<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)

        nodes = [[[] for _ in range(N)] for _ in range(N)]
        cur = 0

        for i in range(N):
            row = grid[i]
            for j,ch in enumerate(row):
                if ch in ("/","\\"):
                    nodes[i][j] = (cur,cur+1)
                    cur += 2
                else:
                    nodes[i][j] = cur
                    cur += 1
        # print(nodes)
        adj = defaultdict(set)
        for i in range(N):
            row = grid[i]
            for j,ch in enumerate(row):

                if ch == "/":
                    _,r = nodes[i][j]
                    if j < N-1:
                        adj[r].add(r+1)
                        adj[r+1].add(r)
                    
                    if i < N-1:
                        if grid[i+1][j] == "/":
                            adj[r].add(nodes[i+1][j][0])
                            adj[nodes[i+1][j][0]].add(r)

                        elif grid[i+1][j] == "\\":
                            adj[r].add(nodes[i+1][j][1])
                            adj[nodes[i+1][j][1]].add(r)
                        else:
                            adj[r].add(nodes[i+1][j])
                            adj[nodes[i+1][j]].add(r)
                        
                elif ch == "\\":
                    l,r = nodes[i][j]
                    if j < N-1:
                        adj[r].add(r+1)
                        adj[r+1].add(r)
                    
                    if i < N-1:
                        if grid[i+1][j] == "/":
                            adj[l].add(nodes[i+1][j][0])
                            adj[nodes[i+1][j][0]].add(l)

                        elif grid[i+1][j] == "\\":
                            adj[l].add(nodes[i+1][j][1])
                            adj[nodes[i+1][j][1]].add(l)
                        else:
                            adj[l].add(nodes[i+1][j])
                            adj[nodes[i+1][j]].add(l)

                else:
                    n = nodes[i][j]
                    if j < N-1:
                        adj[n].add(n+1)
                        adj[n+1].add(n)
                    
                    if i < N-1:
                        if grid[i+1][j] == "/":
                            adj[n].add(nodes[i+1][j][0])
                            adj[nodes[i+1][j][0]].add(n)

                        elif grid[i+1][j] == "\\":
                            adj[n].add(nodes[i+1][j][1])
                            adj[nodes[i+1][j][1]].add(n)
                        else:
                            adj[n].add(nodes[i+1][j])
                            adj[nodes[i+1][j]].add(n)
        # print(adj)

        def dfs(u):
            seen.add(u)
            for v in adj[u]:
                if v in seen:
                    continue
                dfs(v)
            return

        res = 0
        seen = set()
        for node in range(cur):
            if node in seen:
                continue
            res += 1

            dfs(node)
        
        return res
        
21691