List Data StructureList Data Structure

What is List?What is List?

A list is a sequential data A list is a sequential data structure. structure.

It differs from the stack and It differs from the stack and queue data, structures in that queue data, structures in that additions and removals can be additions and removals can be made at any position in the list.made at any position in the list.

List operationsList operations AddAdd : adds a new node: adds a new node SetSet : update the contents of a : update the contents of a

nodenode RemoveRemove : removes a node: removes a node IsEmptyIsEmpty : reports whether the list : reports whether the list

is emptyis empty IsFullIsFull : reports whether the list is full: reports whether the list is full InitializeInitialize : creates/initializes the list: creates/initializes the list DestroyDestroy : deletes the contents of : deletes the contents of

the list (may be implemented by re-the list (may be implemented by re-initializing the list)initializing the list)

Illustration/exampleIllustration/example Initialize(L)Initialize(L)

Create a new empty List named LCreate a new empty List named L Add(1,X,L)Add(1,X,L)

adds the value X to list L at position 1 (the start of the list adds the value X to list L at position 1 (the start of the list is position 0), shifting subsequent elements upis position 0), shifting subsequent elements up

Set(2,Z,L)Set(2,Z,L) updates the values at position 2 to be Zupdates the values at position 2 to be Z

Remove(Z,L)Remove(Z,L) removes the node with value Zremoves the node with value Z

Get(2,L)Get(2,L) returns the value of the third node, i.e. Creturns the value of the third node, i.e. C IndexOf(X,L)IndexOf(X,L)

returns the index of the node with value X, i.e. 1returns the index of the node with value X, i.e. 1

Illustration/exampleIllustration/exampleOperationOperation List’s contentsList’s contents Return valueReturn value

1. Initialiaze(L)1. Initialiaze(L) <empty><empty> --

2. Add(0,A,L)2. Add(0,A,L) AA --

3. Add(0,B,L)3. Add(0,B,L) B A B A --4. Add(1,C,L)4. Add(1,C,L) B C AB C A --5. Set(1,N,L)5. Set(1,N,L) B N AB N A --6. Add(1,D,L)6. Add(1,D,L) B D N AB D N A --7. Remove(A,L)7. Remove(A,L) B D NB D N AA8. Set(3,I,L)8. Set(3,I,L) B D N IB D N I --9. Remove(D,L)9. Remove(D,L) B N IB N I DD

10. Remove(N,L)10. Remove(N,L) B IB I NN

Exercise: List OperationExercise: List OperationWhat would the contents of a list be after the following What would the contents of a list be after the following

operations?operations?Initialise(L)Initialise(L)Add(0,A,L)Add(0,A,L)Add(0,F,L)Add(0,F,L)Add(1,X,L)Add(1,X,L)Add(1,G,L)Add(1,G,L)Add(3,P,L)Add(3,P,L)Add(2,V,L)Add(2,V,L)Set(3,K,L)Set(3,K,L)Set(0,H,L)Set(0,H,L)Remove(V,L)Remove(V,L)Remove(P,L)Remove(P,L)

H G K AH G K A

What values would be returned by the following What values would be returned by the following operations?operations?

IndexOf(A,L)IndexOf(A,L)IndexOf(H,L)IndexOf(H,L)Get(3,L)Get(3,L)

Storing a list in a static data Storing a list in a static data structure (Array List)structure (Array List) This implementation stores the list in an array. This implementation stores the list in an array. The position of each element is given by an index The position of each element is given by an index

from 0 to n-1, where n is the number of elements.from 0 to n-1, where n is the number of elements. Given any index, the element with that index can Given any index, the element with that index can

be accessed in constant time – i.e. the time to be accessed in constant time – i.e. the time to access does not depend on the size of the list.access does not depend on the size of the list.

To add an element at the end of the list, the time To add an element at the end of the list, the time taken does not depend on the size of the list. taken does not depend on the size of the list. However, the time taken to add an element at However, the time taken to add an element at any other point in the list does depend on the size any other point in the list does depend on the size of the list, as all subsequent elements must be of the list, as all subsequent elements must be shifted up. Additions near the start of the list take shifted up. Additions near the start of the list take longer than additions near the middle or end.longer than additions near the middle or end.

