L09_hash - Hashing and Hash Tables Nyhoff: 12 COMP152...

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Unformatted text preview: Hashing and Hash Tables Nyhoff: 12 COMP152 Spring 2010 D.Y. Yeung 1 2 Outline  Motivation  Hashing Algorithms and Improving the Hash Functions  Collision Strategies  Open addressing and linear probing  Separate chaining 3 Searching  BST trees  Balanced BST trees (such as an AVL tree) have a search time of O(logN)  This is optimal when we consider a comparison-based searching mechanism  Can we make searching even faster?  O(1)?  Yes, with hashing  Has some limitations, but for some applications where insertions and deletions are not frequent it is very suitable C E M O P T U C E T M U O P Balanced BST 3 steps to locate U Lopsided BST 7 steps to locate U 4 Re-thinking Keys Again  Tree structures discussed so far assume that we can only use the keys for comparison while other operations on the keys are not considered  In practice, however, the key can be decomposed into smaller units, for example: 1. Integers consist of digits: can be used as array index 2. Strings consist of letters: we may even perform arithmetic operations on the letters 5 Idea behind Hashing  Given a key in the key universe, compute an index into a hash table  Index is computed using a hash function Hash Table Index = hash_function( Key ) This is an ultra-fast way to search! Time complexity = O(1). What are the things we need to consider? 1. A good hash function for the keys. 2. The table size is limited, so multiple keys may be mapped to the same location! (We call this a collision ) Need to resolve collisions. Hash Tables COMP152 6 Collection of data items x 0 1 2 3 … h(x) x Hash table h a s h f u n c t i o n 7 General Terms  Universe U = { u 0 , u 1 , . . . , u n-1 }  Relatively easy to compute some index given a key  Hash support operations:  Find()  Insert()  Delete()  Deletion may be unnecessary in some applications 8 Hash Tables vs. Trees  Hash tables are only for problems that require fast search  Unlike trees  No notion of order  remember that a tree is sorted if we visit the nodes in-order  No way to find the range  min and max elements  No notion of successor or predecessor  Hash tables are generally implemented using an array structure with fixed size 9 Example Applications  Compilers use hash tables to keep track of declared variables  On-line spell checkers  We can “hash” an entire dictionary (or the most common words)  Allows us to quickly check if words are spelled correctly in constant time 10 Bit Vector Representation  entry = 0 if u i is absent; other entry = 1  Find: test entry  Insert: set entry to 1  Delete: set entry to 0  Constant time each, independent of the number of keys!...
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This note was uploaded on 08/25/2010 for the course COMP COMP152 taught by Professor D.y.yeung during the Spring '10 term at HKUST.

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L09_hash - Hashing and Hash Tables Nyhoff: 12 COMP152...

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