<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:

    # Directions for traversal: right, left, down, up
    DIRECTIONS = [
        (0, 1),
        (0, -1),
        (1, 0),
        (-1, 0),
    ]

    def regionsBySlashes(self, grid):
        grid_size = len(grid)
        # Create a 3x3 matrix for each cell in the original grid
        expanded_grid = [[0] * (grid_size * 3) for _ in range(grid_size * 3)]

        # Populate the expanded grid based on the original grid
        # 1 represents a barrier in the expanded grid
        for i in range(grid_size):
            for j in range(grid_size):
                base_row = i * 3
                base_col = j * 3
                # Check the character in the original grid
                if grid[i][j] == "\\":
                    # Mark diagonal for backslash
                    expanded_grid[base_row][base_col] = 1
                    expanded_grid[base_row + 1][base_col + 1] = 1
                    expanded_grid[base_row + 2][base_col + 2] = 1
                elif grid[i][j] == "/":
                    # Mark diagonal for forward slash
                    expanded_grid[base_row][base_col + 2] = 1
                    expanded_grid[base_row + 1][base_col + 1] = 1
                    expanded_grid[base_row + 2][base_col] = 1

        region_count = 0
        # Count regions using flood fill
        for i in range(grid_size * 3):
            for j in range(grid_size * 3):
                # If we find an unvisited cell (0), it's a new region
                if expanded_grid[i][j] == 0:
                    # Fill that region
                    self._flood_fill(expanded_grid, i, j)
                    region_count += 1

        return region_count

    # Flood fill algorithm to mark all cells in a region
    def _flood_fill(self, expanded_grid, row, col):
        queue = [(row, col)]
        expanded_grid[row][col] = 1

        while queue:
            current_cell = queue.pop(0)
            # Check all four directions from the current cell
            for direction in self.DIRECTIONS:
                new_row = direction[0] + current_cell[0]
                new_col = direction[1] + current_cell[1]
                # If the new cell is valid and unvisited, mark it and add to queue
                if self._is_valid_cell(expanded_grid, new_row, new_col):
                    expanded_grid[new_row][new_col] = 1
                    queue.append((new_row, new_col))

    # Check if a cell is within bounds and unvisited
    def _is_valid_cell(self, expanded_grid, row, col):
        n = len(expanded_grid)
        return (
            row >= 0
            and col >= 0
            and row < n
            and col < n
            and expanded_grid[row][col] == 0
        )
16363