1. CS212D: Data Structures
Week 5-6 Linked List

2. Outline
Singly Linked Lists
Doubly Linked Lists
Recursions

3. Data Structures and Algorithms
A data structure is a way of storing data in a computer so that it can be used efficiently.
Algorithms
An algorithm is a finite sequence of well-defined instructions for solving a problem and guaranteed to terminate in a finite time.
An algorithm does not necessarily need to be executable in a computer, but can be converted into a program.

4. Algorithms versus Heuristics
A heuristic is a finite sequence of well-defined instructions for partially solving a hard problem and guaranteed to terminate in a finite time.
A heuristic is not always guaranteed to find a solution while an algorithm is.
Descriptions of algorithms
We will use Java-like pseudo code mixed with English to describe algorithms.

5. Abstract Data Types
An Abstract Data Type (ADT) is a specification of a set of data and the set of operations that can be performed on the data.
Such a data type is abstract in the sense that it is independent of various concrete implementations.
The definition can be mathematical, or it can be programmed as an interface.
We need to implement an ADT by using a class to make it usable.

6. Linked Lists

7. Singly Linked List
linked list, in its simplest form, is a collection of nodes that collectively form a linear sequence.
In a singly linked list, each node stores
a reference to an object that is an element of the sequence,
as well as a reference to the next node of the list.
next
node
elem  A B C D

8. Singly Linked List (Example)
The node’s element field refers to an object that is an element of the sequence (the airport code MSP, in this example),
while the next field refers to the subsequent node of the linked list (or null if there is no further node).
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9. Singly Linked List
The linked list instance must keep a reference to the first node of the list, known as the head.
Without an explicit reference to the head, there would be no way to locate that node.
The last node of the list is known as the tail.
The tail of a list can be found by traversing the linked list
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10. Implementing a single linked list class
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11. Implementing a single linked list class cont.
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12. Implementing a single linked list class cont.
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13. Inserting an Element at the Head of Single Linked List(1/2)
Allocate a new node
Insert the new element
Have the new node point to old head
Update head to point to the new node

14. Inserting an Element at the Head of Single Linked List (2/2)

15. Inserting an Element at the Tail of Single Linked List (1/2)
Allocate a new node
Insert the new element
Have the new node point to null
Have the old last node point to new node
Update tail to point to new node

16. Inserting an Element at the Tail of Single Linked List(2/2)

17. Removing an Element from the Head of Single Linked List (1/2)
Update head to point to next node in the list
Allow garbage collector to reclaim the former first node

18. Removing an Element from the Head of Single Linked List(2/2)

19. Removing at the Tail (1/2)
Removing the tail node of a singly linked list cannot be done in constant time.
We need to traverse the whole linked list to remove the tail node, which takes O(n) time, where n is the number of nodes in the linked list.

20. Removing at the Tail (2/2)
Algorithm removeLast() {
if ( size = 0 )
Indicate an error: the list is empty;
else
{ if ( size = 1 ) // only one node
head = null;
tail=null;
else // at least two nodes
{ t = head; /* make t point to the head */
while ( t.getNext != null ) /* find the last node */
{ s = t;
t = t.getNext(); }
s.setNext(null); //null out the next pointer of the last node }
size = size - 1; //decrement the node count

21. Exercises
Add a member method called Print to the Single Linked List class, that prints all the list elements.
State wither the following sentence is True or False, explain your answer:
we cannot easily delete the last node of a singly linked list.
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22. Doubly Linked List
A doubly linked list is a linked list in which each node keeps an explicit reference to the node before it and a reference to the node after it. Each node stores:
element
link to the previous node “prev”
link to the next node “next”
Special trailer and header nodes
prev
next
elem
node

23. Inserting with Double Linked List
Every insertion into our doubly linked list representation will take place between a pair of existing nodes.
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24. Inserting at the Head of the Double Linked List (1/2)
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25. Inserting at the Head of the Double Linked List (1/2)
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26. Inserting an Element in the Middle of the Double Linked List
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27. Inserting an Element at the Trailer
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28. Deletion with Double Linked List
The deletion of the node proceeds in the opposite fashion of an insertion.
The two neighbors of the node to be deleted are linked directly to each other, thereby bypassing the original node.
As a result, that node will no longer be considered part of the list and it can be reclaimed by the system.
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29. Removing in the Middle
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30. Implementing a Doubly Linked List Class
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31. Implementing a Doubly Linked List Class Cont.
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32. Implementing a Doubly Linked List Class Cont.
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33. Implementing a Doubly Linked List Class Cont.
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34. Exercises
Add a member method called PrintOpposite to the Double Linked List class, that prints all the double linked list elements in an opposite order.
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35. References
Chapter 3, Data Structures and Algorithms by Goodrich and Tamassia.
Garbage Collection by Bill Venners (