A data file has $100,000$ records of fixed length. The blocking factor of the file is $5.$ We build an index on field A of the data file which is a key field of the data file. The index blocking factor is $25.$ Assume that we want to find a record with a specific value for field A which exists in the data file. We measure the cost of such an operation in terms of block accesses $($I$/$O cost$).$ We build an index on field A$.$ We want to calculate the cost of finding the record with and without using the index and see how much improvement we have with the index, if any, when field A is the ordering field of the data file.

Answer the following questions:

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$1.$ Calculate the number of blocks needed to store the data file.

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$2.$ Calculate the cost of finding the record without using the index.

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$3.$ What type of index is a single level index on field A$?$

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$4.$ How many index entries does the single level index have?

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$5.$ What is a dense index? Is this single level index a dense index?

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$6.$ Calculate the cost of finding the record using the single level index.

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$7.$ How much improvement we have using the single level index? $($Calculate the ratio of the two costs$).$

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$8.$ Turn $$now the single level index on field A into a multilevel index. How many levels it has?

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$9.$ Calculate the cost of finding the record using the multilevel index.