Relation and difference between associative array and hashing table?
I thought associative array (i.e. map, or dictionary) and hashing table were the same concept, until I saw in Wikipedia that
For dictionaries with very small numbers of bindings, it may make sense to implement the dictionary using an association list, a linked list of bindings. ...
The most frequently used general purpose implementation of an associative array is with a hash table: an array of bindings, together with a hash function that maps each possible key into an array index. ...
Dictionaries may also be stored in binary search trees or in data structures specialized to a particular type of keys such as radix trees, tries, Judy arrays, or van Emde Boas trees. ...
So I think my problem lies in that I don't know that associative array (i.e. map, or dictionary) is an abstract data type and hashing table is a concrete data structure, and different concrete data structures can be used to implement the same abstract data type. So my questions would be
what are the difference and relation between abstract data structures and concrete data structures?
what examples are for each of them (abstract and concrete data structures)? The more the better.
Is there a list of what concrete data structures can be used to implement what abstract data structures? It would be nice to have one.
Thanks!
Asked By : Tim
Best Answer from StackOverflow
Question Source : http://cs.stackexchange.com/questions/6678
Answered By : Joe
The abstract data type (ADT) is essentially an API, and a concrete data structure provides an implementation of that API. For a given ADT, there are often several different choices of concrete data structures which support the query and update operations described by the ADT. Every concrete data structure for a given ADT must support all the operations described by the ADT (possibly with some probability of success in the case of randomized structures), but each concrete structure may make different guarantees of the running times of each operation. The choice of which concrete data structure to implement for a given ADT usually depends on the priorities of efficiency of each operation (including initializing the structure) and the complexity of implementing and maintaining the various data types. Some concrete data structures have excellent theoretical guarantees, but the overhead is such that a slightly less theoretically optimal data structure may be a better choice in practice.
There are far too many ADT and corresponding concrete structures to list in a single answer, but here are a few examples:
A dictionary supports
Find(x)
queries. For an a key $x$, return the element in the dictionary with key $x$, if such an element exists. A dynamic dictionary also supportsInsert(x)
andDelete(x)
. Common implementations of a dictionary include different kinds of balanced binary search trees (e.g. red black tree) and various kinds of hash tables.In addition to
Find
an ADT may require support ofsuccessor(x)
queries. That is, maintain a set of keys $S$, and given key $x$, find the smallest key $t \in S$ such that $s < t$. Concrete data structures which support the Successor ADT include various binary search trees, and more complicated structures such as an X-fast trie or van Emde Boas tree (if the keys are integers).A Priority Queue is an ADT that requires
insert
anddelete-min
operations (and sometimes other operations as well, such asfind-min
increase-key
ordelete-key
). Data structures that implement the priority queue ADT include:an unsorted linked list, which has fast
insert
but slowdelete-min
.a sorted linked list which has fast
delete-min
but slowinsert
a binary search tree, which has logarithmic
insert
anddelete-min
, and $sort(n)$ initialization time.a binary heap which has logarithmic
insert
anddelete-min
, and linear time initialization.There are also other variants of heap implementations.
An interval stabbing ADT maintains a set of intervals on the real line, and supports a
stabbing(x)
query, which returns the subset of intervals which contain (are stabbed by) the point $x$. Data structures that implement the stabbing query ADT include a Segment Tree and an Interval Tree.
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