How do HashTables deal with collisions

Question

I ve heard in my degree classes that a HashTable will place a new entry into the  next available  bucket if the new Key entry collides with another   How would the HashTable still return the correct Value if this collision occurs when calling for one back with the collision key   I m assuming that the Keys are String type and the hashCode   returns the default generated by say Java   If I implement my own hashing function and use it as part of a look-up table  i e  a HashMap or Dictionary   what strategies exist for dealing with collisions   I ve even seen notes relating to prime numbers  Information not so clear from Google search

User · Answer

I strongly suggest you to read this blog post which appeared on HackerNews recently: How HashMap works in Java

In short, the answer is

What will happen if two different HashMap key objects have same hashcode?

They will be stored in same bucket but no next node of linked list. And keys equals () method will be used to identify correct key value pair in HashMap.

User · Answer

There are various methods for collision resolution Some of them are Separate Chaining Open addressing Robin Hood hashing Cuckoo Hashing etc   Java uses Separate Chaining for resolving collisions in Hash tables Here is a great link to how it happens  http   javapapers com core-java java-hashtable

User · Answer

When you talked about  Hash Table will place a new entry into the  next available  bucket if the new Key entry collides with another    you are talking about the Open addressing strategy of Collision resolution of hash table     There are several strategies for hash table to resolve collision   First kind of big method require that the keys  or pointers to them  be stored in the table  together with the associated values  which further includes    Separate chaining       Open addressing      Coalesced hashing Cuckoo hashing Robin Hood hashing 2-choice hashing Hopscotch hashing     Another important method to handle collision is by Dynamic resizing  which further has several ways    Resizing by copying all entries Incremental resizing Monotonic keys     EDIT  the above are borrowed from wiki hash table  where you should go to have a look to get more info

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here s a very simple hash table implementation in java  in only implements put   and get    but you can easily add whatever you like  it relies on java s hashCode   method that is implemented by all objects  you could easily create your own interface   interface Hashable     int getHash        and force it to be implemented by the keys if you like   public class Hashtable lt K  V gt        private static class Entry lt K V gt            private final K key          private final V val           Entry K key  V val                this key   key              this val   val                       private static int BUCKET COUNT   13        SuppressWarnings  unchecked       private List lt Entry gt    buckets   new List BUCKET COUNT        public Hashtable             for  int i   0  l   buckets length  i  lt  l  i                  buckets i    new ArrayList lt Entry lt K V gt  gt                          public V get K key            int b   key hashCode     BUCKET COUNT          List lt Entry gt  entries   buckets b           for  Entry e  entries                if  e key equals key                     return e val                                  return null             public void put K key  V val            int b   key hashCode     BUCKET COUNT          List lt Entry gt  entries   buckets b           entries add new Entry lt K V gt  key  val

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I ve heard in my degree classes that a   HashTable will place a new entry into   the  next available  bucket if the new   Key entry collides with another    This is actually not true  at least for the Oracle JDK  it is an implementation detail that could vary between different implementations of the API   Instead  each bucket contains a linked list of entries prior to Java 8  and a balanced tree in Java 8 or above      then how would the HashTable still   return the correct Value if this   collision occurs when calling for one   back with the collision key    It uses the equals   to find the actually matching entry      If I implement my own hashing function   and use it as part of a look-up table    i e  a HashMap or Dictionary   what   strategies exist for dealing with   collisions    There are various collision handling strategies with different advantages and disadvantages  Wikipedia s entry on hash tables gives a good overview

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Hash tables deal with collisions in one of two ways    Option 1  By having each bucket contain a linked list of elements that are hashed to that bucket  This is why a bad hash function can make lookups in hash tables very slow   Option 2  If the hash table entries are all full then the hash table can increase the number of buckets that it has and then redistribute all the elements in the table  The hash function returns an integer and the hash table has to take the result of the hash function and mod it against the size of the table that way it can be sure it will get to bucket  So by increasing the size  it will rehash and run the modulo calculations which if you are lucky might send the objects to different buckets   Java uses both option 1 and 2 in its hash table implementations

