Singly Linked List Lists - Nottinghampsznza/G5BADS06/lecture6.pdf · Singly Linked List A singly linked list is a ... single object is stored ... circular array storing positions

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Lists 1© 2004 Goodrich, Tamassia

Lists


Singly Linked ListA singly linked list is a concrete data structure consisting of a sequence of nodesEach node stores

elementlink to the next node

next

elem node

A B C D

∅


Position ADT (4th edition – 6.2.2)

The Position ADT models the notion of place within a data structure where a single object is storedIt gives a unified view of diverse ways of storing data, such as

a cell of an arraya node of a linked list

Just one method:object element(): returns the element stored at the position


Node List ADT (4th edition – 6.2.3)

The List ADT models a sequence of positions storing arbitrary objectsIt establishes a before/after relation between positions(for positions, think node references)Generic methods:

size(), isEmpty()

Accessor methods:first(), last()prev(p), next(p)

Update methods:replace(p, e) addBefore(p, e), addAfter(p, e),addFirst(e), addLast(e)remove(p)


Node List ADT error conditions

As with previous ADTs, in some situations calling a method would result in an error condition:prev(p) if p is the first positionnext(p) if p is the last positionreplace(p), remove(p), addBefore(p,e), addAfter(p,e) if p is not a valid position

Accessor methods:first(), last()prev(p), next(p)

Update methods:replace(p, e) addBefore(p, e), addAfter(p, e),addFirst(e), addLast(e)remove(p)


Doubly Linked ListA doubly linked list provides a natural implementation of the List ADTNodes implement Position and store:

elementlink to the previous node (new in DNode)link to the next node

Special trailer and header nodes (new)

prev next

elem

trailerheader nodes/positions

elements

node

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InsertionWe visualize operation addAfter(p, X), which returns position v

A B X C

A B C

p

A B C

p

X

v

p v


Insertion AlgorithmAlgorithm addAfter(p,e):

Create a new node vv.setElement(e)v.setPrev(p) {link v to its predecessor}v.setNext(p.getNext()) {link v to its successor}(p.getNext()).setPrev(v) {link p’s old successor to v}p.setNext(v) {link p to its new successor, v}return v {the position for the element e}


DeletionWe visualize remove(p), where p = last()

A B C D

p

A B C

D

p

A B CLists 10© 2004 Goodrich, Tamassia

Deletion Algorithm

Algorithm remove(p):t = p.element {a temporary variable to hold the

return value}(p.getPrev()).setNext(p.getNext()) {linking out p}(p.getNext()).setPrev(p.getPrev())p.setPrev(null) {invalidating the position p}p.setNext(null)return t


Full implementation

Full Java implementation of the NodePositionList in Goodrich and Tamassia 4th edition, 6.2.4

… or on http://ww0.java4.datastructures.net/source/


PerformanceIn the implementation of the List ADT by means of a doubly linked list

The space used by a list with n elements is O(n)The space used by each position of the list is O(1)All the operations of the List ADT run in O(1) timeOperation element() of the Position ADT runs in O(1) time

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Sequence ADT (just for didactic purposes…)


Sequence ADTThe Sequence ADT is the union of the Vector and Node List ADTsElements accessed by

Rank, orPosition

Generic methods:size(), isEmpty()

Vector-based methods:elemAtRank(r), replaceAtRank(r, o), insertAtRank(r, o), removeAtRank(r)

List-based methods:first(), last(), prev(p), next(p), replace(p, o), addBefore(p, o), addAfter(p, o), addFirst(o), addLast(o), remove(p)

Bridge methods:atRank(r), rankOf(p)


Linked List ImplementationA doubly linked list provides a reasonable implementation of the Sequence ADTNodes implement Position and store:

elementlink to the previous nodelink to the next node

Special trailer and header nodes

trailerheader nodes/positions

elements

Position-based methods run in constant timeRank-based methods require searching from header or trailer while keeping track of ranks; hence, run in linear time


Array-based ImplementationWe use a circular array storing positions A position object stores:

ElementRank

Indices f and lkeep track of first and last positions

0 1 2 3positions

elements

S

lf


Sequence Implementations

nninsertAtRank(i,e), removeAtRank(i,e)11addFirst(e)*, addLast(e)1naddAfter(p,e), addBefore(p,e)

n1replaceAtRank(i,e)11replace(p,e)* (next slide)

n1atRank(i), elemAtRank(i), rankOf(p)*11size(), isEmpty()

1nremove(p,e)

11first(), last(), prev(), next()

ListCircularArray

Operation


Some explanations

The reason rankOf(p) is O(1) in the circular array implementation is that p is a position and position object for this implementation stores the rank (index) as well as an element. So p is not a stored data element here, but a new object which corresponds to a cell in the array + its content. (slide 16 –sorry for confusion).Same for replace(p,e) – once we have p, we have the index to go and write e.addFirst(e) is O(1) in the circular array implementation – just move f (front) left.

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Lists in Java Collections Framework and Iterators


Java.util.LinkedList

Java’s LinkedList looks different from the one in the textbookMost importantly, it does not expose positions in the listIf you want to walk through the list and see/modify the elements in the list, you use an Iterator object for that list (same as with other collections which implement Iterableinterface; they all have an iterator() method which returns an Iterator)


Java IteratorsAn Iterator has access to elements of some Collection and can produce them in some orderCan think of it as an temporary sequence of elements with a bookmark (current) elementMethods of the Iterator<E> interface (over Collection of elements of type E):

boolean hasNext() // says whether there are any elements left to seeE next() // returns the next elementvoid remove() // removes the current element from the Collection


ConclusionThis is all on sequences (until we come back with sorting)Main point: you can have random access implementations of sequences, usually of fixed size, with constant time access to indices in the sequence; or linked implementations, which grow easily, but where it takes linear time to reach index i Which one is more appropriate depends on the application.

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Singly Linked List Lists - Nottinghampsznza/G5BADS06/lecture6.pdf · Singly Linked List A singly linked list is a ... single object is stored ... circular array storing positions