<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 find(int point, vector<int> &parent){
        if(parent[point] == point){
            return point;
        }
        parent[point] = find(parent[point],parent);
        return parent[point];
    }

    void doUnion(int point1, int point2, int &ans, vector<int> &parent, vector<int> &ranks){
        int p1 = find(point1,parent);
        int p2 = find(point2,parent);
        if(p1 == p2){
            ans++;
            return;
        }
        if(ranks[p1] < ranks[p2]){
            parent[p1] = p2;
        }
        else if(ranks[p1] > ranks[p2]){
            parent[p2] = p1;
        }
        else{
            ranks[p1]++;
            parent[p2] = p1;
        }

    }

    int regionsBySlashes(vector<string>& grid) {
        int n = grid.size();
        int dots = n+1;
        vector<int> parent(dots*dots);
        vector<int> ranks(dots*dots);
        for(int i=0;i<parent.size();i++){
            parent[i] = i;
            ranks[i] = 1;
        }
        int ans = 1;
        for(int i=0;i<dots;i++){
            for(int j=0;j<dots;j++){
                if(i == 0 || i == dots - 1 || j == 0 || j == dots - 1){
                    int point = i*dots + j;
                    if(point != 0)
                        doUnion(0,point,ans,parent,ranks);
                }
            }
        }
        for(int i=0;i<n;i++){
            for(int j=0;j<n;j++){
                if(grid[i][j] == '/'){
                    int point1 = i*dots + (j+1);
                    int point2 = (i+1)*dots + j;
                    doUnion(point1,point2,ans,parent,ranks); 
                }
                else if(grid[i][j] == '\\'){
                    int point1 = i*dots + j;
                    int point2 = (i+1)*dots + j+1;
                    doUnion(point1,point2,ans,parent,ranks);
                }
            }
        }
        return ans;
    }

};
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