$(10$ points$)$ Show the sequence of stack changes when parsing the input num $**$ num $+$ num $**$ num using

the LR parsing algorithm $($slide $8)$ and the parse table $($slide $10)$ from the notes, "Bottom$-$Up Parsing",

in class

Shift$-$Reduce Algorithm

Stack.Push$(\{$:$S_0)$

repeat $\{$

else if action$[$s$,$a$]=$ accept then $\{$

Emit$($Success$")$;

$s=$ Stack. Top$()$;$,$ return;

a $=$ NextToken$()$; else

if action$[s,$a 'shift $S_k\text{'}$ then error$()$

Stack.Push$($a$)$; Stack.Push$(\{$:$S_k)$;$,\}$

else

if action$[$s$,$a$]==$ 'reduce $A\text{'},$cdotsdotsdots

then $\{$

Stack.Pop$(2*||$;

$S_k=$ Stack.Top$()$;

The Bison action

associated with $A$

is executed here

Stack.Push$($A$)$;

Stack.Push$($goto $S_k,A)$;

UnPutToken$()$;

Emit$(A)$;

$\}$