Data Structures and Algorithms

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# Data Structures and Algorithms - PowerPoint PPT Presentation

Data Structures and Algorithms. (Linked List) Instructor: Quratulain . Why need Link List?. The array implementation has serious drawbacks: you must know the maximum number of items in your collection when you create it. must be in continuous manner.

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### Data Structures and Algorithms

Instructor: Quratulain

• The array implementation has serious drawbacks:
• you must know the maximum number of items in your collection when you create it.
• must be in continuous manner.
• We can use a structure called a linked list to overcome this limitation.

CSE 246 Data Structures and Algorithms Quratulain

• The linked list is a very flexible dynamic data structure
• A programmer need not worry about how many items a program will have to accommodate
• In a linked list, each item is allocated space as it is added to the list. A link is kept with each item to the next item in the list.

next

node

elem

CSE 246 Data Structures and Algorithms Quratulain

myList

a

b

c

d

• A linked list consists of:
• A sequence of nodes
• Each node contains a value

and a link (pointer or reference) to some other node

The last node contains a null link

The list may have a header

CSE 246 Data Structures and Algorithms Quratulain

More terminology
• A node’s successor is the next node in the sequence
• The last node has no successor
• A node’s predecessor is the previous node in the sequence
• The first node has no predecessor
• A list’s length is the number of elements in it
• A list may be empty (contain no elements)

CSE 246 Data Structures and Algorithms Quratulain

Pointers and references
• In C and C++ we have “pointers,” while in Java we have “references”
• These are essentially the same thing
• The difference is that C and C++ allow you to modify pointers in arbitrary ways, and to point to anything
• In Java, a reference is more of a “black box,” or ADT Available operations are:
• dereference (“follow”)
• copy
• compare for equality
• There are constraints on what kind of thing is referenced: for example, a reference to an array of intcan only refer to an array of int

CSE 246 Data Structures and Algorithms Quratulain

• Linear collection of self-referential class objects, called nodes
• Accessed via a pointer to the first node of the list
• Link pointer in the last node is set to null to mark the list’s end
• You have an unpredictable number of data elements
• You want to insert and delete quickly.

CSE 246 Data Structures and Algorithms Quratulain

3

2

100

500

Data member and pointer

NULL pointer (points to nothing)

Self-Referential Class
• Self-referential structures
• Class that contains a pointer to a class of the same type
• Can be linked together to form useful data structures such as lists, queues, stacks and trees
• Terminated with a NULL reference
• Diagram of two self-referential class objects linked together

class node { int data; node next;…}

CSE 246 Data Structures and Algorithms Quratulain

Creating references
• The keyword new creates a new object, but also returns a reference to that object
• For example, Person p = new Person("John")
• new Person("John")creates the object and returns a reference to it
• We can assign this reference to p, or use it in other ways

CSE 246 Data Structures and Algorithms Quratulain

myList:

44

97

23

17

• class node { int value;node next;
• node (int v, node n) { // constructor value = v; next = n;}
• }
• node temp = new node(17, null);
• temp = new node(23, temp);
• temp = new node(97, temp);
• node myList = new node(44, temp);

CSE 246 Data Structures and Algorithms Quratulain

Each node contains a value and a link to its successor (the last node has no successor)

The header points to the first node in the list (or contains the null link if the list is empty)

myList

a

b

c

d

CSE 246 Data Structures and Algorithms Quratulain

Private node start;

this.first = null;}

// methods...

}

Public void getlistnode(){

…}

}

However, the entire list is accessible from this header

Users can think of the SLL as being the list

Users shouldn’t have to worry about the actual implementation

CSE 246 Data Structures and Algorithms Quratulain

Singly Linked List nodes in Java
• public class node {
• protected Object element;
• protected node next;
• protected node(Object elem, node next) {
• this.element= elem;
• this.next= next;
• }}

CSE 246 Data Structures and Algorithms Quratulain

numerals

two

three

one

Creating a simple list
• To create the list ("one", "two", "three"):
• Numerals.start= new node("one", new node("two", new node("three", null)));

CSE 246 Data Structures and Algorithms Quratulain

• The following method traverses a list (and prints its elements):
• public void printFirstToLast() {
• for (node curr = start;
• curr != null;
• curr = curr.next) {
• System.out.print(curr.element + " ");
• }}
• You would write this as an instance method of the SLinkListclass

CSE 246 Data Structures and Algorithms Quratulain

curr

numerals

two

three

one

CSE 246 Data Structures and Algorithms Quratulain

Inserting a node into a SLinkList
• There are many ways you might want to insert a new node into a list:
• As the new first element
• As the new last element
• Before a given node (specified by a reference)
• After a given node
• Before a given value
• After a given value
• All are possible, but differ in difficulty

CSE 246 Data Structures and Algorithms Quratulain

Inserting as a new first element
• This is probably the easiest method to implement
• void insertAtFront(node n) {n.next= this.start;this.start= n;}
• Notice that this method works correctly when inserting into a previously empty list

CSE 246 Data Structures and Algorithms Quratulain

Inserting a node after a given value

void insertAfter(Object obj, node n) {

for(node here =this.start; here != null;here= here.next) {

if (here.element.equals(obj)) {

n.next= here. next;

here. next = n;

return;

}// if

}// for

// Couldn't insert--do something reasonable!