When an element is removed, subsequent When an element is removed, subsequent elements must be shifted down, so removals near elements must be shifted down, so removals near the start of the list take longer than removals near the start of the list take longer than removals near the middle or end.the middle or end.

Storing a list in a dynamic data Storing a list in a dynamic data structure (Linked List)structure (Linked List) The Link List is stored as a sequence of linked nodes.The Link List is stored as a sequence of linked nodes. As in the case of the stack and the queue, each node in a As in the case of the stack and the queue, each node in a

linked list contains data AND a reference to the next node.linked list contains data AND a reference to the next node. The list can grow and shrink as neededThe list can grow and shrink as needed The position of each element is given by an index from 0 to n-The position of each element is given by an index from 0 to n-

1, where n is the number of elements.1, where n is the number of elements. Given any index, the time taken to access an element with Given any index, the time taken to access an element with

that index depends on the index. This is because each that index depends on the index. This is because each element of the list must be traversed until the required index is element of the list must be traversed until the required index is found.found.

The time taken to add an element at any point in the list does The time taken to add an element at any point in the list does not depend on the size of the list, as no shifts are required. It not depend on the size of the list, as no shifts are required. It does, however, depend on the index. Additions near the end does, however, depend on the index. Additions near the end of the list take longer than additions near the middle or start. of the list take longer than additions near the middle or start. The same applies to the time taken to remove an element.The same applies to the time taken to remove an element.

The first node is accessed using the name The first node is accessed using the name LinkedList.HeadLinkedList.Head Its data is accessed using Its data is accessed using LinkedList.Head.DataItemLinkedList.Head.DataItem The second node is accessed using The second node is accessed using

LinkedList.Head.NextNodeLinkedList.Head.NextNode

Adding a node Adding a node The new node is to be added at a specified index in the listThe new node is to be added at a specified index in the list

A special case is that the A special case is that the list is emptylist is empty. In this case, the first . In this case, the first node is set to be the new node.node is set to be the new node.

Another special case is that the Another special case is that the specified index is 0specified index is 0 (the (the node is to be added at the node is to be added at the front of the listfront of the list).).

Adding a node (2)Adding a node (2)In the general case, an object reference Probe moves In the general case, an object reference Probe moves

through the list until the nodethrough the list until the nodebefore the required index is reached. Here, the node is to be before the required index is reached. Here, the node is to be

added at index 2.added at index 2.

If the new node is to be added at the end of the list, then the If the new node is to be added at the end of the list, then the NextNode of the last element is set to refer to the new NextNode of the last element is set to refer to the new node.node.

Adding a node (3)Adding a node (3)A possible algorithm (pseudocode) for the Add operationA possible algorithm (pseudocode) for the Add operation

AddAdd(index, Data, LinkedList)(index, Data, LinkedList)Declare NewNode and initialise NewNode.DataItem with dataDeclare NewNode and initialise NewNode.DataItem with dataIf(List.isEmpty)If(List.isEmpty)

Set NewNode.NextNode to NULLSet NewNode.NextNode to NULLCopy NewNode to LinkedList.HeadCopy NewNode to LinkedList.Head

ElseElseIf (index is 0)If (index is 0)

Copy LinkedList.Head to NewNode.NextNodeCopy LinkedList.Head to NewNode.NextNodeCopy NewNode to LinkedList.HeadCopy NewNode to LinkedList.Head

ElseElseCopy LinkedList.Head to ProbeCopy LinkedList.Head to Probei = 0i = 0While i < index-1 And end of list not reachedWhile i < index-1 And end of list not reached Copy Probe.NextNode to ProbeCopy Probe.NextNode to Probe Increment iIncrement iEnd WhileEnd WhileCopy Probe.NextNode to NewNode.NextNodeCopy Probe.NextNode to NewNode.NextNodeCopy NewNode to Probe.NextNodeCopy NewNode to Probe.NextNode

End IfEnd IfEnd IfEnd IfSet NewNode to NULLSet NewNode to NULLSet Probe to NULLSet Probe to NULL

Additional operations can also be implemented to add to the Additional operations can also be implemented to add to the beginning and end of the list.beginning and end of the list.

