<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:
    vector<pair<int, int>> fwd = {{0,2},{1,1},{2,0}} ;
    vector<pair<int, int>> bwd= {{0,0},{1,1},{2,2}};
    vector<pair<int, int>> rldu = {{0,1},{0,-1},{1,0}, {-1,0}};
    int regionsBySlashes(vector<string>& grid) {
        int n = grid.size();
        vector<vector<bool>> mat(3*n, vector<bool>(3*n, 0));

        int rowStart, colStart;
        int ans = 0;
        for(int i = 0; i<n; i++){
            rowStart = 3*i;
            for(int j = 0; j<n;j++){
                colStart = 3*j;
                // cout<< grid[i][j]<< rowStart<< " "<< colStart<< "--> ";
                // if(grid[i][j] == "\\"){}
                markMat(grid[i][j],rowStart,  colStart, mat);
            }
        }

        // print(mat);

        vector<vector<bool>> vis(3*n, vector<bool>(3*n, false));
        n= mat.size();
        int regionCnt = 0;
        for(int i = 0; i<n; i++){
            for(int j = 0; j<n;j++){
               if(!vis[i][j] && mat[i][j] == 0){
                    dfs(mat, vis, i, j);
                    regionCnt++;
                    // cout<< i<< endl;
                    // print(vis);
               }
            }
        }

        return regionCnt;

    }

    void dfs(vector<vector<bool>>& mat,  vector<vector<bool>>& vis, int row, int col){
        int r, c;
        for (auto p : rldu){
            r = row + p.first;
            c = col + p.second;
            if(isValid(r,c, mat.size()) && !vis[r][c] && mat[r][c]==0){
                vis[r][c] = true;
                dfs(mat, vis, r, c);
            }
        }

        return;

    }

    bool isValid(int r, int c, int n ){
        if( r >=0 && r < n && c >=0 && c <n)
            return true;
        return false;
    }
    void print (vector<vector<bool>>& mat){
        int n= mat.size();
        for(int i = 0; i<n; i++){
            for(int j = 0; j<n;j++){
               cout<< mat[i][j]<< " ";
            }

            cout<<endl;
        }
        return;
        
    }

    void markMat(char ch, int rowStart, int colStart , vector<vector<bool>>& mat){
        int r,c;
        if(ch == '/'){
            // cout<< ch<< " ";
            for(auto p : fwd){
                r = rowStart+p.first;
                c = colStart+p.second;
                // cout<< r<< " "<< c << "; ";
                mat[r][c] = 1;
            }
        }
        else if(ch == '\\'){
            // cout<< ch<< " ";
            for(auto p : bwd){
                r = rowStart+p.first;
                c = colStart+p.second;
                // cout<< r<< " "<< c << "; ";
                mat[r][c] = 1;
            }
        }

        // cout<<endl;
        return;

    }
};
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