}

CSE 246 Data Structures and Algorithms Quratulain

n

2.5

numerals

two

three

one

Inserting after (animation)

Find the node you want to insert after

Then, change the link in the node that's already in the list

CSE 246 Data Structures and Algorithms Quratulain

Deleting a node from a SLinkList
• In order to delete a node from a SLL, you have to change the link in its predecessor
• This is slightly tricky, because you can’t follow a pointer backwards
• Deleting the first node in a list is a special case, because the node’s predecessor is the list header

CSE 246 Data Structures and Algorithms Quratulain

numerals

two

three

one

numerals

two

three

one

Deleting an element from a SLL

• To delete the first element, change the link in the header

• To delete some other element, change the link in its predecessor

• Deleted nodes will eventually be garbage collected

CSE 246 Data Structures and Algorithms Quratulain

• public void delete(node del) {
• node temp = del. next;
• if (del == first) first = temp;
• else { // find predecessor and change its link
• node pred = first;
• while (pred.next!= del) pred = pred.next;
• pred. next= temp;
• }
• }

CSE 246 Data Structures and Algorithms Quratulain

Garbage Collection

What happens to objects that have no references to them?

• They are inaccessible to the program
• Java system will remove them and recycle the memory (usually when low on memory)
• How this is done is up to the implementation
• I’ll describe two approaches:
• Reference counting (has problems with cycles)
• Mark and sweep, or tracing
• Compaction is also important

CSE 246 Data Structures and Algorithms Quratulain

Each node contains a value, a link to its successor (if any), and a link to its predecessor (if any)

The header points to the first node in the list and to the last node in the list (or contains null links if the list is empty)

a

b

c

CSE 246 Data Structures and Algorithms Quratulain

Can be traversed in either direction (may be essential for some programs)

Some operations, such as deletion and inserting before a node, become easier

Requires more space

List manipulations are slower (because more links must be changed)

Greater chance of having bugs (because more links must be manipulated)

CSE 246 Data Structures and Algorithms Quratulain

private node first;

this.first = null;}

// methods...

}

private node first;

private node last;

this.first = null;

this.last = null;}

// methods...

}

CSE 246 Data Structures and Algorithms Quratulain

• public class node {
• protected Object element;
• protected node pred, succ;
• protected node(Object elem,node pred,node succ) {
• this.element = elem;
• this.pred = pred;
• this.succ = succ;
• }}

CSE 246 Data Structures and Algorithms Quratulain

Deletion of the first node or the last node is a special case

Garbage collection will take care of deleted nodes

a

b

c

Deleting a node from a DLinkList

CSE 246 Data Structures and Algorithms Quratulain

• Most “algorithms” on linked lists—such as insertion, deletion, and searching—are pretty obvious; you just need to be careful
• Sorting a linked list is just messy, since you can’t directly access the nth element—you have to count your way through a lot of other elements

CSE 246 Data Structures and Algorithms Quratulain

Method

Time

O(1)

Inserting at the tail

O(1)

O(1)

Deleting at the tail

O(n)

CSE 246 Data Structures and Algorithms Quratulain

• Begins with a pointer to the first node
• Terminates with a null pointer
• Only traversed in one direction
• Pointer in the last node points

back to the first node

• Two “start pointers” – first element and last element
• Each node has a forward pointer and a backward pointer
• Allows traversals both forwards and backwards
• Forward pointer of the last node points to the first node and backward pointer of the first node points to the last node

CSE 246 Data Structures and Algorithms Quratulain

10

20

40

70

55

• A Circular Linked List is a special type of Linked List
• It supports traversing from the end of the list to the beginning by making the last node point back to the head of the list
• A Rear pointer is often used instead of a Head pointer

Rear

CSE 246 Data Structures and Algorithms Quratulain

• Circular linked lists are usually sorted
• Circular linked lists are useful for playing video and sound files in “looping” mode
• They are also a stepping stone to implementing graphs.

CSE 246 Data Structures and Algorithms Quratulain

Issues with circular list
• How do you know when you’re done?
• Make sure you save the head reference.
• When (cur.next == head) you’ve reached the end
• How are insertion and deletion handled?
• No special cases!
• Predecessor to head node is the last node in the list.

CSE 246 Data Structures and Algorithms Quratulain

The Josephus Problem
• (One of many variations…)

The founder of a startup is forced to lay off all but one employee. Not having any better way to decide, he arranges all employees in a circle and has them count off. The 10th employee in the circle is laid off, and the count begins again. The last person is not laid off.

• If there are N employees, where should you sit to avoid being laid off?

CSE 246 Data Structures and Algorithms Quratulain

Solution
• Model the circle of employees as a circular linked list
• Implement the counting off process, and delete the 10th employee each time
• After N-1 people are deleted, there should be only one employee left.
• That employee’s original position number is the solution to the problem.

CSE 246 Data Structures and Algorithms Quratulain