Sorted sequence: Difference between revisions

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# [[B-Trees]]
# [[B-Trees]]
# [[Binary Search Tree]]
# [[Binary Search Tree]]
== Remark ==
* The '''''number''''', '''''find''''', '''''find at position''''', and '''''remove''''' methods are identical to those of [[Linear sequences]], so they are omitted here.
* For method '''''traverse''''' see also the remark on iterators for [[Linear sequences]].

Revision as of 13:59, 9 May 2015


General Information

Representation invariant:

  1. The abstract data structure sorted sequence implements sorted sequences as defined here.
  2. This abstract data structure is generic and parameterized by a fixed key type [math]\displaystyle{ \kappa }[/math] and a fixed comparison [math]\displaystyle{ c }[/math] defined on [math]\displaystyle{ \kappa }[/math].

Constructor: Gets a comparison [math]\displaystyle{ c }[/math] and initializes ths sequence so as to be empty.

Insert

Input: A key [math]\displaystyle{ K \in \kappa }[/math].

Output:

Precondition:

Postcondition: A new element with the key [math]\displaystyle{ K }[/math] is inserted at the appropriate position in sorting order.

Traverse

Input:

Output: A linear list structure [math]\displaystyle{ L }[/math] containing all elements of the sorted sequence in ascending order.

Precondition:

Postcondition: All keys of the sorted sequence are appended to [math]\displaystyle{ L }[/math] in ascending order.

Find

Input: A key [math]\displaystyle{ K \in \kappa }[/math].

Output: A Boolean value, which is true if, and only if, [math]\displaystyle{ K }[/math] is currently contained in the sequence.

Precondition:

Postcondition:

Remove

Input: A key [math]\displaystyle{ K \in \kappa }[/math].

Output: A Boolean value, which is true if, and only if, [math]\displaystyle{ K }[/math] is currently stored in the sequence.

Precondition:

Postcondition: If the output is true, one occurrence of [math]\displaystyle{ K }[/math] is removed.

Known Implementations

  1. B-Trees
  2. Binary Search Tree