<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) {
        // for all i,j:
        // i -> 3i + 1
        // j -> 3j + 1
        int n = grid.size();
        vector<vector<int>> map(3 * n, vector<int>(3 * n, 0));
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < grid[i].size(); j++) {
                // '/' -> 1, '\' -> 2, ' ' -> 0
                if (grid[i][j] == ' ') {
                    continue;
                } else if (grid[i][j] == '/') {
                    map[3 * i + 2][3 * j] = 1;
                    map[3 * i + 1][3 * j + 1] = 1;
                    map[3 * i][3 * j + 2] = 1;
                } else {
                    // '\\' character
                    map[3 * i][3 * j] = 2;
                    map[3 * i + 1][3 * j + 1] = 2;
                    map[3 * i + 2][3 * j + 2] = 2;
                }
            }
        }
        // mark visited -> -1
        // flood fill
        int regions = 0;
        // for (int i = 0; i < 3 * n; i++) {
        //     for (int j = 0; j < 3*n; j++) {
        //         cout << map[i][j];
        //     }
        //     cout << "\n";
        // }

        for (int i = 0; i < 3 * n; i++) {
            for (int j = 0; j < 3 * n; j++) {
                if (map[i][j] == -1 || map[i][j] == 2 || map[i][j] == 1) continue;
                regions++;
                bfs(make_pair(i, j), map);
            }
        }
        return regions;
    }

    void bfs(pair<int, int> start, vector<vector<int>>& map) {
        int n = map.size();
        vector<pair<int, int>> directions{ make_pair(-1, 0), make_pair(0, 1), make_pair(1, 0), make_pair(0, -1) };
        deque<pair<int, int>> pts;
        pts.push_back(start);
        map[start.first][start.second] = -1;
        while (!pts.empty()) {
            pair<int, int> curr = pts.front();
            pts.pop_front();

            for (int i = 0; i < directions.size(); i++) {
                int new_row = curr.first + directions[i].first;
                int new_col = curr.second + directions[i].second;
                // skip invalid coord
                if (new_row < 0 || new_row >= n || new_col < 0 || new_col >= n) continue;
                // skip if already visited or boundary
                if (map[new_row][new_col] == -1 || 
                    map[new_row][new_col] == 1 || 
                    map[new_row][new_col] == 2) continue;
                map[new_row][new_col] = -1;
                pts.push_back(make_pair(new_row, new_col));
            }
        }
    }
};
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