Ordered sequence: Difference between revisions
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'''Output:''' a Boolean value, which is '''true''' if, and only if, <math>\ell\in\{0,\ldots,n\}</math>, where <math>n</math> is the length of the list. | '''Output:''' a Boolean value, which is '''true''' if, and only if, <math>\ell\in\{0,\ldots,n\}</math>, where <math>n</math> is the length of the list. | ||
'''Precondition:''' | '''Precondition:''' None. | ||
'''Postcondition:''' If the output ist '''true''', a new element with the key <math>K</math> is inserted at position <math>\ell</math>. | '''Postcondition:''' If the output ist '''true''', a new element with the key <math>K</math> is inserted at position <math>\ell</math>. If <math>\ell=0</math>, this means the new element is attached before the prior first element. Otherwise, this means it is inserted immediately after the <math>(\ell-1)</math>-th element. | ||
== Find == | == Find == | ||
Revision as of 12:49, 21 May 2015
General Information
Representation invariant:
- The abstract data structure ordered sequence implements sorted sequences as defined here.
- This abstract data structure is generic and parameterized by a fixed key type [math]\displaystyle{ \mathcal{K} }[/math].
Insert at position
Input: A key [math]\displaystyle{ K \in \mathcal{K} }[/math] and a nonnegative integral position [math]\displaystyle{ \ell }[/math].
Output: a Boolean value, which is true if, and only if, [math]\displaystyle{ \ell\in\{0,\ldots,n\} }[/math], where [math]\displaystyle{ n }[/math] is the length of the list.
Precondition: None.
Postcondition: If the output ist true, a new element with the key [math]\displaystyle{ K }[/math] is inserted at position [math]\displaystyle{ \ell }[/math]. If [math]\displaystyle{ \ell=0 }[/math], this means the new element is attached before the prior first element. Otherwise, this means it is inserted immediately after the [math]\displaystyle{ (\ell-1) }[/math]-th element.
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.