Doubly Linked Lists• Deleting from the end of the list

– Have to traverse the entire list to stop right in front of tail to delete it, so O(n)

– With head and tail pointer, still O(n), tail has to point to the node in front of the original tail (original tail’s predecessor).

– To avoid this, redefine the linked list so that each node has 2 pointers, one to the successor and one to the predecessor

Which Operation of DLL is More Efficient than SLL

• ?

Circular Lists

• In some situations, a circular list is needed in which nodes form a ring– E.g., resource sharing among process– The pointer current points to the next process to

which the resource should be assigned

Insertion at the Front and End of a Circular List

Time complexities?

Circular List (cont’d)

• Time complexity of deletion from the end?

• Circular doubly linked list

Define Circular Linked List

Example of Add a Node to the Head of a Circular LinkedList

• Different Cases• Discuss for each case

Self-Organizing Lists

• Linked lists have one serious drawback– Sequential scanning to locate a searched-for element– Time complexity of search is O(n)

• Can improve search efficiency by dynamically organizing the list in a certain manner– Move-to-front method (i.e., Most Recently Used)

• After desired element is located, put it at the beginning– Transpose method

• After desired element is located, swap it with predecessor– Count method (i.e., Most Frequently Used)

• Order the list by number of times elements are accessed– Ordering method

• Order the list using certain criteria

Self-Organizing Lists (cont’d)

• With first 3 methods, try to locate elements most likely to be looked for near the beginning of the list– Move-to-front vs. Transpose

• The ordering method is particularly advantageous when searching for information that is not in the list, because the search can terminate without scanning the entire list

• But, if the desired element is not in the list, the first 3 methods just add a new node at the end of the list O(1), whereas the ordering method must maintain the order

Optimal Static Ordering

• Analysis of the efficiency of these methods usually compares their efficiency to that of optimal static ordering (i.e., all data already ordered by the frequency of their occurrence)

• Optimal static ordering requires two passes through the body of data– Build the list– Use the list for search alone

Optimal Static Ordering (cont’d)

• Example: Find the optimal static ordering of the following stream of data:

A C B C D A D A C A C C E E

• Optimal static ordering used for comparison purposes only

An Application

Sparse Tables

• In many applications, the choice of a table seems to be the most natural one, but space considerations may preclude this choice

• Particularly true if only a small portion of the table is actually used (i.e., a sparse table)

• A sparse table can be replaced by a system of linked lists

Sparse Tables (cont’d)

• Consider the problem of storing one semester grades for 8000 students and 300 classes

• Natural implementation is a 2D array of classes and students

• Assuming, on the average, students take 4 classes per semester, each column has only 4 cells occupied and the rest (296 or 98.7%) are wasted

Sparse Tables (cont’d)

• A better implementation is to use 2 1D arrays of linked lists– Each element of array class is a pointer to a linked

list of students taking a class– Each element of array student is a pointer to a

linked list of the classes taken by a student

• The space needed will be approximately 10% of the space needed for the sparse table implementation

Template DLL

• Make the linked list to store any type of contents