The.Algorithm.Design.Manual.Springer-Verlag.1998

Dictionaries
Next: Binary Search Trees Up: Fundamental Data Types Previous: Containers
Dictionaries
Dictionaries are a form of container that permits access to data items by content. You put a word into a
dictionary because you know you can look it up when you need it.
The primary operations dictionaries support are:
● Search(D,k): Given a search key k, return a pointer to the element in dictionary D whose key
value is k, if one exists.
● Insert(D,x): Given a data item x, add it to the set of items in the dictionary D.
● Delete(D,x): Given a pointer to a given data item x in the dictionary D, remove it from D.
Perhaps the simplest possible dictionary implementation maintains an unsorted linked list as a data
structure. Insertion and deletion are supported in constant time, although a query requires potentially
traversing the entire linked list. Basing an implementation on a stored array speeds up the query
operation to by binary search. Making room for a new item or filling a hole left by a deletion may
require moving arbitrarily many items, so insertion and deletion become linear-time operations.
Many other dictionary implementations are available. Binary search trees are discussed in some detail in
the next section. Hash tables are another attractive option in practice. A complete discussion of different
dictionary data structures is presented catalog Section . We encourage the reader to browse through
the data structures section of the catalog in order to learn what your options are.
Certain dictionary data structures also efficiently support the following useful operations:
● Max(D) or Min(D): Retrieve the item with the largest (or smallest) key from D. This enables the
dictionary to serve as a priority, as discussed below.
● Predecessor(D,k) or Successor(D,k): Retrieve the item from D whose key is immediately before
(or after) k in sorted order. By starting from the first item Min(D) and repeatedly calling Successor
until we obtain Max(D), we traverse all elements in sorted order.
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