<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 {
private:
    int fa[1005];
    int ans;
public:
    int find(int x){
        return x == fa[x] ? x : fa[x] = find(fa[x]);
    }
    void Union(int p, int q){
        int fp = find(p);
        int fq = find(q);
        if(fp != fq){
            fa[fp] = fq;
        }else{
            ans++;
        }
    }
    int regionsBySlashes(vector<string>& grid) {
        ans = 0;
        int n = grid.size();
        int m = n + 1;
        for(int i = 0; i < m * m; i++){
            fa[i] = i;
            int x = i / m;
            int y = i % m;
            if((x == 0 || x == n) && y > 0){
                Union(i, i - 1);
            }
            if((y == 0 || y == n) &&  x > 0){
                Union(i,i - m);
            }
        }
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                if(grid[i][j] == '\\'){
                    int x1 = i;
                    int y1 = j;
                    int x2 = i + 1;
                    int y2 = j + 1;
                    Union(x1 * m + y1, x2 * m + y2);
                }else if(grid[i][j] == '/'){
                    int x1 = i;
                    int y1 = j + 1;
                    int x2 = i + 1;
                    int y2 = j;
                    Union(x1 * m + y1, x2 * m + y2);
                }
            }
        }
        return ans;
    }
};
11176