<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)
        count = 0
        self.result = n * n * 4
        self.nodes = {}
        for i in range(n):
            for j in range(n):
                for k in range(1, 5):
                    self.nodes[str(i) + "*" + str(j) + "*" + str(k)] = count
                    count += 1

        self.parent = [i for i in range(n * n * 4)]
        def find(x):
            if self.parent[x] == x:
                return x
            return find(self.parent[x])
        def union(x, y):
            px, py = find(x), find(y)
            if px != py:
                self.result -= 1
                self.parent[px] = py
        edges = []
        for i in range(n):
            for j in range(n):
                if i - 1 >= 0:
                    edges.append([str(i-1) + "*" + str(j) + "*" + '3', str(i) + "*" + str(j) + "*" + '1'])
                if j - 1 >= 0:
                    edges.append([str(i) + "*" + str(j-1) + "*" + '2', str(i) + "*" + str(j) + "*" + '4'])
                if grid[i][j] == " ":
                    edges.append([str(i) + "*" + str(j) + "*" + '1', str(i) + "*" + str(j) + "*" + '2'])
                    edges.append([str(i) + "*" + str(j) + "*" + '2', str(i) + "*" + str(j) + "*" + '3'])
                    edges.append([str(i) + "*" + str(j) + "*" + '3', str(i) + "*" + str(j) + "*" + '4'])
                    edges.append([str(i) + "*" + str(j) + "*" + '4', str(i) + "*" + str(j) + "*" + '1'])
                elif grid[i][j] == "/":
                    edges.append([str(i) + "*" + str(j) + "*" + '1', str(i) + "*" + str(j) + "*" + '4'])
                    edges.append([str(i) + "*" + str(j) + "*" + '2', str(i) + "*" + str(j) + "*" + '3'])
                else:
                    edges.append([str(i) + "*" + str(j) + "*" + '1', str(i) + "*" + str(j) + "*" + '2'])
                    edges.append([str(i) + "*" + str(j) + "*" + '3', str(i) + "*" + str(j) + "*" + '4'])
        print(edges)
        for x, y in edges:
            union(self.nodes[x], self.nodes[y])
        
        return self.result
22018