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Lists

Lists. Position ADT. The Position ADT models the notion of place within a data structure where a single object is stored It gives a unified view of diverse ways of storing data, such as a cell of an array a node of a linked list Just one method:

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Lists

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  1. Lists Lists

  2. Position ADT • The Position ADT models the notion of place within a data structure where a single object is stored • It gives a unified view of diverse ways of storing data, such as • a cell of an array • a node of a linked list • Just one method: • object element(): returns the element stored at the position Lists

  3. Node List ADT • The Node List ADT models a sequence of positions storing arbitrary objects • It establishes a before/after relation between positions • Generic methods: • size(), isEmpty() Accessor methods: • first(), last() • prev(p), next(p) • Update methods: • set(p, e) • addBefore(p, e), addAfter(p, e), • addFirst(e), addLast(e) • remove(p) Lists

  4. Doubly Linked List • A doubly linked list provides a natural implementation of the Node List ADT • Nodes implement Position and store: • element • link to the previous node • link to the next node • Special trailer and header nodes prev next elem node trailer nodes/positions header elements Lists

  5. Insertion • We visualize operation insertAfter(p, X), which returns position q p A B C p q A B C X p q A B X C Lists

  6. Insertion Algorithm Algorithm addAfter(p,e): Create a new node v v.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} Lists

  7. p A B C D Deletion • We visualize remove(p), where p = last() A B C p D A B C Lists

  8. 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 Lists

  9. Performance • In 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) time • Operation element() of the Position ADT runs in O(1) time Lists

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