Build the hash table that results when the keys D$,$ A$,$ T$,$ A$,$ S$,$ T$,$ R$,$ U$,$ C$,$ T$,$ U$,$ R$,$ E$,$ S are inserted in that order into an initially empty table of size $13$ using double hashing. Then, answer the questions from $8$ to $14$ based on your solution.

Use hi$($k$)=$ k mod $13$ for the first hash function for the kth letter of the English alphabet.

Use ha$($k$)=1+($k mod $11)$ for the second hash function.

Hint: You can use the following pre$-$calculated hash values for the related keys.

$21$

h$2($k$)$

c u o

$8.$ What are the indexes of $\text{'}$A$\text{'}$s in the hashtable in the order of insertion?

A$.)1,3$

B$.)1,2$

C$.)1,1$

D$.)2.1$

E$.)3,$ i

$9.$ What are the indexes of $\text{'}$T$\text{'}$s in the hashtable in the order of insertion?

A$.)7,1,4$

B$.7.8.9$

C$.)7,11,12$

D$.)7,17.27$

E$.)10,7,12$

$10.$ What are the indexes of $\text{'}$U$\text{'}$s in the hashtable in the order of insertion?

A$.)0,8$

B$.)8.9$

C$.)8.0$

D$.)8,11$

E$.)11,8$

$11.$ What are the indexes that have been tried for $\text{'}$C$\text{'}$ until it is put into its final position?

A$.)3,2$

B$.)3,7$

C$.)3,7,2$

D$.)3,7,11,2$

E$.)2,3.7$

$12.$ What are the indexes that have been tried for the second $\text{'}$R$\text{'}$ until it is put into its final position?

A$.)5,0,8,3,11,6,1,9$

B$.)0,1,3,5,6,8,9,11$

C$.)5.1.9,11$

D$.)5,13,21,9$

E$.)5,6,0,1,3,11,9$

$3.$ What are the indexes that have been tried for $\text{'}$E$\text{'}$ until it is put into its final position?

A$.)4,5,10,11$

B$.)4,11,5,10$

C$.)5,6,11,10$

D$.)5,11,4,10$

E$.)5.11,17,23$

$.$ What is the index of the second $\text{'}$S$\text{'}$ in the hashtable?

A$.)2$

B$.)6$

C$.)9$

D$.)11$

E$.)$ Second S$\text{'}$ cannot be inserted into the hashtable.