AddFirstAddFirst(Data, LinkedList) calls Add(0, Data, LinkedList)(Data, LinkedList) calls Add(0, Data, LinkedList)AddLastAddLast(Data, LinkedList) calls Add(Size, LinkedList), where (Data, LinkedList) calls Add(Size, LinkedList), where

Size is itself a call to the Size operation of the list.Size is itself a call to the Size operation of the list.

Removing a nodeRemoving a nodeA A TargetNodeTargetNode object is created. object is created.There is a special case when There is a special case when TargetNodeTargetNode is equal to the first is equal to the first

node. In this case, LinkedList is set to point to the node. In this case, LinkedList is set to point to the second node.second node.

In the general case, an object reference Probe moves In the general case, an object reference Probe moves through the list until the required node is reached – at through the list until the required node is reached – at each node the current node (Probe) is compared with each node the current node (Probe) is compared with TargetNode.TargetNode.

A Previous object reference is also required to keep track of A Previous object reference is also required to keep track of the predecessor of the node to be removed. A special the predecessor of the node to be removed. A special case is when both references point to the same node – case is when both references point to the same node – this happens when the first node is to be deleted.this happens when the first node is to be deleted.

To delete the current node we can set Previous.NextNode to To delete the current node we can set Previous.NextNode to be equal to Probe.NextNode.be equal to Probe.NextNode.

Removing a node (2)Removing a node (2)

Accessing nodes (Get, Set, Accessing nodes (Get, Set, IndexOf, View)IndexOf, View)

GetGet and and SetSet work in a similar way to work in a similar way to AddAdd – Probe moves through the – Probe moves through the list until the required list until the required indexindex is is reached, and the reached, and the DataItemDataItem is is returnedreturned ( (GetGet) or ) or updatedupdated ( (SetSet).).

IndexOfIndexOf works in a similar way to works in a similar way to RemoveRemove – Probe moves through – Probe moves through the list until the the list until the target nodetarget node is is found, and returns the index. found, and returns the index.

ViewView – Probe moves through the list – Probe moves through the list from beginning to end and the from beginning to end and the DataItemDataItem is is returned returned at each node.at each node.

Variations on Linked ListsVariations on Linked ListsCircularly linked listsCircularly linked listsThe tail of the list always points to the head of the listThe tail of the list always points to the head of the list

Doubly linked listsDoubly linked listsThese permit scanning or searching of the list in both These permit scanning or searching of the list in both

directions. (To go backwards in a simple list, it is directions. (To go backwards in a simple list, it is necessary to go back to the start and scan forwards.) In necessary to go back to the start and scan forwards.) In this case, the node structure is altered to have two links:this case, the node structure is altered to have two links:

Sorted listsSorted listsLists can be designed to be maintained in a given order. In this Lists can be designed to be maintained in a given order. In this

case, the Add method will search for the correct place in case, the Add method will search for the correct place in the list to insert a new data item.the list to insert a new data item.

List ImplementationList Implementation

List Implementation in JavaList Implementation in Java The Java Collections Framework in the most recent The Java Collections Framework in the most recent

version of Java now includes list classes. version of Java now includes list classes. As you did for the stack & queue, you will create As you did for the stack & queue, you will create

your own List class in order to learn how a list is your own List class in order to learn how a list is implemented. implemented.

Your class will again be a bit simpler than the Your class will again be a bit simpler than the Collections Framework one but it will do essentially Collections Framework one but it will do essentially the same jobthe same job

In this case you will look at Java implementations of In this case you will look at Java implementations of an an ArrayListArrayList and a and a LinkedListLinkedList. Both lists have the . Both lists have the same operations, so we can define a class same operations, so we can define a class ListList which includes minimal implementations of the which includes minimal implementations of the operations. The ArrayList and operations. The ArrayList and LinkedListLinkedList classes classes will be subclasses of will be subclasses of ListList..

The List class will define the set of operations which The List class will define the set of operations which a list class must have. This is sometimes known as a list class must have. This is sometimes known as the interface of a list. Both kinds of list will have the the interface of a list. Both kinds of list will have the same interface.same interface.

List Implementation in JavaList Implementation in Java

Notice that the LinkedList class makes use of Notice that the LinkedList class makes use of a Node class which is exactly the same as a Node class which is exactly the same as the one used for the dynamic queue.the one used for the dynamic queue.