<p>Two strings, <code>X</code> and <code>Y</code>, are considered similar if either they are identical or we can make them equivalent by swapping at most two letters (in distinct positions) within the string <code>X</code>.</p>

<p>For example, <code>&quot;tars&quot;</code>&nbsp;and <code>&quot;rats&quot;</code>&nbsp;are similar (swapping at positions <code>0</code> and <code>2</code>), and <code>&quot;rats&quot;</code> and <code>&quot;arts&quot;</code> are similar, but <code>&quot;star&quot;</code> is not similar to <code>&quot;tars&quot;</code>, <code>&quot;rats&quot;</code>, or <code>&quot;arts&quot;</code>.</p>

<p>Together, these form two connected groups by similarity: <code>{&quot;tars&quot;, &quot;rats&quot;, &quot;arts&quot;}</code> and <code>{&quot;star&quot;}</code>.&nbsp; Notice that <code>&quot;tars&quot;</code> and <code>&quot;arts&quot;</code> are in the same group even though they are not similar.&nbsp; Formally, each group is such that a word is in the group if and only if it is similar to at least one other word in the group.</p>

<p>We are given a list <code>strs</code> of strings where every string in <code>strs</code> is an anagram of every other string in <code>strs</code>. How many groups are there?</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> strs = [&quot;tars&quot;,&quot;rats&quot;,&quot;arts&quot;,&quot;star&quot;]
<strong>Output:</strong> 2
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> strs = [&quot;omv&quot;,&quot;ovm&quot;]
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= strs.length &lt;= 300</code></li>
	<li><code>1 &lt;= strs[i].length &lt;= 300</code></li>
	<li><code>strs[i]</code> consists of lowercase letters only.</li>
	<li>All words in <code>strs</code> have the same length and are anagrams of each other.</li>
</ul>


struct DSU
{
    vector<int> parent, com_size, com_max, com_min;

    //  parent --> parent of the component
    //	com_size --> component_size
    //  com_max --> component_max
    //  com_min --> component_min
    DSU(int n)
    {
        parent.resize(n + 1);
        com_size.resize(n + 1);
        com_max.resize(n + 1);
        com_min.resize(n + 1);

        for (int i = 1; i <= n; i++)
        {
            parent[i] = i;
            com_size[i] = 1;
            com_max[i] = i;
            com_min[i] = i;
        }
    }

    int get_par(int x)
    {
        if (x == parent[x])
            return x;
        return parent[x] = get_par(parent[x]);
    }

    //	True return value indicates that the nodes are already connected
    bool unite(int a, int b)
    {
        a = get_par(a);
        b = get_par(b);
        if (a == b)
            return false;
        parent[a] = b;
        com_size[b] += com_size[a];
        com_max[b] = max(com_max[b], com_max[a]);
        com_min[b] = min(com_min[b], com_min[a]);
        return true;
    }
};

class Solution {
public:
    int numSimilarGroups(vector<string>& v) {
        int n = v.size();
        DSU dsu(n);
        for (int i=0; i<n; i++)
        {
            for (int j=i+1; j<n; j++)
            {
                vector<int> diff;
                for (int k=0; k < v[i].size(); k++)
                {
                    if (v[i][k] != v[j][k])
                        diff.push_back(k);
                    if (diff.size() > 2)
                        break;
                }
                if (diff.size() == 0)
                    dsu.unite(i+1, j+1);
                else if (diff.size() == 2)
                {
                    int a = diff[0];
                    int b = diff[1];
                    if (v[i][a] == v[j][b] && v[i][b] == v[j][a])
                    {
                        dsu.unite(i+1, j+1);
                    }
                }
            }
        }

        int comp_cnt = 0;
        for (int i=1; i<=n; i++)
        {
            if (dsu.get_par(i) == i)
                comp_cnt++;
        }

        return comp_cnt;
    }
};
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