Dictionary Arrays ( d_array )

Definition

An instance A of the parameterized data type d_array<I,E> (dictionary array) is an injective mapping from the linearly ordered data type I, called the index type of A, to the set of variables of data type E, called the element type of A. We use A(i) to denote the variable with index i and we use dom(A) to denote the set of ``used indices''. This set is empty at the time of creation and is modified by array accesses. Each dictionary array has an associated default value xdef. The variable A(i) has value xdef for all i $\notin$dom(A).

Related data types are h_arrays, maps, and dictionaries.

#include < LEDA/d _array.h >

Types

d_array<I,E>::item	the item type.
d_array<I,E>::index_type	the index type.
d_array<I,E>::element_type
	the element type.

Creation

d_array<I,E>	A	creates an injective function a from I to the set of unused variables of type E, sets xdef to the default value of type E (if E has no default value then xdef stays undefined) and dom(A) to the empty set, and initializes A with a.
d_array<I,E>	A(E x)	creates an injective function a from I to the set of unused variables of type E, sets xdef to x and dom(A) to the empty set, and initializes A with a.

Operations

E&	A[I i]	returns the variable A(i).
bool	A.defined(I i)	returns true if i $\in$ dom(A) and false otherwise.
void	A.undefine(I i)	removes i from dom(A) and sets A(i) to xdef.
void	A.clear()	makes dom(A) empty.
int	A.size()	returns | dom(A)|.

Iteration

forall_defined(i, A) { ``the elements from dom(A) are successively assigned to i'' }

forall(x, A) { ``for all i $\in$ dom(A) the entries A[i] are successively assigned to x'' }

Implementation

Dictionary arrays are implemented by randomized search trees [2]. Access operations A[i] take time O(logdom(A)). The space requirement is O(dom(A)).

Example

Program 1:

We use a dictionary array to count the number of occurrences of the elements in a sequence of strings.

#include <LEDA/d_array.h>

main()
{ 
  d_array<string,int> N(0);
  string s;

  while (cin >> s) N[s]++;

  forall_defined(s,N) cout << s << "  " << N[s] << endl;

}

Program 2:

We use a d_array<string,string> to realize an english/german dictionary.

#include <LEDA/d_array.h>

main()
{ 
  d_array<string,string> dic;

  dic["hello"] = "hallo";
  dic["world"] = "Welt";
  dic["book"]  = "Buch";
  dic["key"]   = "Schluessel";
  
  string s;
  forall_defined(s,dic) cout << s << "  " << dic[s] << endl;

}