<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)
        parent = [i for i in range(n*n*4)]
        rank = [1 for i in range(n*n*4)]

        def find(x):
            if x != parent[x]:
                parent[x] = find(parent[x])
            return parent[x]
        
        def union(x,y):
            rx,ry = find(x), find(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    parent[rx] = ry
                else:
                    parent[ry] = rx
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                return
        
        def getNode(x,y,index):
            return x*4*n + y*4 + index
        
        # 0 > up, 1 -> right, 2 -> bottom, 3 -> left
        for x in range(n):
            for y in range(n):
                if grid[x][y] == ' ':
                    union(getNode(x,y,0),getNode(x,y,1))
                    union(getNode(x,y,0),getNode(x,y,2))
                    union(getNode(x,y,0),getNode(x,y,3))
                elif grid[x][y] == '/':
                    union(getNode(x,y,0),getNode(x,y,3))
                    union(getNode(x,y,1),getNode(x,y,2))
                else:
                    union(getNode(x,y,0),getNode(x,y,1))
                    union(getNode(x,y,2),getNode(x,y,3))
                
                #merge sides
                for di,dj,a,b in [(0,1,1,3), (1,0,2,0), (0,-1,3,1),(-1,0,0,2)]:
                    ni,nj = x+di, y+dj
                    if 0 <= ni < n and 0 <= nj < n:
                        union(getNode(x,y,a), getNode(ni,nj,b))


        regions = set()
        for i in range(n*n*4):
            regions.add(find(i))
        return len(regions)


17776