can you help me find where the problem is as i cant seem to have the function does not seem to rebalcne the height of the tree after inserting $8,5,2$na d$2/**$

$*$ Helper function to returns the height of the tree

$*/$

int height$($struct node $*$tree$)\{$

if $($tree $==$ NULL$)$

return $0$;

return tree$->$height;

$\}$

$/**$

$*$ Helper function to update height

$*/$

void updateHeight $($struct node $*$root$)\{$

if $($root $!=$ NULL$)\{$

root$->$height $=1+$ max$($height$($root$->$left$),$height$($root$->$right$))$;

$\}$

$\}/**$

$*$ Helper function to check balance

$*/$

int checkBalance $($struct node $*$tree$)\{$

if $($tree $==$ NULL$)\{$

return $0$;

$\}$

return height$($tree$->$left$)-$ height$($tree$->$right$)$;

$\}$

$/**$

$*$ Helper function to perform left rotation

$*/$

struct node $*$rotateLeft$($struct node $*$tree$)\{$

struct node $*$newRoot $=$ tree$->$right;

struct node $*$temp $=$ newRoot$->$right;

newRoot$->$left $=$ tree;

tree$->$right $=$ temp;

updateHeight$($tree$)$;

updateHeight$($newRoot$)$;

return newRoot;

$\}$

$/**$

$*$ Helper function to perform right rotation

$*/$

struct node $*$rotateRight$($struct node $*$tree$)\{$

struct node $*$newRoot $=$ tree$->$left;

struct node $*$temp $=$ newRoot$->$right;

newRoot$->$right $=$ tree;

tree$->$left $=$ temp;

updateHeight$($tree$)$;

updateHeight$($newRoot$)$;

return newRoot;

$\}$

$/**$

$*$ Helper function to balance tree after insertion

$*/$

struct node $*$balanceTree $($struct node $*$tree$,$ int item$)\{$

int balance $=$ checkBalance$($tree$)$;

$//$ Left$-$left case

if $($balance $>1$ && item $<$ tree$->$left$->$item$)\{$

return rotateRight$($tree$)$;

$\}$

$//$ Left$-$Right case

if $($balance $>1$ && item $>$ tree$->$left$->$item$)\{$

tree$->$left $=$ rotateLeft$($tree$->$left$)$;

return rotateRight$($tree$)$;

$\}$

$//$ Right$-$Right case

if $($balance $<-1$ && item $>$ tree$->$right$->$item$)\{$

return rotateLeft$($tree$)$;

$\}$

$//$ Right$-$Left case

if $($balance $<-1$ && item $<$ tree$->$right$->$item$)\{$

tree$->$right $=$ rotateRight$($tree$->$right$)$;

return rotateLeft$($tree$)$;

$\}$

return tree;

$\}$

$/**$

$*$ Helper function to insert a node into the tree

$*/$

void insertNode$($struct node $**$tree$,$ int item$)\{$

if $(*$tree $==$ NULL$)\{$

$*$tree $=$ createNode$($item$)$;

$\}$ else if $($item $<(*$tree$)->$item$)\{$

insertNode$($&$(*$tree$)->$left, item$)$;

$\}$ else if $($item $>(*$tree$)->$item$)\{$

insertNode$($&$(*$tree$)->$right, item$)$;

$\}$

$*$tree $=$ balanceTree$(*$tree$,$ item$)$;

$\}/**$

$*$ Inserts an item into the set

$*/$

void SetInsert$($Set s$,$ int item$)\{$

$//$ TODO

$//$ Case where UNDEFINED cannot be inserted

if $($item $==$ UNDEFINED$)\{$

return;

$\}$

if $(!$SetContains$($s$,$ item$))\{$

$//$ Duplicate items should not be inserted

insertNode$($&$($s$->$tree$),$ item$)$;

s$->$size $+=1$;

$\}$

$\}$