Please help with moveDisk and isPuzzleSolved functions to be used to help user make moves and solve a tower of hanoi puzzle given this program class Stack $\{$

public:

Stack$()$;

~Stack$()$;

bool isEmpty$()$;

bool isFull$()$;

void push$($int val$)$;

int pop$()$;

int count$()$;

int peek$($int pos$)$;

void change$($int pos, int val$)$;

void display$()$;

private:

int top;

int arr$[4]$;

$\}$;

using namespace std;

Stack::Stack$()\{$

top $=-1$;

for $($int i $=0$; i $<4$; i$++)\{$

arr$[$i$]=0$;

$\}$

$\}$

Stack::~Stack$()\{\}$

bool Stack::isEmpty$()\{$

if$($top $==-1)\{$

cout $<<"$ is empty" $<<$ endl;

return true;

$\}$

else$\{$

cout $<<"$ is not empty." $<<$ endl;

return false;

$\}$

$\}$

bool Stack::isFull$()\{$

if$($top $==3)\{$

cout $<<"$ is full." $<<$ endl;

return true;

$\}$

else$\{$

cout $<<"$is not full." $<<$ endl;

return false;

$\}$

$\}$

void Stack::push$($int val$)\{$

if $($isFull$())\{$

cout $<<$ "Overflow" $<<$ endl;

$\}$ else $\{$

top$++$;

arr$[$top$]=$ val;

$\}$

$\}$

int Stack::pop$()\{$

if $($isEmpty$())\{$

cout $<<$ "Stack underflow" $<<$ endl;

return $0$;

$\}$ else $\{$

int popValue $=$ arr$[$top$]$;

arr$[$top$]=0$;

top$--$;

return popValue;

$\}$

$\}$

int Stack::count$()\{$

return $($top $+1)$;

$\}$

int Stack::peek$($int pos$)\{$

if $($isEmpty$())\{$

cout $<<$ "Stack underflow" $<<$ endl;

return $0$;

$\}$ else $\{$

return arr$[$pos$]$;

$\}$

$\}$

void Stack::change$($int pos, int val$)\{$

arr$[$pos$]=$ val;

cout $<<$ "Value changed at position $"<<$ pos $<<$ endl;

$\}$

void Stack::display$()\{$

cout $<<$ "All items in stack are:" $<<$ endl;

for $($int i $=$ top; i $>=0$; i$--)\{$

cout $<<$ arr$[$i$]<<$ endl;

$\}$

$\}$

void towerOfHanoi$($int disks, Stack &source, Stack &auxiliary, Stack &destination$)\{$

if $($disks $==1)\{$

int disk $=$ source.pop$()$;

destination.push$($disk$)$;

cout $<<$ "Move disk $"<<$ disk $<<"$ from Tower $"<<$ &source $<<"$ to Tower $"<<$ &destination $<<$ endl;

return;

$\}$

towerOfHanoi$($disks $-1,$ source, destination, auxiliary$)$;

int disk $=$ source.pop$()$;

destination.push$($disk$)$;

cout $<<$ "Move disk $"<<$ disk $<<"$ from Tower $"<<$ &source $<<"$ to Tower $"<<$ &destination $<<$ endl;

towerOfHanoi$($disks $-1,$ auxiliary, source, destination$)$;

$\}$

void moveDisk$($Stack& towerA, Stack& towerB, Stack& towerC, int fromTower, int toTower$)\{$

int top$1,$ top$2$;

if $($fromTower $==\text{'}$A$\text{'})$

top$1=$ towerA.pop$()$;

else if $($fromTower $==\text{'}$B$\text{'})$

top$1=$ towerB.pop$()$;

else if $($fromTower $==\text{'}$C$\text{'})$

top$1=$ towerC.pop$()$;

if $($toTower $==\text{'}$A$\text{'})$

top$2=$ towerA.pop$()$;

else if $($toTower $==\text{'}$B$\text{'})$

top$2=$ towerB.pop$()$;

else if $($toTower $==\text{'}$C$\text{'})$

top$2=$ towerC.pop$()$;

if $($top$1==0)$

towerA.push$($top$2)$;

else if $($top$2==0)$

towerA.push$($top$1)$;

else if $($top$1>$ top$2)\{$

if $($fromTower $==\text{'}$A$\text{'}$ && toTower $==\text{'}$B$\text{'})$

towerB.push$($top$1)$;

else if $($fromTower $==\text{'}$B$\text{'}$ && toTower $==\text{'}$A$\text{'})$

towerA.push$($top$1)$;

else if $($fromTower $==\text{'}$A$\text{'}$ && toTower $==\text{'}$C$\text{'})$

towerC.push$($top$1)$;

else if $($fromTower $==\text{'}$C$\text{'}$ && toTower $==\text{'}$A$\text{'})$

towerA.push$($top$1)$;

else if $($fromTower $==\text{'}$B$\text{'}$ && toTower $==\text{'}$C$\text{'})$

towerC.push$($top$1)$;

else if $($fromTower $==\text{'}$C$\text{'}$ && toTower $==\text{'}$B$\text{'})$

towerB.push$($top$1)$;

$\}$ else $\{$

if $($fromTower $==\text{'}$A$\text{'}$ && toTower $==\text{'}$B$\text{'})$

towerB.push$($top$2)$;

else if $($fromTower $==\text{'}$B$\text{'}$ && toTower $==\text{'}$A$\text{'})$

towerC.push$($top$2)$;

else if $($fromTower $==\text{'}$A$\text{'}$ && toTower $==\text{'}$C$\text{'})$

towerC.push$($top$2)$;

$\}$

$\}$

bool isPuzzleSolved$($const Stack& towerC, int numDisks$)\{$

return $0$;

$\}$

int main$()\{$

switch $($choice$)\{$

case $1$:

$//$ Self$-$solving program

towerOfHanoi$($numDisks$,$ towerA, towerB, towerC$)$;

break;

case $2$:

$//$ Help the user move discs between towers as directed

int fromTower, toTower;

while $(!$isPuzzleSolved$($towerC$,$ numDisks$))\{$

cout $<<$ "Enter the move $($e$.$g$.,$ A B to move a disk from Tower A to Tower B$)$: $"$;

cin $>>$ fromTower $>>$ toTower;

moveDisk$($towerA$,$ towerB, towerC, fromTower, toTower$)$;

$\}$

std::cout $<<$ "Congratulations! You solved the puzzle." $<<$ std::endl;

break;

default:

std::cout $<<$ "Invalid choice" $<<$ std::endl;

break;

$\}$

$\}$

return $0$;

$\}$