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When the search argument is not the key attribute used to sequence the le, the search is always sequential The process is similar to the search through a pile le Since the total size of the le will be di erent from the size of a pile le due to the di erence in record organization, the relative performance will depend on the attribute density a /a as well as on the relative length of attribute descriptors A and data values V Half the le will be searched on the average to fetch a record, so that 1 R main le 3-15 TF = n 2 t For small les this time may be better than the direct methods presented below If the le has received o new records into a transaction log or over ow le, this le should be searched also The entire over ow le has to be processed to assure that any record found in the main part or earlier part of the over ow le has not been updated or deleted This le will be in chronological order and processed sequentially With the assumption that the over ow is on the average half-full (o = 1 o), we obtain 2

10 15 20

over ow 3-16

10 15 20

as the term needed to process changes made to the main le We cannot expect that the simple systems which use sequential les will search through both the main le and the log le in parallel The total fetch time, if both parts of the le are searched sequentially, is the sum TF = R 1 (n + o) 2 t 3-17

We ve dispensed with the Employee class to save room, but of course you can enqueue user-defined objects as well. The output shows that queuing an object adds it to the Queue, and Dequeue( ) returns the object as well as removes it from the Queue. The Queue class also provides a Peek( ) method that allows you to see, but not remove, the next element. Take a closer look at the PrintValues( ) method:

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Exercise 41 Explain the statement that relational algebra operators can be composed Why is the ability to compose operators important Exercise 42 Given two relations R1 and R2, where R1 contains N1 tuples, R2 contains N2 tuples, and N2 > N1 > 0, give the minimum and maximum possible sizes (in tuples) for the result relation produced by each of the following relational algebra expressions In each case, state any assumptions about the schemas for R1 and R2 that are needed to make the expression meaningful: (1) R1 R2, (2) R1 R2, (3) R1 R2, (4) R1 R2, (5) a=5 (R1), (6) a (R1), and (7) R1/R2 Exercise 43 Consider the following schema: Suppliers(sid: integer, sname: string, address: string) Parts(pid: integer, pname: string, color: string) Catalog(sid: integer, pid: integer, cost: real)

A well-known search technique for memory can be adapted to provide an alternate access method for sequential les The binary search begins, as shown in Fig 3-5, with a direct access to the middle of the le, and partitions the le iteratively according to a comparision of the key value found and the search argument Whenever a block is fetched, the rst and last records in this block will be inspected to determine if the goal record is within this block The number of fetches does not depend on the number of records, n, but rather on the number of blocks, b = n/Bfr We nd, using the expected number of block access for the binary search log2 (b) (Knuth73S ), that

public static void PrintValues(IEnumerable<Int32> myCollection) { IEnumerator<Int32> myEnumerator = myCollection.GetEnumerator( ); while (myEnumerator.MoveNext( )) { Console.Write("{0} ", myEnumerator.Current); }

binary 3-18

Because the Queue class is enumerable, you can pass it to the PrintValues( ) method, which takes an IEnumerable interface. The conversion is implicit. In the PrintValues method, you call GetEnumerator, which is the single method required by all IEnumerable classes, as we mentioned earlier in the chapter. GetEnumerator( ) returns an IEnumerator, which you then use to enumerate all the objects in the collection. MoveNext( ) is a method of IEnumerator, so no matter what collection type you re using, you can always call MoveNext( ) to retrieve the next value. Current is the property of IEnumerator that represents the current value, so you can output the current value in the queue by outputting myEnumerator.Current. When there are no more values in the collection, MoveNext( ) returns false, which ends the while loop. Note that we re using a while loop here to demonstrate how IEnumerator works; in practice, you d probably use a foreach loop instead.

Sec 3-2

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