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

        // turn grid into extended
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == '/') {
                    extended[3 * i + 2][3 * j] = 'x';
                    extended[3 * i + 1][3 * j + 1] = 'x';
                    extended[3 * i][3 * j + 2] = 'x';
                } else if (grid[i][j] == '\\') {
                    extended[3 * i][3 * j] = 'x';
                    extended[3 * i + 1][3 * j + 1] = 'x';
                    extended[3 * i + 2][3 * j + 2] = 'x';
                }
            }
        }

        int cnt = 0;
        vector<vector<int>> dirs{{0, 1}, {1, 0}, {-1, 0}, {0, -1}};
        for (int i = 0; i < n * 3; i++) {
            for (int j = 0; j < n * 3; j++) {
                if (extended[i][j] == ' ') {
                    cnt++;

                    // use bfs to find all connected
                    queue<pair<int, int>> q;
                    q.push(make_pair(i, j));
                    while (!q.empty()) {
                        int r = q.front().first;
                        int c = q.front().second;
                        q.pop();

                        for (const auto& dir : dirs) {
                            int nr = r + dir[0];
                            int nc = c + dir[1];
                            if (nr >= 0 && nc >= 0 && nr < 3 * n && nc < 3 * n &&
                                extended[nr][nc] == ' ') {
                                extended[nr][nc] = 'x';
                                q.push(make_pair(nr, nc));
                            }
                        }
                    }
                }
            }
        }
        return cnt;
    }
};
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