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Update since Java 8  Java 8 uses a self-balanced tree for collision-handling  improving the worst case from O n  to O log n  for lookup  The use of a self-balanced tree was introduced in Java 8 as an improvement over chaining  used until java 7   which uses a linked-list  and has a worst case of O n  for lookup  as it needs to traverse the list  To answer the second part of your question  insertion is done by mapping a given element to a given index in the underlying array of the hashmap  however  when a collision occurs  all elements must still be preserved  stored in a secondary data-structure  and not just replaced in the underlying array   This is usually done by making each array-component  slot  be a secondary datastructure  aka bucket   and the element is added to the bucket residing on the given array-index  if the key does not already exist in the bucket  in which case it is replaced   During lookup  the key is hashed to it s corresponding array-index  and search is performed for an element matching the  exact  key in the given bucket  Because the bucket does not need to handle collisions  compares keys directly   this solves the problem of collisions  but does so at the cost of having to perform insertion and lookup on the secondary datastructure  The key point is that in a hashmap  both the key and the value is stored  and so even if the hash collides  keys are compared directly for equality  in the bucket   and thus can be uniquely identified in the bucket  Collission-handling brings the worst-case performance of insertion and lookup from O 1  in the case of no collission-handling to O n  for chaining  a linked-list is used as secondary datastructure  and O log n  for self-balanced tree  References   Java 8 has come with the following improvements changes of HashMap objects in case of high collisions   The alternative String hash function added in Java 7 has been removed   Buckets containing a large number of colliding keys will store their entries in a balanced tree instead of a linked list after certain threshold is reached    Above changes ensure performance of O log n   in worst case scenarios  https   www nagarro com en blog post 24 performance-improvement-for-hashmap-in-java-8

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It will use the equals method to see if the key is present even and especially if there are more than one element in the same bucket

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As there is some confusion about which algorithm Java s HashMap is using  in the Sun Oracle OpenJDK implementation   here the relevant source code snippets  from OpenJDK  1 6 0 20  on Ubuntu           Returns the entry associated with the specified key in the    HashMap   Returns null if the HashMap contains no mapping    for the key      final Entry lt K V gt  getEntry Object key        int hash    key    null    0   hash key hashCode         for  Entry lt K V gt  e   table indexFor hash  table length             e    null           e   e next            Object k          if  e hash    hash  amp  amp                k   e key     key     key    null  amp  amp  key equals k                 return e            return null      This method  cite is from lines 355 to 371  is called when looking up an entry in the table  for example from get    containsKey   and some others  The for loop here goes through the linked list formed by the entry objects   Here the code for the entry objects  lines 691-705   759    static class Entry lt K V gt  implements Map Entry lt K V gt        final K key      V value      Entry lt K V gt  next      final int hash                  Creates new entry              Entry int h  K k  V v  Entry lt K V gt  n            value   v          next   n          key   k          hash   h               methods left away  they are straight-forward implementations of Map Entry       Right after this comes the addEntry   method          Adds a new entry with the specified key  value and hash code to    the specified bucket   It is the responsibility of this    method to resize the table if appropriate        Subclass overrides this to alter the behavior of put method      void addEntry int hash  K key  V value  int bucketIndex        Entry lt K V gt  e   table bucketIndex       table bucketIndex    new Entry lt K V gt  hash  key  value  e       if  size    gt   threshold          resize 2   table length       This adds the new Entry on the front of the bucket  with a link to the old first entry  or null  if no such one   Similarily  the removeEntryForKey   method goes through the list and takes care of deleting only one entry  letting the rest of the list intact   So  here is a linked entry list for each bucket  and I very doubt that this changed from  20 to  22  since it was like this from 1 2 on    This code is  c  1997-2007 Sun Microsystems  and available under GPL  but for copying better use the original file  contained in src zip in each JDK from Sun Oracle  and also in OpenJDK

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There are multiple techniques available to handle collision  I will explain some of them  Chaining  In chaining we use array indexes to store the values  If hash code of second value also points to the same index then we replace that index value with an linked list and all values pointing to that index are stored in the linked list and actual array index points to the head of the the linked list  But if there is only one hash code pointing to an index of array then the value is directly stored in that index  Same logic is applied while retrieving the values  This is used in Java HashMap Hashtable to avoid collisions   Linear probing  This technique is used when we have more index in the table than the values to be stored  Linear probing technique works on the concept of keep incrementing until you find an empty slot  The pseudo code looks like this   index   h k    while  val index  is occupied    index    index 1  mod n   Double hashing technique  In this technique we use two hashing functions h1 k  and h2 k   If the slot at h1 k  is occupied then the second hashing function h2 k  used to increment the index  The pseudo-code looks like this   index   h1 k   while  val index  is occupied   index    index   h2 k   mod n   Linear probing and double hashing techniques are part of open addressing technique and it can only be used if available slots are more than the number of items to be added  It takes less memory than chaining because there is no extra structure used here but its slow because of lot of movement happen until we find an empty slot  Also in open addressing technique when an item is removed from a slot we put an tombstone to indicate that the item is removed from here that is why its empty   For more information see this site

[java] How do HashTables deal with collisions?

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