Lecture2a Hashing and Collisions(7).ppt - HASHING and...

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Hashing Hash tables are a common approach to the storing/searching techniques and also Used in encryption methods. implemented as an array of objects, where the search keys correspond to the array indexes Example: Empdata[1000], index = employee ID number search for employee with emp. number = 500 return: Empdata[500] 2
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Hashing In the Example shown, it was relatively easy since employee number is an integer Problem 1 : possible integer key values might be too large; creating an appropriate array might be impractical Need to map large integer values to smaller array indexes Problem 2 : what if the key is a word in the English Alphabet (e.g. last names)? Need to map names to integers (indexes) 3
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Hash Functions and Hash Tables Hashing has 2 major components Hash function h Hash Table Data Structure of size N A hash function h maps keys (a identifying element of record set) to hash value or hash key which refers to specific location in Hash table Example: h ( x ) x mod N is a hash function for integer keys The integer h ( x ) is called the hash value of key x 4
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Hash Table Size Should be appropriate for the hash function used Too big will waste memory; too small will increase collisions and may eventually force rehashing (copying into a larger table) Rule of thumb: the table size should be about twice the size of the data set (2s) for 50,000 words, use table of 100,000 elements 5
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Example We design a hash table for a dictionary storing items (SSN, Name), where SSN (social security number) is a nine-digit positive integer The actual data is not stored in hash table Pin points the location of actual data or set of data Our hash table uses an array of size N 10,000 and the hash function h ( x ) last four digits of x 6 0 1 2 3 4 9997 9998 9999 451-229-0004 981-101-0002 200-751-9998 025-612-0001
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Hash Function The mapping of keys into the table is called Hash Function A hash function, Ideally, it should distribute keys and entries evenly throughout the table It should be easy and quick to compute. It should minimize collisions , where the position given by the hash function is already occupied It should be applicable to all objects 7
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Hash Table The simplest kind of hash table is an array of records. This example has 701 records. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] An array of records . . . [ 700]
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What is a Hash Table ? Each record has a special field, called its key . In this example, the key is a long integer field called Number . [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] . . . [ 700] [ 4 ] Number 506643548
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What is a Hash Table ? The number might be a person's identification number, and the rest of the record has information about the person. [ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] . . . [ 700] [ 4 ] Number 506643548
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What is a Hash Table ? When a hash table is in use, some spots contain valid records, and other spots are "empty".
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