count-caesar-cipher-pairs

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Algorithms

You are given an array <code>words</code> of <code>n</code> strings. Each string has length <code>m</code> and contains only lowercase English letters.

Two strings <code>s</code> and <code>t</code> are similar if we can apply the following operation any number of times (possibly zero times) so that <code>s</code> and <code>t</code> become equal.

<ul>
	<li>Choose either <code>s</code> or <code>t</code>.</li>
	<li>Replace every letter in the chosen string with the next letter in the alphabet cyclically. The next letter after <code>&#39;z&#39;</code> is <code>&#39;a&#39;</code>.</li>
</ul>

Count the number of pairs of indices <code>(i, j)</code> such that:

<ul>
	<li><code>i &lt; j</code></li>
	<li><code>words[i]</code> and <code>words[j]</code> are similar.</li>
</ul>

Return an integer denoting the number of such pairs.

&nbsp;
Example 1:

<div class="example-block">
Input: words = [&quot;fusion&quot;,&quot;layout&quot;]

Output: 1

Explanation:

<code>words[0] = &quot;fusion&quot;</code> and <code>words[1] = &quot;layout&quot;</code> are similar because we can apply the operation to <code>&quot;fusion&quot;</code> 6 times. The string <code>&quot;fusion&quot;</code> changes as follows.

<ul>
	<li><code>&quot;fusion&quot;</code></li>
	<li><code>&quot;gvtjpo&quot;</code></li>
	<li><code>&quot;hwukqp&quot;</code></li>
	<li><code>&quot;ixvlrq&quot;</code></li>
	<li><code>&quot;jywmsr&quot;</code></li>
	<li><code>&quot;kzxnts&quot;</code></li>
	<li><code>&quot;layout&quot;</code></li>
</ul>
</div>

Example 2:

<div class="example-block">
Input: words = [&quot;ab&quot;,&quot;aa&quot;,&quot;za&quot;,&quot;aa&quot;]

Output: 2

Explanation:

<code>words[0] = &quot;ab&quot;</code> and <code>words[2] = &quot;za&quot;</code> are similar. <code>words[1] = &quot;aa&quot;</code> and <code>words[3] = &quot;aa&quot;</code> are similar.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n == words.length &lt;= 105</code></li>
	<li><code>1 &lt;= m == words[i].length &lt;= 105</code></li>
	<li><code>1 &lt;= n * m &lt;= 105</code></li>
	<li><code>words[i]</code> consists only of lowercase English letters.</li>
</ul>