Sorted sequence

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{ \mathcal{K} }[/math] and a fixed comparison [math]\displaystyle{ c }[/math] defined on [math]\displaystyle{ \mathcal{K} }[/math].

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

Insert

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

Output:

Precondition:

Postcondition: A new element with the key [math]\displaystyle{ K }[/math] is inserted at an 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 \mathcal{K} }[/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 \mathcal{K} }[/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