$3.$ Implement a list with recursive methods:

The class Q$3\_$RecList implements a list. We will implement the methods: $$printList$,$find$$ and $$sumOfList$$

The implementation is via a linked list, and all operations must be done recursively, so NO LOOPS.

The method $$append$$ is implemented as a reference.

public class Q$3\_$RecList $\{$

Link head;

public void append$($int e$)\{$

if $($head $==$ null$)\{$

head $=$ new Link$($e$)$;

$\}$

else $\{$

recAppend$($head$,$ e$)$;

$\}$

$\}$

$/**$

$*$ Helper function for append

$*/$

private void recAppend$($Link curr, int e$)\{$

if $($curr$.$next $==$ null$)\{$

curr.next $=$ new Link$($e$)$;

$\}$

else $\{$

recAppend$($curr$.$next, e$)$;

$\}$

$\}$

$/**$

$*$ Prints the list in format $[$ a$0$ a$1$ a$2$ a$3$ a$4]$

$*$ Where a$0$ is the integer at index $0,$ a$1$ is the integer at index $1$ etc.

$*/$

public void printList$()\{$

System.out.print$("[")$;

System.out.print$($recPrint$($head$))$;

System.out.println$("]")$;

$\}$

$/**$

$*$ Helper function for printList

$*/$

private String recPrint$($Link curr$)\{$

return $""$; $//$STUB

$\}$

$/*$

$*$ Returns the index $(0$ based$)$ of the first occurrence of e$,$ if not found, return the size of the list

$*$ Example: find $4$ in $[2,5,4,3,4]$ returns $2$

$*$ find $8$ in $[2,5,4,3,4]$ returns $5$

$*$ find $4$ in $[]$ returns $0$

$*/$

public int find$($int e$)\{$

if $($head $==$ null$)\{$

return $0$;

$\}$

else $\{$

return $0$; $//$ STUB

$\}$

$\}$

$/**$

$*$ Helper function for find

$*/$

private int recFind$($Link curr, int e$)\{$

return $0$; $//$ STUB

$\}$

$/**$

$*$ Returns the sum of elements recursively

$*$ You cannot change this signature, however you can use a helper recursive function

$*/$

public int sumOfList$()\{$

return $0$; $//$ STUB

$\}$

$//$ inner class link

class Link$\{$

int val $=0$;

Link next $=$ null;

Link$($int n$)\{$

val $=$ n;

$\}$

Link$($int n$,$ Link next$)\{$

val $=$ n;

this.next $=$ next;

$\}$

$\}$

$\}$