HASH TABLES -Paritosh Gupta

Problem.

Required

Search for The Precious One way would be to map all the data. And get key-value pairs. This means providing a unique identifier to each item and then making the compiler search when either is given to it.. But that method is long as the compiler will still be searching and comparing all the map values until it finds the black shirt.

Hash tables exist to speed the searching process Obtain a key, in this case the shirt Create a lot of buckets into which key/value pairs can be distributed. Choose a rule for assigning specific keys into specific buckets The rule that we choose to associate keys with buckets is called a hash function Data structures that distribute items using hash function are called hash tables Buckets are the cells in a hash tables

Overview of approach Analyze data Store data Designing a hash function Hash key to find bucket Retrieving data Hash key Lookup table

Hash Function design Hash functions are pre defined and differ for different data types A hash function gives out a particular value for each key. So for example passing xyzBlack Shirt to the function gives the value=20 We can then access memory location 20 to get the value Good hash function spreads out values to memory locations perfectly randomly Create if not found But it is also possible that the hash function gives the same value for another key. containervalue The amazing black shirt 21 22Blue jeans 23Cap 24hat

What if two keys give the same hash value (collision) What can we do when two different values attempt to occupy the same place in an array? Solution #1: Search from there for an empty location Can stop searching when we find the value or an empty location Search must be end-around Solution #2: Use a second hash function...and a third, and a fourth, and a fifth,... Solution #3: Use the array location as the header of a linked list of values that hash to this location All these solutions work, provided: We use the same technique to add things to the array as we use to search for things in the array

Sample of Chaining Symtab[NHASH] shoes NULL pants Name 1 Value 1 NULL Name 3 Value 3 NULL Name 2 Value 2

Example

Efficiency Hash tables are actually surprisingly efficient Until the table is about 70% full, the number of probes (places looked at in the table) is typically only 2 or 3 Sophisticated mathematical analysis is required to prove that the expected cost of inserting into a hash table, or looking something up in the hash table, is O(1 +n/m) where n/m is the loading factor. ( number of stored elements/number of slots) Even if the table is nearly full (leading to long searches), efficiency is usually still quite high

Uses Compilers use hash tables to keep track of variables browsers user it to keep track of recent websites or tabs Use by processor to manage cache memory Application in search algorithms. Password search

Source HYPERLINK " is.upenn.edu/~adhilton/cse399/hashtable.html course text-book /Slides18.pdf