I need help creating the logic for the union, concatenate, plus, star, singleCharNFA$,$

public class RegularExpression $\{$

$$ private String regularExpression;

$$ private NFA nfa;

$//$ You are not allowed to change the name of this class or this constructor at all.

$$ public RegularExpression$($String regularExpression$)\{$

$$ this.regularExpression $=$ regularExpression.replaceAll$("\backslash \backslash$s$+","")$;

$$ nfa $=$ generateNFA$()$;

$\}$

$//$ TODO: Complete this method so that it returns the nfa resulting from unioning the two input nfas.

$$ private NFA union$($NFA nfa$1,$ NFA nfa$2)\{$

$$ return null;

$\}$

$//$ TODO: Complete this method so that it returns the nfa resulting from concatenating the two input nfas.

$$ private NFA concatenate$($NFA nfa$1,$ NFA nfa$2)\{$

$$ return null;

$\}$

$//$ TODO: Complete this method so that it returns the nfa resulting from "staring" the input nfa.

$$ private NFA star$($NFA nfa$)\{$

$$ return null;

$\}$

$//$ TODO: Complete this method so that it returns the nfa resulting from "plussing" the input nfa.

$$ private NFA plus$($NFA nfa$)\{$

$$ return null;

$\}$

$//$ TODO: Complete this method so that it returns the nfa that only accepts the character c$.$

$$ private NFA singleCharNFA$($char c$)\{$

$$ return null;

$\}$

$//$ You are not allowed to change this method's header at all.

$$ public boolean test$($String string$)\{$

$$ return nfa.accepts$($string$)$;

$\}$

$//$ Parser. I strongly recommend you do not change any code below this line.

$//$ Do not change any of the characters recognized in the regex $($e$.$g$.,$ U$,*,+,0,1)$

$$ private int position $=-1,$ ch;

$$ public NFA generateNFA$()\{$

$$ nextChar$()$;

$$ return parseExpression$()$;

$\}$

$$ public void nextChar$()\{$

$$ ch $=(++$position $<$ regularExpression.length$())?$ regularExpression.charAt$($position$)$ : $-1$;

$\}$

$$ public boolean eat$($int charToEat$)\{$

$$ if $($ch $==$ charToEat$)\{$

$$ nextChar$()$;

$$ return true;

$\}$

$$ return false;

$\}$

$$ public NFA parseExpression$()\{$

$$ NFA nfa $=$ parseTerm$()$;

$$ while $($true$)\{$

$$ if $($eat$(\text{'}$U$\text{'}))\{$

$//$ Create the nfa that is the union of the two passed nfas.

$$ nfa $=$ union$($nfa$,$ parseTerm$())$;

$\}$ else $\{$

$$ return nfa;

$\}$

$\}$

$\}$

$$ public NFA parseTerm$()\{$

$$ NFA nfa $=$ parseFactor$()$;

$$ while $($true$)\{$

$//$ Concatenate NFAs.

$$ if $($ch $==\text{'}0\text{'}||$ ch $==\text{'}1\text{'}||$ ch $==\text{'}(\text{'})\{$

$//$ Create the nfa that is the concatentaion of the two passed nfas.

$$ nfa $=$ concatenate$($nfa$,$ parseFactor$())$;

$\}$ else $\{$

$$ return nfa;

$\}$

$\}$

$\}$

$$ public NFA parseFactor$()\{$

$$ NFA nfa $=$ null;

$$ if $($eat$(\text{'}(\text{'}))\{$

$$ nfa $=$ parseExpression$()$;

$$ if $(!$eat$(\text{'})\text{'}))\{$

$$throw new RuntimeException$("$Missing $\text{'})\text{'}")$;

$\}$

$\}$ else if $($ch $==\text{'}0\text{'}||$ ch $==\text{'}1\text{'})\{$

$//$ Create the nfa that only accepts the character being passed $($regularExpression$.$charAt$($position$)==\text{'}0\text{'}$ or $\text{'}1\text{'}).$

$$ nfa $=$ singleCharNFA$($regularExpression$.$charAt$($position$))$;

$$ nextChar$()$;

$\}$

$$ if $($eat$(\text{'}*\text{'}))\{$

$//$ Create the nfa that is the star of the passed nfa.

$$ nfa $=$ star$($nfa$)$;

$\}$ else if $($eat$(\text{'}+\text{'}))\{$

$//$ Create the nfa that is the plus of the passed nfa.

$$ nfa $=$ plus$($nfa$)$;

$\}$

$$ return nfa;

$\}$

$\}$