<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 {
    class Node {
    public:
        bool visited = false;
        vector<Node*> edges;
    };
public:
    int regionsBySlashes(vector<string>& grid) {
        int n = grid.size();
        int numNodes = 2 * (n * n + n);
        int numNodesPerRow = 2 * n + 1;
        vector<Node*> nodes;
        for (int i = 0; i < numNodes; i++) {
            nodes.push_back(new Node());
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                int index = i * numNodesPerRow + j;
                Node* top = nodes[index];
                index += n;
                Node* left = nodes[index];
                index++;
                Node* right = nodes[index];
                index += n;
                Node* bottom = nodes[index];
                if (grid[i][j] == ' ') {
                    top->edges.push_back(left);
                    top->edges.push_back(right);
                    left->edges.push_back(top);
                    left->edges.push_back(bottom);
                    right->edges.push_back(top);
                    right->edges.push_back(bottom);
                    bottom->edges.push_back(left);
                    bottom->edges.push_back(right);
                } else if (grid[i][j] == '/') {
                    top->edges.push_back(left);
                    left->edges.push_back(top);
                    right->edges.push_back(bottom);
                    bottom->edges.push_back(right);
                } else if (grid[i][j] == '\\') {
                    top->edges.push_back(right);
                    right->edges.push_back(top);
                    left->edges.push_back(bottom);
                    bottom->edges.push_back(left);
                }
            }
        }
        int ans = 0;
        for (int i = 0; i < numNodes; i++) {
            if (!nodes[i]->visited) {
                bfs(nodes[i]);
                ans++;
            }
        }
        return ans;
    }
    void bfs(Node* current) {
        current->visited = true;
        for (Node* edge : current->edges) {
            if (!edge->visited) bfs(edge);
        }
    }
};
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