<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:
        regions = (len(grid) ** 2) * 4
        parents = [-1] * regions
        def findParent(x):
            while parents[x] != -1:
                x = parents[x]
            return x
        def mergeRegions(x, y):
            xParent = findParent(x)
            yParent = findParent(y)
            if xParent != yParent:
                parents[xParent] = yParent
                return 1
            return 0
        def getPos(i, j, triNum):
            return (i * len(grid) + j) * 4 + triNum
        for i in range(len(grid)):
            for j in range(len(grid)):
                if i > 0:
                    regions -= mergeRegions(getPos(i, j, 0), getPos(i - 1, j, 2))
                if j > 0:
                    regions -= mergeRegions(getPos(i, j, 3), getPos(i, j - 1, 1))
                if grid[i][j] != '/':
                    regions -= mergeRegions(getPos(i, j, 0), getPos(i, j, 1))
                    regions -= mergeRegions(getPos(i, j, 2), getPos(i, j, 3))
                if grid[i][j] != '\\':
                    regions -= mergeRegions(getPos(i, j, 0), getPos(i, j, 3))
                    regions -= mergeRegions(getPos(i, j, 1), getPos(i, j, 2))
        return regions

16471