ESc101: (Linear, Circular, Doubly) Linked Lists, Stacks, Queues ...
Traversing the Linked List - dsauet.weebly.com · While traversing the circular linked lists we...
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• Traversing the list • Inserting an item in the list • Deleting an item from the list Traversing the Linked List Let us assume that the head points to the first node of the list. To traverse the list we do the following • Follow the pointers. • Display the contents of the nodes (or count) as they are traversed. • Stop when the next pointer points to NULL. The ListLength() function takes a linked list as input and counts the number of nodes in the list. The function given below can be used for printing the list data with extra print function. Time Complexity: O(n), for scanning the list of size n. Space Complexity: O(1), for creating a temporary variable. Singly Linked List Insertion Insertion into a singly-linked list has three cases:
Transcript of Traversing the Linked List - dsauet.weebly.com · While traversing the circular linked lists we...
• Traversingthelist• Insertinganiteminthelist• Deletinganitemfromthelist
TraversingtheLinkedList
Let us assume that thehead points to the first node of the list. To traverse the listwe do thefollowing
• Followthepointers.• Displaythecontentsofthenodes(orcount)astheyaretraversed.• StopwhenthenextpointerpointstoNULL.
TheListLength()functiontakesalinkedlistasinputandcountsthenumberofnodesinthelist.Thefunctiongivenbelowcanbeusedforprintingthelistdatawithextraprintfunction.
TimeComplexity:O(n),forscanningthelistofsizen.SpaceComplexity:O(1),forcreatingatemporaryvariable.
SinglyLinkedListInsertion
Insertionintoasingly-linkedlisthasthreecases:
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• Insertinganewnodebeforethehead(atthebeginning)• Insertinganewnodeafterthetail(attheendofthelist)• Insertinganewnodeatthemiddleofthelist(randomlocation)
Note:To insertanelement in the linked listat somepositionp, assume thatafter inserting theelementthepositionofthisnewnodeisp.
InsertingaNodeinSinglyLinkedListattheBeginning
Inthiscase,anewnodeisinsertedbeforethecurrentheadnode.Onlyonenextpointerneedstobemodified(newnode’snextpointer)anditcanbedoneintwosteps:
• Updatethenextpointerofnewnode,topointtothecurrenthead.
• Updateheadpointertopointtothenewnode.
InsertingaNodeinSinglyLinkedListattheEnding
In thiscase,weneed tomodify twonextpointers (lastnodesnextpointerandnewnodesnextpointer).
• NewnodesnextpointerpointstoNULL.
• Lastnodesnextpointerpointstothenewnode.
InsertingaNodeinSinglyLinkedListattheMiddle
Letusassumethatwearegivenapositionwherewewant to insert thenewnode. In thiscasealso,weneedtomodifytwonextpointers.
• Ifwewanttoaddanelementatposition3thenwestopatposition2.Thatmeanswetraverse 2 nodes and insert the new node. For simplicity let us assume that thesecondnodeiscalledpositionnode.Thenewnodepoints to thenextnodeof thepositionwherewewanttoaddthisnode.
• Positionnode’snextpointernowpointstothenewnode.
Letuswritethecodeforallthreecases.Wemustupdatethefirstelementpointerinthecallingfunction,not just in thecalled function.For this reasonweneed to sendadoublepointer.Thefollowingcodeinsertsanodeinthesinglylinkedlist.
Note:Wecanimplementthethreevariationsoftheinsertoperationseparately.
TimeComplexity:O(n),since,intheworstcase,wemayneedtoinsertthenodeattheendofthelist.SpaceComplexity:O(1),forcreatingonetemporaryvariable.
SinglyLinkedListDeletion
Similartoinsertion,herewealsohavethreecases.
• Deletingthefirstnode• Deletingthelastnode• Deletinganintermediatenode.
DeletingtheFirstNodeinSinglyLinkedList
Firstnode(currentheadnode)isremovedfromthelist.Itcanbedoneintwosteps:
• Createatemporarynodewhichwillpointtothesamenodeasthatofhead.
