Chap 3Chap 3Linked ListsLinked Lists

VocabularyVocabulary

Linear List 线性表Linked List 链表Retrieval 检索Traversal 遍历Node 结点Circularly Linked Lists 循环链表Doubly Linked Lists 双向链表Multilinked Lists 多重链表

3.1 Linear List3.1 Linear List

Definition: A linear list is a list in which each element has a unique successor. Array is a typical linear list structure.

Property: sequential

Element 1 Element 2 Element 3 Element 4

Classification

Linear Lists

General Restricted

Unordered Ordered FIFO(queue)

LIFO(stack)

Operation Insertion: Depending on the type of general list, an insertion can be

made at the beginning of the list, in the middle of the list, or at the end of the list. If data is inserted into ordered lists, the ordering of the list must be maintained. Maintaining the order may require a search algorithm to determine where the data are to be placed.

10 20 30

data25 Insertion

10 20 25 30

Inserted Data

list

Deletion: Deletion from a general list requires that the list be searched to locate the data being deleted. Any sequential search algorithm can be used to locate the data. When data are deleted from a random array, the data following the deleted item must be shifted to replace the empty element.

blue green yellow

redDeletion

blue green red yellow

Delete element identified searchlist

Retrieval: List retrieval requires that data be located in a list and presented to the calling module without changing the contents of the list.

dogRetrieval

cat goldfishdog zebralist

cat goldfishdog zebra

Retrieved element identified by search

Traversal: List traversal is a special case of retrieval in which all elements are retrieval in sequence. List traversal requires a looping algorithm rather than a search. Each execution of the loop processes one element in the list. The loop terminates when all elements have been processed.

3.2 Linked list 3.2 Linked list Definition: A linked list is an ordered

collection of data in which each element contains the location of the next element; that is , each element contains two parts: data and link. The data part holds the useful information, the data to be processed. The link is used to chain the data together. It contains a pointer that identified the next element in the list.

a singly linked list: a linked list contains only one link to a single successor.

The major advantage of the linked list: the data of the linked list can be easily inserted and deleted.

Nodes: The elements in a linked list are called nodes.

pHead data link data link data link

A linked list with a head pointer: pHead

pHead

An empty linked list

Linked List Data Structure Head Node Structure: It usually

contains two parts: a pointer and metadata which are data about data in the list.

Data Node Structure: The data type for the list depends entirely on the application. A typical data type is like:

dataType

key <keyType>

field1 <…>

field2 <…>

…

fieldN <…>

End dataType

count head

Head structure

data link

Data node structure

metadataList

count <integer>

head <pointer>

End List

Node

data <datatype>

link <pointer>

End Node

3.3 Linked List Algorithms3.3 Linked List Algorithms Create List: it receives the head structure and initia

lizes the metadata for the list. The pseudocode algorithms: Algorithm createList(ref list <metadata

>)

Initializes metadata for a linked list.

Pre list is metadata structure passed by reference

Post metadata initialized

1 list.head = null

2 list.count = 0

3 return

End createList

list.head = null list.count = 0

(a) before create

? ?listcount head

(b) after create

0listcount head

Insert Node: 1.Allocate memory for the new node and insert data. 2.Point the new node to its successor. 3.Point the new node’s predecessor to the new node. We discuss four situation :

insert into empty listinsert at beginninginsert in middleinsert at end

pNew->link = list.head Set link to null pointer

List.head = pNew Point list to first node

0count head

75

pNew (a) before add

1count head

75

pNew (b) after add

Insert into empty list:

Insert at beginning:

pNew->link = list.head

List.head = pNew

1

39pNew

75

count head

Before add

After add

1

39pNew

count head75

Logically,inserting into an empty list is the same as inserting at the beginning of a list.

