$3.(6$ points$)$ Consider the following extendable hashing index.

$2$

$0*4*8*12*$

$3$

$1*$ g$*17*$

$3$

$3$

$000$

$001$

$010$

$011$

$100$

$101$

$110$

$2$

$111$

$3*$

$7*$

$11*15*$

$3$

$6*$

$14$

$2*10"26"$

$513$

a$)(3$ points$)$ Show the index that would result from inserting a data entry with key $16.$

b$)(3$ points$)$ Given the result of $($a$),$ show the index that would result from inserting a data entry with key $20.$

$4.(6$ points$)$ Consider the following schedules.

S: W$3($A$)$;R$1($B$)$;W$1($B$)$; R$1($B$)$;W$3($C$)$;W$2($B$)$;W$2($D$)$;R$2($C$)$;W$2($C$)$;R$3($A$)$;R$3($C$)$;R$3($A$)$;C$1$;C$3$;C$2$

$$ Draw the precedence graph for the schedule. Is the schedule conflict$-$serializable? $$ Is the schedule recoverable?

$5.(6$ points$)$ Consider the following schedule.

S: W$1($B$)$;R$2($A$)$;W$3($A$)$;W$1($C$)$;R$3($B$)$;W$1($A$)$;R$3($B$)$;R$1($A$)$;W$1($A$)$;R$1($A$)$;C$1$;C$2$;C$3$

Assume that Strict $2$PL is applied to the schedules. Draw both timetables $($including shared and exclusive locks and unlock actions$)$ and wait$-$for$-$graph. Does the schedule have a deadlock?