• Now,move theheadnodespointer to thenext node anddisposeof the temporarynode.
DeletingtheLastNodeinSinglyLinkedList
Inthiscase,thelastnodeisremovedfromthelist.Thisoperationisabittrickierthanremovingthefirstnode,becausethealgorithmshouldfindanode,whichisprevioustothetail.Itcanbedoneinthreesteps:
• Traversethelistandwhiletraversingmaintainthepreviousnodeaddressalso.Bythetimewereachtheendofthelist,wewillhavetwopointers,onepointingtothetailnodeandtheotherpointingtothenodebeforethetailnode.
• Updatepreviousnode’snextpointerwithNULL.
• Disposeofthetailnode.
DeletinganIntermediateNodeinSinglyLinkedList
Inthiscase,thenodetoberemovedisalwayslocatedbetween twonodes.Headandtail linksarenotupdatedinthiscase.Sucharemovalcanbedoneintwosteps:
• Similar to theprevious case,maintain thepreviousnodewhile traversing the list.Oncewefindthenodetobedeleted,changethepreviousnode’snextpointertothenextpointerofthenodetobedeleted.
• Disposeofthecurrentnodetobedeleted.
TimeComplexity:O(n).Intheworstcase,wemayneedtodeletethenodeattheendofthelist.SpaceComplexity:O(1),foronetemporaryvariable.
DeletingSinglyLinkedList
Thisworksbystoringthecurrentnodeinsometemporaryvariableandfreeingthecurrentnode.After freeing the current node, go to the next node with a temporary variable and repeat thisprocessforallnodes.
TimeComplexity:O(n),forscanningthecompletelistofsizen.SpaceComplexity:O(1),forcreatingonetemporaryvariable.
3.7DoublyLinkedLists
Theadvantageofadoublylinkedlist(alsocalledtwo–waylinkedlist)isthatgivenanodeinthe list,we can navigate in both directions.A node in a singly linked list cannot be removedunlesswehavethepointertoitspredecessor.Butinadoublylinkedlist,wecandeleteanodeevenifwedon’thavethepreviousnode’saddress(sinceeachnodehasaleftpointerpointingtothepreviousnodeandcanmovebackward).
Theprimarydisadvantagesofdoublylinkedlistsare:
• Eachnoderequiresanextrapointer,requiringmorespace.• Theinsertionordeletionofanodetakesabitlonger(morepointeroperations).
Similar to a singly linked list, let us implement the operations of a doubly linked list. If youunderstand the singly linked list operations, then doubly linked list operations are obvious.Followingisatypedeclarationforadoublylinkedlistofintegers:
DoublyLinkedListInsertion
Insertionintoadoubly-linkedlisthasthreecases(sameassinglylinkedlist):
• Insertinganewnodebeforethehead.• Insertinganewnodeafterthetail(attheendofthelist).• Insertinganewnodeatthemiddleofthelist.
InsertingaNodeinDoublyLinkedListattheBeginning
In thiscase,newnode is insertedbefore theheadnode.Previousandnextpointersneed tobemodifiedanditcanbedoneintwosteps:
• Update the rightpointerof thenewnode topoint to thecurrentheadnode (dottedlinkinbelowfigure)andalsomakeleftpointerofnewnodeasNULL.
• Update head node’s left pointer to point to the new node andmake new node ashead.Head
InsertingaNodeinDoublyLinkedListattheEnding
Inthiscase,traversethelisttilltheendandinsertthenewnode.
• NewnoderightpointerpointstoNULLandleftpointerpointstotheendofthelist.
• Updaterightpointeroflastnodetopointtonewnode.
InsertingaNodeinDoublyLinkedListattheMiddle
Asdiscussedinsinglylinkedlists,traversethelisttothepositionnodeandinsertthenewnode.
• Newnoderightpointerpointstothenextnodeofthepositionnodewherewewanttoinsertthenewnode.Also,newnodeleftpointerpointstothepositionnode.
