<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 find(int u, vector<int>& p) {
        if (u != p[u]) p[u] = find(p[u], p);
        return p[u];
    }

    void merge(int u, int v, vector<int>& p, vector<int>& sz, int& count) {
        u = find(u, p);
        v = find(v, p);

        if (u != v) {
            if (sz[u] > sz[v]) {
                p[v] = u;
                sz[u] += sz[v];
            } else {
                p[u] = v;
                sz[v] += sz[u];
            }
            count--;
        }
    }

    int regionsBySlashes(vector<string>& grid) {
        int n = grid.size();
        int row = n * 2;
        int count = n * row;
        vector<int> p(n * row);
        iota(p.begin(), p.end(), 0);
        vector<int> sz(n * row, 1);

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                int l = i * row + j * 2;
                int r = l + 1;
                int ll = l - 1;
                int rr = r + 1;
                int ul = l - row;
                int ur = r - row;
                int dl = l + row;
                int dr = r + row;

                if (j > 0) merge(ll, l, p, sz, count);
                if (j < n - 1) merge(r, rr, p, sz, count);

                if (grid[i][j] == ' ') {
                    merge(l, r, p, sz, count);
                    if (i > 0) merge(r, grid[i - 1][j] == '/' ? ur : ul, p, sz, count);
                    if (i < n - 1) merge(l, grid[i + 1][j] == '/' ? dl : dr, p, sz, count);
                } else if (grid[i][j] == '/') {
                    if (i > 0) merge(l, grid[i - 1][j] == '/' ? ur : ul, p, sz, count);
                    if (i < n - 1) merge(r, grid[i + 1][j] == '/' ? dl : dr, p, sz, count);
                } else {
                    if (i > 0) merge(r, grid[i - 1][j] == '/' ? ur : ul, p, sz, count);
                    if (i < n - 1) merge(l, grid[i + 1][j] == '/' ? dl : dr, p, sz, count);
                }
            }
        }
        return count;
    }
};
12091