Insert in middle:

pNew->link = pPre->link

pPre->link = pNew

2

pNew

39

count head

Before add75

52pPre

After add

3

52pNew

count head

39 75

pPre

Insert at end:

pNew->link = pPre->link

pPre->link = pNew

3count head

39 7552

pNew 134pPre

Before add

After add

3count head

39 7552

pPre pNew 134

Insert node algorithm:Algorithm insertNode (ref list < metadata >,

val pPre <node pointer>,

val dataIn <dataType>)

1 allocate(pNew)

2 if (memory overflow)

1 return false

3 end if

4 pNew->data=dataIn

5 if (pPre null)

1 pNew-.link =list.head

2 list.head = new

6 else

1 pNew->link = pPre->link

2 pPre->link = pNew

7 end if

8 list.count = list.count+1

9 Return ture

end insertNode

Insert data into a new node in the linked list

Pre

List is metadata structure to a valid list

pPre is pointer to data’s logical predecessor

dataIn contains data to be inserted

Post

data have been inserted in sequence

Return

true if successful , false is memory overflow

Delete Node: this algorithm logically removes a node from the linked list by:1. changing various link pointers and then 2. physically deleting the node from dynamic memory.

We discuss two situation :

delete first node (delete the only node in the list)

general delete case (delete the middle or last node)

Delete first node:

list.head = pLoc->link

recycle(pLoc)

3 39 13475

Before delete

pLocpPre

count head

2 13475After delete

pLocpPre

(Recyled)count head

General delete case:

pPre->link = pLoc->link

recycle(pLoc)

39 13475

pPre

3

Before delete

pLoccount head

After delete

39 134

pPre

3

pLoccount head

(Recycled)

Delete node algorithm:Algorithm insertNode (ref list < metadata >,

val pPre <node pointer>,

val pLoc <node pointer>,

ref dataOut <dataType>)

1 Dataout = pLoc->data

2 if (pPre null)

1 list.head = pLoc->link

3 else

1 pPre->link = pLoc->link

4 end if

5 list.count = list.count - 1

6 recycle(pLoc)

7 Return

end deleteNode

Deletes data from a linked list and returns it to calling module.

Pre

List is metadata structure to a valid list

pPre is pointer to predecessor node

dataIn is variable to received deleted data

Post

data have been deleted and returned to caller

Search list: it is used by several algorithms to locate data in a list. When we insert or delete or retrieve data from a list, we need to search the list and find the data.

Algorithm searchList (val list <metadata>

ref pPre <node pointer>

ref pLoc <node pointer>

ref target <key type>

1 pPre = null

2 pLoc = list.head

3 Loop (pLoc not null AND target > pLoc->data.key)

1 pPre =pLoc

2 pLoc = pLoc->link

4 end loop

5 If (pLoc null)

1 found = false

6 else

1 if (target equal pLoc->data.key)

1 found = true

2 else

1 found = false

3 end if

7 end if

8 return found

end searchList

Searches list and passes back address of node containing target and its logical predecessor.

Pre List is metadata structure to a valid list pPre is pointer to predecessor node pLoc is pointer variable for current node target is the being sought

Post pLoc point to first node with equal /greater key -or- null if targer > key of last node pPre points to largest node smaller than key -or- null if targer < key of first node

Return

true if found , false if not found

Unordered List Search: The problem with unordered searches is that multiple elements often satisfy the search criteria. One simple solution is to return a list of all elements that satisfy the criteria.

Retrieve Node: 1. Use search algorithm to locate the data in the

list. 2. If the data are found, move the data to the output

area in the calling module and returns true. 3. If the data are not found, return false.

Empty list:

algorithm retrieveNode (val list < metadata >,

val key <key type>,

ref dataOut <dataType>)

1 found = searchList(List, pPre, pLoc, key)

2 If (found)

1 dataOut = pLoc->data

3 End if

4 Return found

End retreiveNode

Algorithm emtpyList (val list <metadata>)

1 return (list.count equal to zero)

End emptyList

Full list:

List count:

Algorithm fullList (val list <metatype>)

1 Allocate (pNew)

2 If (allocation successful)

1 recycle (pNew)

2 return false

3 End if

4 Return ture

End fullList

Algorithm listCount (val list <metatype>)

1 Return (list.count)

End listCount

Traverse list: Algorithms of this kind start at the first node and examine each node in succession until the last node has been processed. Traverse list is used in changing a value in each node, printing the list, summing a field in the list and so on.

