Please solve it based on the disjoint set "union$-$find.": Adidas and Abibas are not similar

Overview

In the bustling world of startups, brand names are everything. A network of young companies wants to ensure that if two companies have nearly identical names, they$$re aware of each other. Therefore, they wrote a program that processes brand names using two operations:

$-$Operation IS$-$SIMILAR$($A$,$B$)$checks whether a company name A can be changed to match another name B with just one swap between any two letters. For example, IS$-$SIMILAR$("$nadek$","$danek$")$is true because we can swap the d and n in nadek to get danek. However, IS$-$SIMILAR$("$aknor$","$knora$")$is false because no two characters in aknor can be swapped to produce knora.

$-$Operation INDIRECTLY$-$SIMILAR$($A$,$B$,$C$,...)$checks if each of the strings A$,$B$,$C$,$etc$.$is related to each of the other strings using a chain of IS$-$SIMILAR operations that are true. For example, "dark", "kard", "kadr" and "kdar" are indirectly similar as shown below:

IS$-$SIMILAR matrix:

$$dark kard kadr kdar

$$dark $-$T F F

$$kard T $-$T F

$$kadr F T $-$T

$$kdar F F T $-$

While IS$-$SIMILAR$("$dark$","$kdar$")$is false, the two brand names are indirectly similar:

dark $-->$kard

kard $-->$kadr

kadr $-->$kdar

Your Task

A conference is being organized to bring together companies with similar brand names. Participating companies will be distributed over meeting rooms, such that all the companies that are in a room are indirectly $($or directly$)$similar$.$

Given N distinct brand names, each having the same number of characters L$,$where L$$N$,$design an efficient algorithm to find the minimum number of rooms needed in the conference.

Analyze the running time and space requirements of your solution.