Ordered sequence: Difference between revisions
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'''Representation invariant:''' | '''Representation invariant:''' | ||
# The abstract data structure '''ordered sequence''' implements sorted sequences as defined [[Sets and sequences|here]]. | # The abstract data structure '''ordered sequence''' implements sorted sequences as defined [[Sets and sequences|here]]. | ||
# This abstract data structure is [[Genericity|generic]] and parameterized by a fixed key type <math>\ | # This abstract data structure is [[Genericity|generic]] and parameterized by a fixed key type <math>\mathcal{K}</math>. | ||
== Insert at position == | == Insert at position == | ||
'''Input:''' A key <math>K \in \ | '''Input:''' A key <math>K \in \mathcal{K}</math> and a nonnegative integral position <math>\ell</math>. | ||
'''Output:''' a Boolean value, which is true if, and only if, <math> | '''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> | '''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 between the <math>(\ell-1)</math>-th element and the prior <math>\ell</math>-th element. | ||
== Find == | == Find == | ||
'''Input:''' A key <math>K \in \ | '''Input:''' A key <math>K \in \mathcal{K} </math>. | ||
'''Output:''' A Boolean value, which is | '''Output:''' A Boolean value, which is '''true''' if, and only if, <math>K</math> is currently contained in the sequence. | ||
'''Precondition:''' | '''Precondition:''' None. | ||
'''Postcondition:''' | '''Postcondition:''' None. | ||
== Remove == | == Remove == | ||
'''Input:''' A key <math>K \in \ | '''Input:''' A key <math>K \in \mathcal{K}</math>. | ||
'''Output:''' A Boolean value, which is | '''Output:''' A Boolean value, which is '''true''' if, and only if, <math>K</math> is currently stored in the sequence. | ||
'''Precondition:''' | '''Precondition:''' None. | ||
'''Postcondition:''' If the output is | '''Postcondition:''' If the output is '''true''', one occurrence of <math>K</math> is removed. | ||
== Known Implementations == | == Known Implementations == | ||
Latest revision as of 12:52, 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 between the [math]\displaystyle{ (\ell-1) }[/math]-th element and the prior [math]\displaystyle{ \ell }[/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: None.
Postcondition: None.
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: None.
Postcondition: If the output is true, one occurrence of [math]\displaystyle{ K }[/math] is removed.