<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 {
     int get_index(int i, int j, int num, int n) {
        return (i*n+j)*4+num;
     }

     int find(vector<int>& parent, int node) {
        if (parent[node] == -1) return node;
        return parent[node] = find(parent, parent[node]);
     }

     int unite(vector<int>& parent, int x, int y) {
        int px = find(parent, x);
        int py = find(parent, y);

        if (px != py) {
            parent[px] = py;
            return 1;
        }
        return 0;
     }
public:
    int regionsBySlashes(vector<string>& grid) {
        int n = grid.size();
        int total = n*n*4;
        int region = total;

        vector<int> parent(total, -1);

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (i > 0) {
                    region -= unite(parent, get_index(i-1, j, 2, n), get_index(i, j, 0, n));
                }
                if (j > 0) {
                    region -= unite(parent, get_index(i, j-1, 1, n), get_index(i, j, 3, n));
                }
                if (grid[i][j] != '\\') {
                    region -= unite(parent, get_index(i, j, 0, n), get_index(i, j, 3, n));
                    region -= unite(parent, get_index(i, j, 1, n), get_index(i, j, 2, n));
                }
                if (grid[i][j] != '/') {
                    region -= unite(parent, get_index(i, j, 0, n), get_index(i, j, 1, n));
                    region -= unite(parent, get_index(i, j, 3, n), get_index(i, j, 2, n));
                }
            }
        }

        return region;
    }
};
12091