<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:
    int h;
    int w;
    vector<vector<vector<bool>>> visited;
    vector<string> grid;
    int regionsBySlashes(vector<string>& _grid) {
        grid = _grid;
        h = grid.size();
        w = grid[0].size();
        int cnt = 0;
        visited.assign(h, vector<vector<bool>>(w, vector<bool>(4, false)));
        for(int row=0; row<h; row++) {
            for(int col=0; col<w; col++) {
                for(int t=0; t<4; t++) {
                    if(!visited[row][col][t]) {
                        dfs(row, col, t);
                        cnt++;
                    }
                }
            }
        }
        return cnt;
    }

    bool inBound(int& row, int& col) {
        return 0<=row && row<h && 0<=col && col<w;
    }

    void dfs(int row, int col, int t) {
        if(!inBound(row, col) || visited[row][col][t]) {
            return;
        }
        visited[row][col][t] = true;
        // Visit outside the square
        switch (t) {
            case 0:
                dfs(row-1, col, 2);
                break;
            case 1:
                dfs(row, col+1, 3);
                break;
            case 2:
                dfs(row+1, col, 0);
                break;
            case 3:
                dfs(row, col-1, 1);
                break;
        }

        // Check regions inside the square
        if(grid[row][col] != '/') {
            dfs(row, col, t^1);
        }
        if(grid[row][col] != '\\') {
            dfs(row, col, t^3);
        }
    }
};
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