groups-of-special-equivalent-strings

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Algorithms

You are given an array of strings of the same length <code>words</code>.

In one move, you can swap any two even indexed characters or any two odd indexed characters of a string <code>words[i]</code>.

Two strings <code>words[i]</code> and <code>words[j]</code> are special-equivalent if after any number of moves, <code>words[i] == words[j]</code>.

<ul>
	<li>For example, <code>words[i] = &quot;zzxy&quot;</code> and <code>words[j] = &quot;xyzz&quot;</code> are special-equivalent because we may make the moves <code>&quot;zzxy&quot; -&gt; &quot;xzzy&quot; -&gt; &quot;xyzz&quot;</code>.</li>
</ul>

A group of special-equivalent strings from <code>words</code> is a non-empty subset of words such that:

<ul>
	<li>Every pair of strings in the group are special equivalent, and</li>
	<li>The group is the largest size possible (i.e., there is not a string <code>words[i]</code> not in the group such that <code>words[i]</code> is special-equivalent to every string in the group).</li>
</ul>

Return the number of groups of special-equivalent strings from <code>words</code>.

&nbsp;
Example 1:

<pre>
Input: words = [&quot;abcd&quot;,&quot;cdab&quot;,&quot;cbad&quot;,&quot;xyzz&quot;,&quot;zzxy&quot;,&quot;zzyx&quot;]
Output: 3
Explanation: 
One group is [&quot;abcd&quot;, &quot;cdab&quot;, &quot;cbad&quot;], since they are all pairwise special equivalent, and none of the other strings is all pairwise special equivalent to these.
The other two groups are [&quot;xyzz&quot;, &quot;zzxy&quot;] and [&quot;zzyx&quot;].
Note that in particular, &quot;zzxy&quot; is not special equivalent to &quot;zzyx&quot;.
</pre>

Example 2:

<pre>
Input: words = [&quot;abc&quot;,&quot;acb&quot;,&quot;bac&quot;,&quot;bca&quot;,&quot;cab&quot;,&quot;cba&quot;]
Output: 3
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= words.length &lt;= 1000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 20</code></li>
	<li><code>words[i]</code> consist of lowercase English letters.</li>
	<li>All the strings are of the same length.</li>
</ul>