use irvine library $!!!!!!!!!!!!!!!!!!$ One hundred students are assigned lockers $1$ through $100$

The student assigned to locker number $1$ opens all $100$ lockers

The student assigned to locker number $2$ then closes all lockers whose numbers are multiples of $2$

The student assigned to locker number $3$ toggles the status of all lockers whose numbers are multiples of $3$

Locker number $3,$ which is open gets closed,

Locker number $6,$ which is closed, gets opened

And so on for as many lockers need to be toggled

The student assigned to locker number $4$ toggles the status of all lockers whose numbers are multiples of $4$

And so on and on for all $100$ students and all $100$ lockers

Which lockers will be left open after everyone completes their turns?

Convert this C$++$ program into x$86$ assembly language and find out!

#include

using namespace std;

$//$ In this case we will be using a global array

$//$ This is not generally the case for any other variables

$//101$ element array, all elements initialized to $0$

$//$ NOTE:$$ For simplicity, element $0$ is unused

int Lockers$[101]\{0\}$;

$//$ Boolean NOT operation just like the exam question

int NotOperation$($int x$)$

$\{$

$$ return $($x $==0)?1$ : $0$;

$\}$

$//$ Student x toggles all lockers $\{$ x$,2$x$,3$x$,4$x$,...\}$

$//$ up to and including locker $100$

void StudentTogglingLockers$($int x$)$

$\{$

$$ for $($int i $=$ x; i $<=100$; i $+=$ x$)$

$\{$

$$ Lockers$[$i$]=$ NotOperation$($Lockers$[$i$])$;

$\}$

$\}$

$//100$ students walk through and toggle lockers

void ToggleLockers$()$

$\{$

$$ for $($int i $=1$; i $<=100$; $++$i$)$

$\{$

$$ StudentTogglingLockers$($i$)$;

$\}$

$\}$

void PrintOpenLockers$()$

$\{$

$$ for $($int i $=1$; i $<=100$; $++$i$)$

$\{$

$$ if $($Lockers$[$i$]==1)$

$\{$

$$ cout $<<$ i;

$$ cout $<<\text{'}\text{'}$;

$\}$

$\}$

$$ cout $<<$ endl;

$\}$

int main$()$

$\{$

$$ ToggleLockers$()$;

$$ PrintOpenLockers$()$;

$$ system$("$PAUSE$")$;

$\}$