step: 1. Set the walking pointer to the first node in the list. 2. Use a loop calling a process module and passes it the data and then

advances the walking pointer to the next node. 3. When the last node is processed, the walking pointer becomes null and

the loop terminates.

pWalker = list.head

Loop (pWalker not null)

process(pWalker ->data)

pWalker = pWalker ->link

End loop

A approach in designing the traverse list in this approach, the user controls the loop, calling traverse to get next element in the list

moredata = getNext (list, o, dataout)Loop (moredata true)process(dataout)moredata = getNext (list, o, dataout)End loop

N • Count pos head

5 10 15 20 … 95 100

Algorithm getNext ( ref list <metatype>,

val fromWhere <Boolean>,

ref dataOut <datatype> )

1 If (fromwhere is 0)

1 if (list.count is zero)

1 success = false

2 Else

1 list.pos = list.head

2 dataOut = list.pos->data

3 success = true

2 Else

1 if (list.pos->link null)

1 success = false

2 else

1 list.pos = list.pos->link

2 dataOut = true

3 end if

3 End if

4 Return success

End getNext

Traverses a linked list, each call return the location of an element in the list

Pre List is metadata structure to a valid list fromWhere is 0 start at the first element dataOut is variable to receive data

Post dataOut contains data and true returned -or- if end of list returns false

Return

true if next element located , false if end of list

Destroy list: It deletes any nodes still in the list and recycles their memory, then sets the metadata to a null list condition..Algorithm destroyList (ref pList <metadata>)

1 Loop (list.count not zero)

1 dltPtr = list.head

2 list.head = dltPtr->link

3 list.count = list.count – 1

4 recycle (dltPtr)

2 End loop

3 list.pos = null

4 Return

End destroyList

Delete all data in list

Pre List is metadata structure to a valid list

Post All data deletedReturn

3.4 Processing A Linked list3.4 Processing A Linked listLinkedList

createList destroyList

getData addNode removeNode printList

menusearchList

insertNode

searchList

deleteNode

getNext

(+) (+)

Algorithm buildLinkedList

1 Print (welcome to exploring linked lists.)

2 CrateList (list)

3 Loop (option not to quit)

1 option = menu ()

2 if (option add)

1 dataIn = getData()

2 addNode (list, dataIn)

3 elseif (option delete)

1 print (Enter key of data to be deleted.)

2 read (deleteKey)

3 removeNode (list, deleteKey)

4 elseif (option print)

1 printList (list)

5 endif

4 End loop

5 DestroyList (list)

6 Print (Exploration complete. Thank you.)

End buildLinkedList

This program builds a linked list that can be modified or printed by the user.

Algorithm menu

1 Print (……MENU……)

2 Print (A: Add new data.)

3 Print (D: Delete data.)

4 Print (P: Print list.)

5 Print (Q: Quit.)

6 Valid = false

7 Loop ( valid false)

1 print ( Enter your choice:’’)

2 read (choice)

3 if (choice equal ‘A’ or ‘D’ or ‘P’ or ‘Q’)

1 valid = true

4 else

1 print ( Invalid choice. Choices are <A,D,P,Q> )

5 endif

8 End loop

9 Return choice

End menu

Display a menu and read user option.

Pre NothingReturn Valid choice

Algorithm addNode ( ref list <metadata>,

val dataIn <dataType>)

1 Found = searchList (list, pPre, pLoc, dataIn.key)

2 If (found)

1 print (Error: Data already in the list. Not added.)

3 Else

1 success = insertNode (list, pPre, dataIn)

2 if (success false)

1 print (Error: Out of memory. Program quitting.)

2 abort algorithm

3 end if

4 Return

End addNode

Add data to a linked list

Pre List is metadata structure to a valid list dataIn are data to be inserted into list

Post Data have been inserted into list in key sequence

Algorithm removeNode (ref list <metadata>,

val key <keyType>)

1 Found = searchList (list, pPre, pLoc, key)

2 If (found)

1 deleteNode (list, pPre, pLoc, deleteData)

3 Else

1 print (Error: Key not in list.)

