<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 m = grid.size();
        int n = grid[0].size();

        int res = 4 * m * n;
        vector<int> roots;

        // set root to be itself
        for(int i = 0;i < res;++i) {
            roots.push_back(i);
        }

        for(int i = 0;i < m;++i) {
            for(int j = 0;j < n;++j) {
                int n0 = get_key(i, j, n, 0);
                int n1 = get_key(i, j, n, 1);
                int n2 = get_key(i, j, n, 2);
                int n3 = get_key(i, j, n, 3);
                if(grid[i][j] == ' ') {
                    if(union_two(roots, n0, n1)) {
                        res--;
                    }
                    if(union_two(roots, n0, n2)) {
                        res--;
                    }
                    if(union_two(roots, n0, n3)) {
                        res--;
                    }

                } else if(grid[i][j] == '/') {
                    if(union_two(roots, n0, n1)) {
                        res--;
                    }
                    if(union_two(roots, n3, n2)) {
                        res--;
                    }
                } else {
                    if(union_two(roots, n0, n3)) {
                        res--;
                    }
                    if(union_two(roots, n1, n2)) {
                        res--;
                    }
                }

                if(i != 0) {
                    if(union_two(roots, n0, get_key(i-1,j,n,2))) {
                        res--;
                    }
                }
                if(j != 0) {
                    if(union_two(roots, n1, get_key(i,j-1,n,3))) {
                        res--;
                    }
                }
            }
        }

        return res;
        
    }
private:
    int get_key(int i, int j, int n, int r) {
        return (i * n + j )*4 + r;
    }
    int find_root(vector<int> &roots, int node) {
        if(roots[node] != node) {
            return find_root(roots, roots[node]);
        } else {
            return node;
        }
    }
    bool union_two(vector<int> &roots, int n1, int n2) {
        int p1 = find_root(roots, n1);
        int p2 = find_root(roots, n2);
        if(p1 != p2) {
            roots[p2] = p1;
            return true;
        } else {
            return false;
        }
    }
};
12853