We have a linear probing table containing $15$ slots, numbered $0,1,2,$dots, and $14.$ For the

sake of simplicity, we'll assume that we're hashing integers and that our hash function

works by taking the input integer and returning its last digit. $($This is a terrible hash function,

by the way, and no one would actually do this$).$

a$.$ Draw the linear probing table formed by inserting $31,41,59,26,53,58,97,133,$ and

$93,$ in that order, into an initially empty table with ten slots.

b$.$ What is the load factor of the table?

c$.$ Draw a different linear probing table that could be formed by inserting the same

elements given above into an empty, ten$-$slot table in a different order than the one

given above, or tell us that it's not possible to do this. Assume that you're using the

same hash function.

d$.$ Which slots do you have to look at to see if the table contains the number $72?$

e$.$ Which slots do you have to look at to see if the table contains the number $137?$

f$.$ Draw the table formed by starting with the table in part a$)$ and the inserting the

elements $106,107,$ and $110,$ in that order.