4 End if

5 Return

End removeNode

This algorithm deletes a node from the linked list

Pre List is metadata structure to a valid list key is the key to be located and deleted

Post the node has been deleted -or- a warning message printed if not found

Algorithm printList ( val list <metadata> )

1 If (emptyList (list))

1 print (No data in list.)

2 Else

1 print (**** Begin Data Print ****)

2 count = 0

3 moreData = getNext (list, 0, dataPtr)

4 loop (moreData true)

1 count = count + 1

2 print (count, dataPtr->key)

3 moreData = getNext (list, 1, dataPtr)

5 end loop

3 End if

4 Return

End printlist

This algorithm traverses a linked list and prints the key in each node.

Pre List is metadata structure to a valid list

Post All key have been printed

3.5 List Applications3.5 List ApplicationsAppend Lists:

5count pos head

5 10 15 20 25

5count pos head

7 12 17 22 27

5count pos head

5 10 15 20 25

5count pos head

7 12 17 22 27

list1

list2

list1

list2

Before Append

After Append

Algorithm appendTwolists

1 Pirint (This program creates two lists and then appends them)

2 Print (Enter first file name)

3 Read (fileName)

4 Open (fileName)

5 Build (list1, fileName)

6 printList (list1)

7 Print (Enter secondt file name)

8 Read (fileName)

9 Open (fileName)

10 Build (list2, fileName)

11 printList (list2)

12 Append (list1, list2)

13 printList (list1)

14 Return

End appendTwoLists

Algorithm build ( ref list <metadata>,

val file <data file>)

1 CreateList (list)

2 Loop (not end of file)

1 read (file into dataIn)

2 searchList (list, pPre, pLoc, dataIn.key)

3 insertNode (list, pPre, dataIn)

3 End loop

4 Return

End build

Algorithm append ( ref list1 <metadata>,

val list2 <metadata>)

1 If (list1.count zero)

1 list1.head = list2.head

2 Else

1 pLoc = list1.head

2 loop(pLoc->link not null)

1 pLoc = pLoc->link

3 end loop

4 pLoc->link = list2.head

3 End if

4 List1.count = list1.count + list2.count

5 Return

End append

Array of lists(count,

pos, and head)

Algorithm arrayOf Lists

1 print (Begin array of linked lists)

2 Print (How many list do you want?)

3 Read (numLists)

4 buildArys (listArray, numLists)

5 printArys (listArray, numLists)

6 Print (End of arry of linked lists)

End arryOfLists

Algorithm buildArrays (ref listArray <metadata>,

val numLists <integer>)

1 row = 0

2 Loop (row < numLists)

1 print (Enter file name)

2 read (fileName)

3 open (fileName)

4 build (listArray[row], fileName)

5 close (fileName)

6 row = row + 1

3 End loop

4 Return

End buildArrays

Algorithm printArys (val listArray <metadata>,

val numLists <integer> )

1 Row = 0

2 Loop (row < numLists)

1 printList (listArray[row])

2 row = row + 1

3 End loop

4 Return

End printAry

3.63.6 Complex Linked List StructurComplex Linked List Structureses

Circularly Linked Lists:In this structure, the last node’s link points to the first node of the list.

Ncount pos rear

5 10 95link

The problem on searching doubly linked list: What is the target does not exit?

The solution: if we start at the fitst node, use the rear pointer; if we start at a middle node , we save the starting

node’s address, use the address

Doubly Linked: In this structure, each node has a pointer to both its successor and its predecessor.

count head rear 105 95B F B F B FList

Doubly Linked List Insertion:–Follow the basic patter.

–Need to connect both the forward and backward pointers.

