<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 {
public:

    void visit(int i,vector<vector<int>>& g, vector<bool>& visited){
        visited[i]=true;
        for(int u: g[i]){
            if(visited[u]) continue;
            visit(u, g, visited);
        }
    }

    int regionsBySlashes(vector<string>& grid) {
        int n=grid.size();
        int m=grid[0].size();
        vector<vector<int>> g;
        for(int i=0;i<2*(n*m);++i) g.push_back(vector<int>());
        
        for(int i=0;i<n;++i){
            for(int j=0;j<m;++j){
                int v0=2*(i*m+j);
                int v1=2*(i*m+j)+1;
                if(grid[i][j]==' '){
                    g[v0].push_back(v1);
                    g[v1].push_back(v0);
                }
                

                // left
                int x=i;
                int y=j-1;
                if(y>=0){
                    int vx=2*(x*m+y)+1;
                    g[vx].push_back(v0);
                    g[v0].push_back(vx);
                }

                // bottom
                x=i+1;
                y=j;
                if(x<n){
                    int v=(grid[i][j]=='\\' ? v0: v1);
                    int vx=2*(x*m+y)+(grid[x][y]=='\\' ? 1 : 0);
                    g[v].push_back(vx);
                    g[vx].push_back(v);
                }
            }
        }

        // for(int i=0;i<2*n*m;++i){
        //     cout<<"g["<<i<<"]=";
        //     for(int j: g[i]) cout<<j<<" ";
        //     cout<<"\n";
        // }

        vector<bool> visited;
        for(int i=0;i<2*(n*m);++i) visited.push_back(false);
        int ans=0;
        for(int i=0;i<2*(n*m);++i){
            if(!visited[i]){
                visit(i, g, visited);
                ans+=1;
            }
        }
        return ans;
    }
};
22461