<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 DisjointSet{
    vector<int> size,parent;
    public:
    DisjointSet(int  n){
        parent.resize(n,0);
        size.resize(n,0);
        for(int i=0;i<n;i++){
            parent[i]=i;
        }
    }
    int findUP(int child){
        if(child==parent[child]){
            return child;
        }
        return parent[child]=findUP(parent[child]);
    }
    void unionBysize(int r,int s){
        int u_r=findUP(r);
        int u_s=findUP(s);
        if(u_s==u_r){
            return ;
        }
        if(size[u_r]>size[u_s]){
            parent[u_s]=u_r;
            size[u_r]+=size[u_s];
        }else{
             parent[u_r]=u_s;
            size[u_s]+=size[u_r];
        }

    }
};


class Solution {
public:

    int regionsBySlashes(vector<string>& grid) {
        int n=grid.size();
        int m=n+1;
        DisjointSet ds(m*m);
        for(int i=0;i<m;i++){
            for(int j=0;j<m;j++){
                int pos=i*m+j;
                if(i==0 || i==m-1 || j==0 || j==m-1){
                    ds.unionBysize(0,pos);
                }
            }
        }
        int ans=1;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j]=='/'){
                    int x=i*m+j+1;
                    int y=(i+1)*m+j;
                    if(ds.findUP(x)==ds.findUP(y)){
                        ans++;
                    }else{
                    ds.unionBysize(x,y);

                    }
                }
                 if(grid[i][j]=='\\'){
                    int x=i*m+j;
                    int y=(i+1)*m+j+1;
                    if(ds.findUP(x)==ds.findUP(y)){
                        ans++;
                    }else{
                    ds.unionBysize(x,y);

                    }
                }
            }
        }
        return ans;
       

    }
};
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