + 1, start_row + 1, start_col) not in diagonals:
                if matrix[start_row + 1][start_col + 1] == 0 and \
                    (start_row + 1, start_col + 1) not in visited:
                    dfs(start_row + 1, start_col + 1)

            # left & up
            if start_col - 1 >= 0 and start_row - 1 >= 0 and (start_row - 1, start_col, start_row, start_col - 1) not in diagonals:
                if matrix[start_row - 1][start_col - 1] == 0 and \
                    (start_row - 1, start_col - 1) not in visited:
                    dfs(start_row - 1, start_col - 1)

            # right & up
            if start_col + 1 < 2 * n and start_row - 1 >= 0 and (start_row - 1, start_col, start_row, start_col + 1) not in diagonals:
                if matrix[start_row - 1][start_col + 1] == 0 and \
                    (start_row - 1, start_col + 1) not in visited:
                    dfs(start_row - 1, start_col + 1)

        k = 0
        for i in range(2 * n):
            for j in range(2 * n):
                if matrix[i][j] == 0 and (i, j) not in visited:
                    dfs(i, j)
                    k += 1
                    
        return k
19951