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Sec 3-5
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Nonunique Record Keys Typically, records of direct les are de ned to be unique
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If in this le application multiple records have the same key, the records to be inserted can still be stored according to the collision resolution scheme used If nonunique records, ie, records with duplicate keys, are to be retrieved, a search up to an empty is needed to nd all matches to the search argument For deletion, either all records with that key must be deleted, or other elds of the record must be inspected We will not consider duplicate source keys further in this chapter When a direct le is created it must be initialized to empty This means that for all slots the eld to be used for the key is set to some tombstone In our examples we use to indicate an empty slot
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Initialization 3-5-11: Randomizing Key-to-Address Transformations The KATs we consider using use a randomizing transformation when translating the key value into relative le addresses Key and File Address Space A key value may range over a large number of possible values, limited only by the maximum size of the key eld, V The number of legal keys is up to 10V for a numeric key, 26V for a simple alphabetic key For a social security number the key space size is 109 , for a 20-character name eld it is nearly 2 1028 The number of records, n, to be kept, and the record space of the le, will be much less for all users, even for the Social Security Administration itself The available le address space is de ned in terms of the record capacity or number of slots, m, of the le Recall that the number of actual records, n, put in the le cannot exceed the number of available slots, m; hence, if the key uses base distinct symbols, baseV m n Using Alphabetic Identi ers Since many of the key-to-address algorithms depend on a numeric key value, it may be desirable to convert alphabetic keys into integers If a value from 0 to 25 (lettervalue) is assigned to each of the 26 letters used, a dense numeric representation can be obtained using a polynomial conversion, as shown in Table 3-6 Numbers and blanks occurring in keys require an appropriate expansion of the lettervalue table which controls the results of this routine For large keys numeric over ow has to be considered
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Table 3-6
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/* Letters to Integers; applied to the key given in array 'string'*/ numeric value = 0; DO i = 1 TO length of key string; numeric value = numeric value * 26 + lettervalue(string(i)); END;
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Basic File-System Organization
Given a numeric key, we apply to yield a relative address For the remainder-of-division algorithm we must choose a divisor, n m Since the desired density, m , is an approximate goal, we have some exibility in choosing m n A value of m of 1 would nearly guarantee a collision for the nal, nth record to be inserted, since only one slot will then be unoccupied A very low density of, n say, m = 010, would yield only a 10% probability of a collision for the last record, but the le space utilization would be very poor We will work below with values n of m 06 The actual value of the divisor, m, is also a concern Values including factors of 2, 10, 26, etc, may lead to results which are not fully random, since some bias from the key argument may be retained Good candidates are prime numbers, or at least numbers of the form 2k 1 The latter are often prime as well, and waste only one slot if the storage allocation is in powers of 2, giving 2k slots We show in Table 3-7 the reasoning to be followed and the resulting program fragment
Table 3-7
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