Doubly Linked Lists

Doubly Linked Lists

One powerful variation of a linked list is the doubly linked list. The doubly linked list structure is one in which each node has a pointer to both its successor and its predecessor.

nextprev elemnextprev elemnextprev elemhead tail

Doubly Linked Lists

struct Node { char element; Node *prev; Node *next; Node(const char& e=char(), Node *p=NULL, Node *n=NULL) : element(e), prev(p), next(n) { }};

Sentinel Nodes

As always, implementation of a data structure is up to the individual. However, one way of implementing a double linked list is to create sentinel nodes at the beginning and end of the list.

– Pointers to the sentinel nodes can be stored in a data structure as data members

– Advantage: Not necessary to treat the front or rear differently when inserting or removing

nextprev elemnextprev elemnextprev elemnextNULL head NULLprev tail

Empty Double Linked List

head = new Node;

tail = new Node;

head->next = tail;

tail->prev = head;

sz = 0;

NULLprevnextNULL

head tail

Deque - Double-Ended Queues

A Deque (pronounced ‘deck’) is a data structure in which items may be added to or deleted from the head or the tail. They are also known as doubly-ended queues.

The Deque is typically implemented with a linked list, providing easy access to the front and the back of the list, although a dynamic array could also be used for this.

Deque - Double-Ended Queues

The deque data structure typically has the following features:– How are the data related?

Sequentially

– Operations insertFirst - inserts an element at the front of a deque insertLast - inserts an element at the rear of a deque removeFirst - removes an element from the front of a deque removeLast - removes an element from the rear of a deque

(Note that the previous 2 functions did not return and data values) First - returns a reference to the element at the front last - returns a reference to the element at the rear size, isEmpty

Deque Advantages

Removing a node from the rear of a singly linked list was inefficient because we had to find the next-to-last by searching from the head

The deque is implemented with a doubly linked list. Therefore, now, removing from the rear is not a problem.

Algorithm: insertFirst()

//Create a new node t//Make “t->prev” point to node head //Make “t->next” point to node head->next (i.e., u) Node *t = new Node(e,head,head->next);//Put the address of t into head->next’s “prev” pointer//Put the address of t into head’s “next” pointer

head->next->prev = t;head->next = t;

nextprev unextprev head NULLprev tail

nextprev t

Algorithm: insertFirst()

Node *t = new Node(e,head,head->next);head->next->prev = t;head->next = t;sz++;

Algorithm: removeLast()

//Save the address of the last node as “old”Node *old = tail->prev;//Make “old->prev->next” point to node “tail”old->prev->next = tail;//Make “tail->prev” point to node “old->prev”tail->prev = old->prev; //Delete “old”delete old-;

nextprev tailnextprev pnextNULL head nextprev old

Algorithm: removeLast()

Node *old = tail->prev;old->prev->next = tail;tail->prev = old->prev;delete old; //Recover the memorysz--;