Consider an index using extendible hashing for which:

Each bucket has a capacity of $3$ records

The index is completely empty initially with a global depth of $1.$

The hashing function maps the d lowest$-$bits of each input to a bucket. e$.$g$.,$ if

$d=3$ then key $5(0101)$ and key $13(1101)$ have a matching hash $(101).$

a$.$ Mark all correct statements below on what can be observed after we insert keys:

$19,25,12,7,39,23$ in that order.

$($a$)$ The global depth $d$ at this point is $2.$

$($b$)$ The local depth d$\text{'}$ of the bucket containing $12$ is $1.$

$($c$)$ A total of three splits have occurred.

$-2$

$($d$)$ A total of two splits have occurred.

b$.$ We continue by inserting keys: $21,9,6,17$ in that order. Mark all correct

statements.

$($a$)$ The global depth $d$ at this point is $4.$

$($b$)$ The local depth d$\text{'}$ of the bucket containing $6$ is $2.$

$($c$)$ The local depth d$\text{'}$ of the bucket containing $21$ is $3.$

$($d$)$ A split was caused by inserting $17.$