<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 UnionFind {
    int n, component;
    vector<int> parent, c;

public:
    UnionFind(int n) {
        this->n = n;
        this->component = n;
        for (int i = 0; i < n; i++){
            parent.push_back(i);
            c.push_back(1);
        }
    }
    int find(int x) {
        while (x != parent[x])
            x = parent[x];
        return x;
    }
    void merge(int u, int v) {
        int i = find(u);
        int j = find(v);
        if (i == j)
            return;
        component--;
        if (c[i] > c[j]) {
            parent[j] = i;
            c[i]++;
        } else {
            parent[i] = j;
            c[j]++;
        }
    }
    void print(){
        for(auto &p:parent)
            cout << p << " ";
        cout << "\n";
    }
    int noOfComponent() { return component; }
};
class Solution {
    set<pair<int, int>> s;
    void add(int u, int v) {
        if (u > v)
            swap(u, v);
        s.insert({u, v});
    }
    int connectedComponented(int n) {
        cout << n << "\n";
        UnionFind uf(n);
        for (auto& i : s){
            uf.merge(i.first, i.second);
        }
        return uf.noOfComponent();
    }

public:
    int regionsBySlashes(vector<string>& grid) {
        int rows = grid.size(), cols = grid[0].size();
        vector<vector<int>> ids(rows, vector<int>(cols, -1));
        int id = 0;
        for (int r = 0; r < rows; r++) {
            for (int c = 0; c < cols; c++) {
                ids[r][c] = (id++);
                if (grid[r][c] != ' ')
                    id++;
                if (r > 0) {
                    int u = ids[r - 1][c];
                    int v = ids[r][c];
                    if (grid[r][c] == '\\')
                        v++;
                    if (grid[r - 1][c] == '/')
                        u++;
                    add(u, v);
                }
                if (c > 0) {
                    int u = ids[r][c - 1];
                    int v = ids[r][c];
                    if (grid[r][c - 1] != ' ')
                        u++;
                    add(u, v);
                }
            }
        }
        return connectedComponented(id);
    }
};
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