<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 dfs(vector<vector<char>>& scale, int i, int j, vector<vector<bool>>& vis, vector<pair<int, int>>& dir) {
        if (i < 0 || i >= scale.size() || j < 0 || j >= scale[0].size()) {
            return;
        }
        if (scale[i][j] == '\\' || scale[i][j] == '/') {
            return;
        }
        if (vis[i][j]) {
            return;
        }
        vis[i][j] = true;
        for (auto& d : dir) {
            int ni = i + d.first;
            int nj = j + d.second;
            dfs(scale, ni, nj, vis, dir);
        }
    }

    int regionsBySlashes(vector<string>& grid) {
        int n = grid.size();
        vector<vector<char>> scale(3 * n, vector<char>(3 * n, ' '));

        vector<vector<char>> emp = {{' ', ' ', ' '}, {' ', ' ', ' '}, {' ', ' ', ' '}};
        vector<vector<char>> fs = {{' ', ' ', '/'}, {' ', '/', ' '}, {'/', ' ', ' '}};
        vector<vector<char>> bs = {{'\\', ' ', ' '}, {' ', '\\', ' '}, {' ', ' ', '\\'}};

        for (int i = 0; i < n; ++i) {
            for (int j = 0; j < n; ++j) {
                char c = grid[i][j];
                int baseRow = 3 * i;
                int baseCol = 3 * j;
                vector<vector<char>> pattern;

                if (c == ' ') {
                    pattern = emp;
                } else if (c == '/') {
                    pattern = fs;
                } else if (c == '\\') {
                    pattern = bs;
                }

                for (int x = 0; x < 3; ++x) {
                    for (int y = 0; y < 3; ++y) {
                        scale[baseRow + x][baseCol + y] = pattern[x][y];
                    }
                }
            }
        }

        vector<vector<bool>> vis(scale.size(), vector<bool>(scale[0].size(), false));
        int ans = 0;
        vector<pair<int, int>> directions = {{1, 0}, {-1, 0}, {0, -1}, {0, 1}};

        for (int i = 0; i < scale.size(); ++i) {
            for (int j = 0; j < scale[0].size(); ++j) {
                if (scale[i][j] == ' ' && !vis[i][j]) {
                    dfs(scale, i, j, vis, directions);
                    ans++;
                }
            }
        }

        return ans;
    }
};

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