<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 __init__(self):
        self.parent = []
        self.rank = []
        self.count = 0

    def regionsBySlashes(self, grid):
        n = len(grid)
        dots = n + 1
        self.parent = [i for i in range(dots * dots)]
        self.rank = [1] * (dots * dots)

        # Connect boundaries to the top-left corner (0,0)
        for i in range(dots):
            for j in range(dots):
                if i == 0 or j == 0 or i == n or j == n:
                    cell = i * dots + j
                    self.union(0, cell)

        # Process each cell and connect regions based on slashes
        for i in range(n):
            for j in range(n):
                if grid[i][j] == '\\':
                    cell1 = i * dots + j
                    cell2 = (i + 1) * dots + (j + 1)
                    self.union(cell1, cell2)
                elif grid[i][j] == '/':
                    cell1 = (i + 1) * dots + j
                    cell2 = i * dots + (j + 1)
                    self.union(cell1, cell2)

        return self.count

    def union(self, a, b):
        parentA = self.find(a)
        parentB = self.find(b)
        if parentA == parentB:
            self.count += 1
        else:
            if self.rank[parentA] > self.rank[parentB]:
                self.parent[parentB] = parentA
            elif self.rank[parentA] < self.rank[parentB]:
                self.parent[parentA] = parentB
            else:
                self.parent[parentB] = parentA
                self.rank[parentA] += 1

    def find(self, a):
        if self.parent[a] == a:
            return a
        self.parent[a] = self.find(self.parent[a])
        return self.parent[a]
16254