Assume one file has r =106 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.
1. Sequential file: (15 points)
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?
2. Single Level Index: (15 points)
e. What is the blocking factor bfri for the 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 using single level primary index and by doing linear search?
h. What is the least number of block accesses to fetch a record by usingsingle level primary index?
3. Multilevel Index: (15 points)
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 usingmultilevel 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?
4. B+-tree Structure: (15 points)
m. What is the order P of the B+-tree if B+-tree access structure on the key is constructed?
n. What is the number of leaf-level blocks needed if blocks are approximately 69% full (round up for convenience)?
o. What is the number of levels needed if internal nodes also 69% full (round up for convenience)?
p. What is the total number of blocks required by the B+-tree?
q. 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?