Improving search performance: Hash tables

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Improving search performance Hash tables

• Instructor Mainak Chaudhuri
• mainakc_at_cse.iitk.ac.in

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Announcements

• No class on Wednesday (8th November)
• Please send your project demo preference to me by
  mail
• 21, 22, 23, 24 November
• May require up to one hour
• Come with your final project report (no more than
  8 pages) to the demo
• Project carries 20 points broken into
• Quality of demo
• Question-answer during demo
• Presentation in report

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Hash tables

• The idea is to divide the incoming data into
  different buckets depending on the value of the
  data
• The mapping of data value to a bucket id is
  called a hash function
• Need to search just one bucket for a particular
  data (example marks to name)
• If the values are well distributed, or, put in a
  different way, the hash function distributes the
  data evenly into the buckets, the search time
  naturally goes down
• The data within a bucket are usually organized as
  a list (often called chaining)
• The array of lists forms a hash table

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Hash functions

• Given a data value, we want to compute an array
  index
• Ideally, two different values should always map
  to two different indices zero collision, O(1)
  search time
• Possible if value range is small and known a
  priori (often this is not known)
• Formally, the value used as the input to the hash
  function is called the key
• Any value is transformed to a natural number key
  (applies to strings also)
• Simple mod function is often used as the hash map

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Hash tables

• public class HashTable
• // An array of integer lists
• private IntegerList table
• // Number of table entries
• private int numEntries
• // Constructor
• public HashTable (int size)
• int i
• numEntries size
• table new IntegerListsize
• for (i0i
• // next slide

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Hash tables

• public void Insert (int x)
• // Apply mod hash function
• int entry x numEntries
• if (tableentry ! null)
• tableentry.Enqueue(x)
• else
• tableentry new IntegerList(x)
• // next slide

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Hash tables

• public void SearchAndDelete (int x)
• // Find out the bucket
• int entry x numEntries
• if (tableentry ! null)
• tableentry tableentry.SearchAndDe
  lete(x)
• // next slide

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Hash tables

• public void Print ()
• int i
• for (i0 i
• if (tablei ! null)
• System.out.println(Entry i
  )
• tablei.Print()
• // end class
• // next slide

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Hash tables

• class HashTableBuilder
• public static void main (String a)
• HashTable ht new HashTable (7)
• ht.Insert(10)
• ht.Insert(64)
• ht.Insert(20)
• ht.Print()
• ht.SearchAndDelete(5)
• ht.SearchAndDelete(64)
• ht.Print()

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Phone directory

• How would you organize a phone directory?
• Simple solution a list of tuples
  drawback linear search time
• Better solution a hash table with name as the
  hash key average search time reduced
• Observation hash key should be the one you want
  to use to search for something e.g., search the
  phone number of Rahul

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Phone directory

• public class DirectoryEntry
• private String name
• private String phoneNumber
• private DirectoryEntry next
• public DirectoryEntry (String name, String
  ph)
• this.name name
• phoneNumber ph
• next null
• // next slide

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Phone directory

• public void SetNext (DirectoryEntry de)
• next de
• public DirectoryEntry InsertAtFront (String
  name, String ph)
• DirectoryEntry newHead new
  DirectoryEntry (name, ph)
• // Note that this refers to the old head
• newHead.SetNext (this)
• return newHead
• // next slide

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Phone directory

• public void Enqueue (String name, String ph)
• if (nextnull)
• next new DirectoryEntry (name, ph)
• else
• next.Enqueue(name, ph)
• // next slide

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Phone directory

• public String SearchForNumber (String name)
• if (this.name.equalsIgnoreCase (name))
• return phoneNumber
• if (nextnull)
• return 0000000000
• return next.SearchForNumber (name)

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Phone directory

• public void Print ()
• if (nextnull)
• System.out.println ( phoneNumber )
• else
• System.out.print (phoneNumber , )
• next.Print()
• // end class

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Phone directory

• class PhoneDirectory
• // Array of directory entry lists
• DirectoryEntry directory
• int numEntries
• public PhoneDirectory (int size)
• int i
• numEntries size
• directory new DirectoryEntrysize
• for (i0 i
• directoryi null
• // next slide

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Phone directory

• public void Insert (String name, String ph)
• // Sort by first letter
• int entry (int)(name.charAt(0))
  numEntries
• if (directoryentry ! null)
• directoryentry.Enqueue (name, ph)
• else
• directoryentry new DirectoryEntry
  (name, ph)
• // next slide

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Phone directory

• public String SearchForNumber (String name)
• // Find out bucket
• int entry (int)(name.charAt(0))
  numEntries
• if (directoryentry ! null)
• return directoryentry.SearchForNumber
  (name)
• else
• return 0000000000

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Phone directory

• public void Print ()
• int i
• for (i0 i
• if (directoryi ! null)
• System.out.println (Entry i
  )
• directoryi.Print()
• // end class

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Phone directory

• class DirectoryBuilder
• public static void main (String a)
• PhoneDirectory d new PhoneDirectory
  (26)
• d.Insert (Emily, 1408999999)
• d.Insert (John, 0123456789)
• d.Insert (Jack, 9876543210)
• d.Insert (Abraham, 2357111317)
• d.Insert (Christina, 0246810121)
• d.Insert (Lucia, 0112345011)
• d.Print()
• System.out.println (Phone number of
  Jack d.SearchForNumber (Jack))
• System.out.println (Phone number of
  Mainak d.SearchForNumber (Mainak))