<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{
    vector<int> parent;
public:
    int count = 0;

    UnionFind(int n){
        parent.assign(n,0);
        for(int i=0; i<n; ++i){
            parent[i] = i;
        }

        count = n;
    }

    int find(int i){
        if(parent[i]==i){
            return i;
        }

        return parent[i] = find(parent[i]);
    }

    int merge(int i, int j){
        int pi = find(i);
        int pj = find(j);

        if(pi==pj){
            return 1;
        }

        parent[pj] = pi;
        count--;

        return 0;
    }
};

class Solution {
public:
    int regionsBySlashes(vector<string>& grid) {
        // return fun1(grid);

        return fun2(grid);
    }

    int fun2(vector<string>& grid) {
        int n = grid.size();
        UnionFind uf(4*n*n);

        for(int i=0; i<n; ++i){
            for(int j=0; j<n; ++j){
                char c = grid[i][j];
                int id = 4*(i*n+j);

                if (c=='/'){
                    uf.merge(id,id+1);
                    uf.merge(id+2,id+3);
                } else if (c=='\\'){
                    uf.merge(id+1, id+2);
                    uf.merge(id, id+3);
                } else {
                    uf.merge(id, id+1);
                    uf.merge(id, id+2);
                    uf.merge(id, id+3);
                }

                if (j+1<n){
                    uf.merge(id+2, 4*(i*n+j+1));
                }

                if (i+1<n){
                    uf.merge(id+3, 4*((i+1)*n+j)+1);
                }
            }
        }

        return uf.count;
    }

    int fun1(vector<string>& grid) {
        int n = grid.size();
        int m = n+1;

        UnionFind uf(m*m);
        for(int i=0; i<m; ++i){
            for(int j=0; j<m; ++j){
                if(i==0||j==0||i==m-1||j==m-1){
                    uf.merge(0, i*m+j);
                }
            }
        }

        int ans = 1;

        for(int i=0; i<n; ++i){
            for(int j=0; j<n; ++j) {
                char c = grid[i][j];
                if(c == '/'){
                    int topRight = i*m+j+1;
                    int bottomLeft = (i+1)*m+j;

                    ans += uf.merge(topRight, bottomLeft);
                } else if (c == '\\'){
                    int topLeft = i*m+j;
                    int bottomRight = (i+1)*m+j+1;

                    ans += uf.merge(topLeft, bottomRight);
                }
            }
        }

        return ans;
    }
};
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