<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:
#         # to build the graph first
#         n = len(grid) + 1
#         nodes = []

#         for i in range(len(grid)):
#             string = grid[i]
#             for j in range(len(string)):
#                 if string[j] == " ":
#                     continue
#                 if string[j] == "/":
#                     nodes.append((i, j + 1))
#                     nodes.append((i+1, j))
#                 if string[j] == "\\":
#                     nodes.append((i, j))
#                     nodes.append((i+1, j + 1))

#         visited = set()
#         count = 0

#         def traverse(x, y):
#             nonlocal n
#             visited.add((x, y))
#             for dx, dy in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
#                 newx, newy = x + dx, y + dy
#                 if 0 <= newx < n and 0 <= newy < n and (newx, newy) not in nodes and (newx, newy) not in visited:
#                     traverse(newx, newy)

#         for i in range(n):
#             for j in range(n):
#                 if (i, j) not in visited and (i, j) not in nodes:
#                     traverse(i, j)
#                     count += 1
#         return count


class Solution:
    def regionsBySlashes(self, grid: List[str]) -> int:
        # to build the graph first
        n = len(grid)
        nodes = []
        board = [[0 for x in range(3 * n)] for y in range(3 * n)]

        for i in range(len(grid)):
            string = grid[i]
            for j in range(len(string)):
                if string[j] == " ":
                    continue
                row = 3 * i
                col = 3 * j
                if string[j] == "/":
                    board[row][col + 2] = 1
                    board[row + 1][col + 1] = 1
                    board[row + 2][col] = 1
                if string[j] == "\\":
                    board[row][col] = 1
                    board[row + 1][col + 1] = 1
                    board[row + 2][col + 2] = 1
        
        visited = set()
        count = 0
        # print(board)
        def traverse(x, y):
            visited.add((x, y))
            board[x][y] = 2
            for dx, dy in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
                newx, newy = x + dx, y + dy
                if 0 <= newx < 3 * n and 0 <= newy < 3* n and board[newx][newy] == 0:
                    traverse(newx, newy)
            return

        for i in range(3*n):
            for j in range(3 * n):
                if board[i][j] == 0 and (i, j) not in visited:
                    # print(i, j)
                    traverse(i, j)
                    count += 1
        return count

24519