<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 DSU {
    vector<int> par, rank;
    public:
    int comp;
    DSU (int n){
        par.resize(n);
        rank.resize(n,0);
        for(int i=0;i<n;i++){
            par[i]=i;
        }
        comp=n;
    }
    int findPar(int u){
        if(par[u]==u) return u;
        return par[u]=findPar(par[u]);
    }
    void merge(int u,int v){
        if(findPar(u)==findPar(v)){
            return;
        }
        int x=par[u];
        int y=par[v];
        if(rank[x]>rank[y]) swap(x,y);
        par[x]=y;
        if(rank[x]==rank[y]) {
            rank[y]++;
        }
        comp--;
        return;
    }
};

class Solution {
public:
    int regionsBySlashes(vector<string>& grid) {
        int k=grid.size();
        vector<vector<int>> newgrid(3*k);
        for(int i=0;i<k;i++){
            for(int j=0;j<k;j++){
                if(grid[i][j]=='/'){
                    newgrid[3*i].push_back(1);
                    newgrid[3*i].push_back(1);
                    newgrid[3*i].push_back(0);
                    newgrid[3*i+1].push_back(1);
                    newgrid[3*i+1].push_back(0);
                    newgrid[3*i+1].push_back(1);
                    newgrid[3*i+2].push_back(0);
                    newgrid[3*i+2].push_back(1);
                    newgrid[3*i+2].push_back(1);
                }
                else if(grid[i][j]==' ') {
                    newgrid[3*i].push_back(1);
                    newgrid[3*i].push_back(1);
                    newgrid[3*i].push_back(1);
                    newgrid[3*i+1].push_back(1);
                    newgrid[3*i+1].push_back(1);
                    newgrid[3*i+1].push_back(1);
                    newgrid[3*i+2].push_back(1);
                    newgrid[3*i+2].push_back(1);
                    newgrid[3*i+2].push_back(1);
                }
                else {
                    newgrid[3*i].push_back(0);
                    newgrid[3*i].push_back(1);
                    newgrid[3*i].push_back(1);
                    newgrid[3*i+1].push_back(1);
                    newgrid[3*i+1].push_back(0);
                    newgrid[3*i+1].push_back(1);
                    newgrid[3*i+2].push_back(1);
                    newgrid[3*i+2].push_back(1);
                    newgrid[3*i+2].push_back(0);
                }
            }
        }

        int n=newgrid.size();
        int m=n;
        // cout << newgrid[2][2];
        DSU dsu(n*n); int countzero=0;
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(newgrid[i][j]==0) { countzero++; continue;}
                if (i + 1 < m && newgrid[i + 1][j] == 1)
                dsu.merge(i * n + j, 
                          (i + 1) * n + j);
                if (i - 1 >= 0 && newgrid[i - 1][j] == 1)
                    dsu.merge(i * n + j, 
                            (i - 1) * n + j);
                if (j + 1 <n && newgrid[i][j + 1] == 1)
                    dsu.merge(i *n + j, 
                            i * n + j + 1);
                if (j - 1 >= 0 && newgrid[i][j - 1] == 1)
                    dsu.merge(i * n + j,
                            i * n + j - 1); 
            }
        }
        cout << dsu.comp;
    //      int *c = new int[n * n];
    // int numberOfIslands = 0;
    // for (int j = 0; j < n; j++)
    // {
    //     for (int k = 0; k < n; k++)
    //     {
    //         if (newgrid[j][k] == 1)
    //         {
    //             int x = dsu.findPar(j * n + k);
 
    //             // If frequency of set is 0,
    //             // increment numberOfIslands
    //             if (c[x] == 0)
    //             {
    //                 numberOfIslands++;
    //                 c[x]++;
    //             }
 
    //             else
    //                 c[x]++;
    //         }
    //     }
    // }
    return dsu.comp-countzero;

    }
};
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