<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 UnionFind {

    private:
      unordered_map<int,long>sz;
      unordered_map<int,long>p;
      int counter;

    public:

    UnionFind(){
        counter = 0;
    }


      int getCounter(){
        return counter;
      }


      int par(int u){
        if(p.find(u) == p.end()){
            p[u] = u;
            sz[u] = 1;
            return u;
        }

        while(p[u] != u){
            u = p[u];
        }
        return u;
      }

      void merge(int u, int v){
            int x = par(u);
            int y = par(v);

            if(x == y){
                counter++;
            }

            if(sz[x] > sz[y]){
                p[y] = x;
                sz[x] += sz[y];
            }
            else {
                p[x] = y;
                sz[y] += sz[x];
            }

      }

};


class Solution {



public:
    int regionsBySlashes(vector<string>& grid) {

        UnionFind u;
        
        int n = grid.size();

        int size = n+1;

        for(int i=0;i<n+1;i++){
            for(int j=0;j<n+1;j++){

                if(i == 0 or j == 0 or i == n or j == n)
                u.merge(0, i*size+j);

            }
        }

        for(int i=0;i<n;i++){
            string s = grid[i];
            for(int j=0;j<n;j++){
                char c = s[j];
                if(c == '/' ){
                    //cout << i*size + j+1 << " " <<  (i+1)*size+j << endl;
                    u.merge(i*size + j+1, (i+1)*size+j);
                }
                else if(c == '\\'){
                    //cout << i*size+j << " <> " <<  (i+1)*size+j+1 << endl;
                    u.merge(i*size+j, (i+1)*size+j+1);
                }
            }
        }

        return u.getCounter();
    }
};

// vertices 8, edges = 8
18038