Hashing Continued and Exam 3

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Hashing (Continued) and Exam 3

• Hashing (Continued)
• Deleting elements
• Dynamic resizing
• Hashing in the Java Collections API
• Hashtable Applications
• Review for Exam 3
• Open Book / Open Notes

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Deleting Chained Implementation

• If we store a reference to another collection in
  each hash table entry, it is easy use that
  collections remove method to delete an element
  in a chained hash implementation
• Otherwise, we must manipulate references
  appropriately to unlink the object being removed
  and maintain the chain based at the original hash
  table entry

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Resolving Collisions

• Open Addressing looks for another open position
  in the table other than the one to which the
  element is originally hashed
• Three variations of open addressing
• Linear probing
• Quadratic probing
• Double hashing

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Open Addressing Linear Probing

• Open Addressing with linear probing means that if
  an element hashes to position p and position p is
  already occupied, we simply try
• position p (p 1) tableSize
• If that element is also occupied, we keep adding
  1 modulo table size until we find
• An empty element and we use it OR
• We are back at the original position p and the
  table is full (expanding capacity is an option)
• Problem Tends to create dense occupied clusters
  which affects the efficiency of adds and searches

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Open Addressing Quadratic Probing

• Open Addressing with quadratic probing means that
  if an element hashes to position p and position p
  is already occupied, we use a formula such as
• new hash original hash (-1)i-1((i1)/2)2
  (for i 1, 2, )
• We must divide the new hash modulo tableSize
• This tries a sequence of positions such as
• p, p1, p-1, p4, p-4, p9, p-9,
• If we get back to the original position, table is
  full (expanding capacity is still an option)
• This does not have as strong a tendency to create
  dense clusters as linear probing

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Open Addressing Double Hashing

• Open Addressing with double hashing means that if
  an element hashes to position p and position p is
  already occupied, we use a formula such as
• new hash(x) original hash(x) secondary
  hash(x)
• We must divide the new hash modulo tableSize
• This tries a sequence of positions that depends
  on the definition of the secondary hash function
• If we get back to the original position, table is
  full (expanding capacity is still an option)
• It is somewhat more costly to compute a second
  hash function, but this tends to further reduce
  the density of clustering over quadratic probing

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Deleting Open Addressing

• If we actually delete any element from an open
  addressing implementation, we may make it
  impossible to find another entry
• If we start a search at the hashed position and
  find any empty space (including one created by a
  deletion), we will stop searching
• Therefore, we remove an element by marking it as
  deleted without actually removing it
• Then, if we start a search at the hashed position
  and find a marked deletion, we know to continue
  searching
• We can reuse deleted elements when possible or
  rehash the table to recover wasted space

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Dynamic Table Resizing

• To dynamically expand the capacity of the hash
  table, we create a new larger array
• However, we note that the size of the table is
  used to select locations in the array
• We cant just copy the smaller array into a
  sub-array area within the new larger array
• We must take all elements from the smaller array
  and rehash them into the larger array

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Java Collections API Hash Tables

• There are seven implementations of hashing
• Hashtable
• HashMap
• HashSet
• IdentityHashMap
• LinkedHashSet
• LinkedHashMap
• WeakHashMap

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Hash Table Applications

• Compilers use a hashtable called a symbol table
  for the variable names in source code
• Game programs use a hashtable called a
  transposition table for positions previously
  encountered to remember the move made in that
  position
• An On-line spell checker can pre-hash its
  dictionary of valid words
• In each case, an O(1) key lookup is achieved

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Review for Exam 3

• Practice Exam is on-line