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the desirable properties not only on the example account le that we have been using, but also on an account le of realistic size for a large bank with many branches Assume that we decide to have 26 buckets, and we de ne a hash function that maps names beginning with the ith letter of the alphabet to the ith bucket This hash function has the virtue of simplicity, but it fails to provide a uniform distribution, since we expect more branch names to begin with such letters as B and R than Q and X, for example Now suppose that we want a hash function on the search key balance Suppose that the minimum balance is 1 and the maximum balance is 100,000, and we use a hash function that divides the values into 10 ranges, 1 10,000, 10,001 20,000 and so on The distribution of search-key values is uniform (since each bucket has the same number of different balance values), but is not random But records with balances between 1 and 10,000 are far more common than are records with balances between 90,001 and 100,000 As a result, the distribution of records is not uniform some buckets receive more records than others do If the function has a random distribution, even if there are such correlations in the search keys, the randomness of the distribution will make it very likely that all buckets will have roughly the same number of records, as long as each search key occurs in only a small fraction of the records (If a single search key occurs in a large fraction of the records, the bucket containing it is likely to have more records than other buckets, regardless of the hash function used) Typical hash functions perform computation on the internal binary machine representation of characters in the search key A simple hash function of this type rst computes the sum of the binary representations of the characters of a key, then returns the sum modulo the number of buckets Figure 1221 shows the application of such a scheme, with 10 buckets, to the account le, under the assumption that the ith letter in the alphabet is represented by the integer i Hash functions require careful design A bad hash function may result in lookup taking time proportional to the number of search keys in the le A well-designed function gives an average-case lookup time that is a (small) constant, independent of the number of search keys in the le.

The percentage level of the special effect during the holding period A frame where the special effect stops the holding period The frame where the special effect ends The percentage level of the special effect at the frame where it ends These settings enable you to specify a gradual ramping up (or dropping off) of the special effect, a length of time when the special effect remains at a specific level, and then a gradual change until the special effect ends To better understand how this might work, consider how the following scenario would appear:

So far, we have assumed that, when a record is inserted, the bucket to which it is mapped has space to store the record If the bucket does not have enough space, a bucket over ow is said to occur Bucket over ow can occur for several reasons: Insuf cient buckets The number of buckets, which we denote nB , must be chosen such that nB > nr /fr , where nr denotes the total number of records that will be stored, and fr denotes the number of records that will t in a bucket This designation, of course, assumes that the total number of records is known when the hash function is chosen Skew Some buckets are assigned more records than are others, so a bucket may over ow even when other buckets still have space This situation is called bucket skew Skew can occur for two reasons:

The Norton equivalent circuit is then obtained by arranging the current source and resistance in parallel as shown in Fig 3-37

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12

1 Multiple records may have the same search key 2 The chosen hash function may result in nonuniform distribution of search keys So that the probability of bucket over ow is reduced, the number of buckets is chosen to be (nr /fr ) (1 + d), where d is a fudge factor, typically around 02 Some space is wasted: About 20 percent of the space in the buckets will be empty But the bene t is that the probability of over ow is reduced Despite allocation of a few more buckets than required, bucket over ow can still occur We handle bucket over ow by using over ow buckets If a record must be inserted into a bucket b, and b is already full, the system provides an over ow bucket for b, and inserts the record into the over ow bucket If the over ow bucket is also full, the system provides another over ow bucket, and so on All the over ow buck-

CHAPTER 15:

Summary

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