Assume one file has records. Each record takes R = 100 bytes, of which 10 bytes are for the key of the record. Suppose the key values range from 1 through 1,000,000, inclusive. Assume the block size B is 1000 bytes for all files, and that an address (block pointer, tree node pointer, or data record pointer) takes 10 bytes.

a. How many levels are there so that top-level index fits on a single block in multilevel index?

b. How many block accesses are needed to fetch a record by using multilevel index?

c. What is the key value of the 4th index record on the top level, assuming each index record points to the record with the highest key value in a block of the next level down?

d. What is the order P of the B+-tree for the internal node if B+-tree access structure on the keyis constructed?

e. What is the order P of the B+-tree for the leaf node if B+-tree access structure on the keyis constructed?