B: Backward pointer F: Forward pointer

0 1

20

pPre

20pNew

Before AfterInsert into null list or before first node

2

20 40

30pNew

3

20 40

30

Before AfterInsert between two nodes

Algorithm insertDbl (ref list <metadata>,

val dataIn <dataType>)

1 If (full list)

1 return 0

2 End if

3 Found = searchList (list, Pre, pSucc, dataIn.key)

4 If (not found)

1 allocate (pNew)

2 pNew->data = dataIn

3 if (pPre is null)

1 pNew->back = null

2 pNew->fore = list.head

3 list.head = pNew

4 else

1 pNew->fore = pPre->fore

2 pNew->back = pPre

5 end if

6 if (pPre->fore null)

1 list.rear = pNew

7 else

1 pSucc->back = pNew

8 end if

9 pFore->fore = pNew

10 list.count = list.count + 1

11 return (1)

5 End if

6 Return (2)

End insertDbl

3

25 7550

pPred pDlt pSucc

3

25 75

Before delete

After deleting 50

50(Recycled)

Doubly Linked List deletion:

Algorithm deleteDbl ( ref list <metadata>,

val pDlt <node pointer>)

1 If (pDlt null)

1 abort (Impossible condition in delete double)

2 End if

3 List.count = list.count + 1

4 If (pDlt->backk not null)

1 pPred = pDlt->back

2 pPred->fore = pDlt->fore

5 Else

1 list.head = pDlt->fore

6 End if

7 If (pDlt->fore not null )

1 pSucc = pDlt->fore

2 pSucc->back = pDlt->back

8 Else

1 list.rear = pDlt->back

9 End if

10 Recycle (pDlt)

11 Return

End deleteDbl

Multilinked Lists: It is a list with two or more logical key sequences.

3 Pres rear

Sp rear

Spouselink

President link

Washington 1789 Cutis

Admas,J 1779 Smith

Jefferson 1801 Skelton

Multilinked List Insert:

Build Multilinked

getData insert

Build Node

InsertPres

InsertSpouse

SearchPres

SearchSpouse

Multilinked List Delete:– The major variation for multilinked list delete: need to r

econnect the pointers for each logical list.– One solution: use the spouse’s name from the president

search and then search the spouse list to find the pointers that need to be updated, but doing so can be very inefficient.

– The standard solution: use a doubly linked list for the spouse links.

3.9 Summary3.9 Summary

A linear list is a list in which each element has a unique successor.

Linear list can be divided into tow categories: general and restricted.– In a general list, data can be inserted and delete

d anywhere and there are no restrictions on the operations that can be used to process the list.

– General lists can be further diveded into random lists and ordered list.

– In a random list, there is no ordering of the data.

– In an ordered list, the data dare arranged according to a key,which is one or more fields used to identify the data or control their use.

– In a restricted list, data ,can be added or deleted at the end of the structure and processing is restricted to the operations on the data at then ends of the list.

– Tow common restricted list structures are stacks, (last in-fist out [LIFO] lists) and queues (fist in-first out [FIFO] lists).

Four common operations are associated with linear lists: insertion, deletion, retrieval, and traversal.

A linked list is an ordered collection of data

in which each element contains the location (address) of the next element; that is, each element contains two parts: data and link.

A head node is a data structure that contains metadata about the list, such as a count, a head pointer to the first node, and a rear pointer to the last node. It may contain any other general list data required by the use of the structure.

The node in s singly linked list contains only one link to a single successor unless it is the last, in which case it is not linked to any other node.

When we want to insert into a linked list contains only one link to a single successor unless it is the

last, in which case it is not linked to any other node.

When we want to insert into a linked list, we must consider four cases: adding to the empty list, adding at the beginning, adding to the middle,, and adding at the end.

When we want to delete a node from a list, we must consider two case: delete the first node or delete any other node.

To search a linked list for an item, we use the ordered list search.

Traversing a linked list means going through the list, node by node, and processing each node. Three examples of list traversals are counting the

number of the nodes, printing the contents of nodes, and summing the values of one or more fields.

A header node contains the same metadata found in the head structure and shares the pointer structure with the data node. It is physically positioned so that it is always the first node in the linked list.

A circularly linked list is a list in which the last node’s link points to the first node of the list.

A doubly linked list is a linked list in which each node has pointer to both its successor and its predecessor.

A multilinked list is a linked list with two or more logical list.