Assume one file has r = 10^6 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.What is the blocking factor bfr for the file?

b. How many data blocks b are needed to hold records?

c. How many data blocks accesses on the average are needed to fetch a record by using

linear search?

d. How many data blocks accesses are needed to fetch a record by using binary search?

e. What is the blocking factor bfri for the single level index ?

f. How many index blocks bi are needed to build the single level primary index ?

g. How many block accesses on the average are needed to fetch a record by doing linear

search on the single level index part?

h. What is the least number of block accesses to fetch a record by using single level primary

index with binary search?

i. What is the fan-out value if multi-level index is used?

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

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

l. 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?

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

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

o. What is the number of leaf-level blocks needed in B-+tree if the tree nodes are approximately

69% full (round up for convenience)?

p. What is the number of B-+tree internal nodes at the lowest level needed if blocks are

approximately 69% full (round up for convenience)?

(Please note this internal level is just above the B-+tree leaf node level).

q. What is the number of B-+tree internal nodes at the next highest level needed if blocks are approximately 69% full (round up for convenience)?

(Please note this internal level is just above the B-+tree lowest internal node level).

r. What is the number of levels of the B+-tree needed if internal nodes also 69% full (round up for convenience)?

s. What is the total number of blocks required by the B+-tree?

t. What is the number of block accesses needed to search for and retrieve a record from the file --given its key value by using B+-tree?