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In a hash le organization, we obtain the address of the disk block containing a desired record directly by computing a function on the search-key value of the record In our description of hashing, we shall use the term bucket to denote a unit of storage that can store one or more records A bucket is typically a disk block, but could be chosen to be smaller or larger than a disk block Formally, let K denote the set of all search-key values, and let B denote the set of all bucket addresses A hash function h is a function from K to B Let h denote a hash function To insert a record with search key Ki , we compute h(Ki ), which gives the address of the bucket for that record Assume for now that there is space in the bucket to store the record Then, the record is stored in that bucket To perform a lookup on a search-key value Ki , we simply compute h(Ki ), then search the bucket with that address Suppose that two search keys, K5 and K7 , have the same hash value; that is, h(K5 ) = h(K7 ) If we perform a lookup on K5 , the bucket h(K5 ) contains records with search-key values K5 and records with searchkey values K7 Thus, we have to check the search-key value of every record in the bucket to verify that the record is one that we want Deletion is equally straightforward If the search-key value of the record to be deleted is Ki , we compute h(Ki ), then search the corresponding bucket for that record, and delete the record from the bucket

The worst possible hash function maps all search-key values to the same bucket Such a function is undesirable because all the records have to be kept in the same bucket A lookup has to examine every such record to nd the one desired An ideal hash function distributes the stored keys uniformly across all the buckets, so that every bucket has the same number of records Since we do not know at design time precisely which search-key values will be stored in the le, we want to choose a hash function that assigns search-key values to buckets in such a way that the distribution has these qualities: The distribution is uniform That is, the hash function assigns each bucket the same number of search-key values from the set of all possible search-key values The distribution is random That is, in the average case, each bucket will have nearly the same number of values assigned to it, regardless of the actual distribution of search-key values More precisely, the hash value will not be correlated to any externally visible ordering on the search-key values, such as alphabetic ordering or ordering by the length of the search keys; the hash function will appear to be random As an illustration of these principles, let us choose a hash function for the account le using the search key branch-name The hash function that we choose must have

FIGURE 15-5

This is the same as the Norton resistance RN , so the only piece of work remaining is to nd the Norton current by using Ohm s law We obtain VS R2 VS R2 R1 + R2 = R1 R2 R1 R2 + R1 R3 + R2 R3 + R3 R1 + R2

The McGraw Hill Companies, 2001

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