Consider a linear hashed index file, where each data page (primary page and overflow page) can hold at most three data entries.

a) Show a linear hashed index (with Level=0, N=N0=2 initial buckets, and Next=0) containing two primary page buckets, where one bucket contains the data entry 2* (with hO(2) = 0(2)) and another bucket contains the data entry 3* (with hO(3) = 1(2)). Please make sure that you show the Level and N Level.

b) Let us assume that each insertion of a data entry into an (existing or new) overflow page triggers the split. Then, what is the resulting linear hashed index after each of the following data entries with key: 5, 7, 11, 13, 17, 19, 23, 29 is inserted (one-by-one in the above order) into the linear hashed index shown in Question 6(a). Please make sure you show the Level and Next info in each resulting index structure. Hint: The final index should contain 10 data entries.

c) Let us assume that, if the last bucket is empty, it can be removed and Next can be decremented. Then, what is the resulting linear hashed index after each of the following data entries with key: 29, 17 is deleted (one-by-one in the above order) from the final linear hashed index for Question 6(b) (which contains 10 data entries)? Please make sure you show the Level and Next info in each resulting index structure.

Hint: The final index should contain 8 data entries.