<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 {
public:
    int regionsBySlashes(vector<string>& grid) {
        int n = grid.size();
        DSU dsu(4 * n * n);
        for (int r = 0; r < n; ++r)
            for (int c = 0; c < n; ++c) {
                int index = 4 * (r * n + c);
                switch (grid[r][c]) {
                case '/':
                    dsu.merge(index + 0, index + 3);
                    dsu.merge(index + 1, index + 2);
                    break;
                case '\\':
                    dsu.merge(index + 0, index + 1);
                    dsu.merge(index + 2, index + 3);
                    break;
                case ' ':
                    dsu.merge(index + 0, index + 1);
                    dsu.merge(index + 1, index + 2);
                    dsu.merge(index + 2, index + 3);
                    break;
                default:
                    break;
                }
                if (r + 1 < n)
                    dsu.merge(index + 2, index + 4 * n + 0);
                if (c + 1 < n)
                    dsu.merge(index + 1, index + 4 + 3);
            }
        int ans = 0;
        for (int i = 0; i < 4 * n * n; ++i)
            if (dsu.find(i) == i)
                ++ans;
        return ans;
    }

private:
    class DSU {
    public:
        DSU(int n) : parent_(n) {
            for (int i = 0; i < n; ++i)
                parent_[i] = i;
        }

        int find(int x) {
            if (parent_[x] != x)
                parent_[x] = find(parent_[x]);
            return parent_[x];
        }

        void merge(int x, int y) { parent_[find(x)] = find(y); }

    private:
        vector<int> parent_;
    };
};
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