• Positionnoderightpointerpointstothenewnodeandthenextnodeofpositionnodeleftpointerpointstonewnode.
Now,letuswritethecodeforallofthesethreecases.Wemustupdatethefirstelementpointerinthe calling function, not just in the called function. For this reasonwe need to send a doublepointer.Thefollowingcodeinsertsanodeinthedoublylinkedlist
TimeComplexity:O(n).Intheworstcase,wemayneedtoinsertthenodeattheendofthelist.SpaceComplexity:O(1),forcreatingonetemporaryvariable.
DoublyLinkedListDeletion
Similartosinglylinkedlistdeletion,herewehavethreecases:
• Deletingthefirstnode• Deletingthelastnode• Deletinganintermediatenode
DeletingtheFirstNodeinDoublyLinkedList
In this case, the firstnode (currentheadnode) is removed from the list. It canbedone in twosteps:
• Createatemporarynodewhichwillpointtothesamenodeasthatofhead.
• Now,movetheheadnodespointertothenextnodeandchangetheheadsleftpointertoNULL.Then,disposeofthetemporarynode.
DeletingtheLastNodeinDoublyLinkedList
Thisoperationisabittrickierthanremovingthefirstnode,becausethealgorithmshouldfindanode,whichisprevioustothetailfirst.Thiscanbedoneinthreesteps:
• Traversethelistandwhiletraversingmaintainthepreviousnodeaddressalso.Bythetimewereachtheendofthelist,wewillhavetwopointers,onepointingtothetailandtheotherpointingtothenodebeforethetail.
• UpdatethenextpointerofpreviousnodetothetailnodewithNULL.
• Disposethetailnode.
DeletinganIntermediateNodeinDoublyLinkedList
Inthiscase,thenodetoberemovedisalwayslocatedbetweentwonodes,andtheheadandtaillinksarenotupdated.Theremovalcanbedoneintwosteps:
• Similar to thepreviouscase,maintain thepreviousnodewhilealso traversing thelist.Uponlocatingthenodetobedeleted,changethepreviousnode’snextpointertothenextnodeofthenodetobedeleted.
• Disposeofthecurrentnodetobedeleted.
TimeComplexity:O(n),forscanningthecompletelistofsizen.SpaceComplexity:O(1),forcreatingonetemporaryvariable.
3.8CircularLinkedLists
Insinglylinkedlistsanddoublylinkedlists,theendoflistsareindicatedwithNULLvalue.Butcircular linked lists do not have ends.While traversing the circular linked listswe should becareful;otherwisewewillbetraversingthelistinfinitely.Incircularlinkedlists,eachnodehasasuccessor.Notethatunlikesinglylinkedlists,thereisnonodewithNULLpointerinacircularlylinkedlist.Insomesituations,circularlinkedlistsareuseful.
Forexample,whenseveralprocessesareusingthesamecomputerresource(CPU)forthesameamount of time, we have to assure that no process accesses the resource before all otherprocessesdo(roundrobinalgorithm).Thefollowing isa typedeclarationforacircular linkedlistofintegers:
In a circular linked list,we access the elementsusing thehead node (similar tohead node insinglylinkedlistanddoublylinkedlists).
CountingNodesinaCircularLinkedList
Thecircularlistisaccessiblethroughthenodemarkedhead.Tocountthenodes,thelisthastobetraversed from the node marked head, with the help of a dummy node current, and stop thecountingwhencurrentreachesthestartingnodehead.
Ifthelistisempty,headwillbeNULL,andinthatcasesetcount=0.Otherwise,setthecurrentpointertothefirstnode,andkeeponcountingtillthecurrentpointerreachesthestartingnode.
TimeComplexity:O(n),forscanningthecompletelistofsizen.SpaceComplexity:O(1),forcreatingonetemporaryvariable.
PrintingtheContentsofaCircularLinkedList
Weassumeherethatthelistisbeingaccessedbyitsheadnode.Sinceallthenodesarearrangedinacircularfashion,thetailnodeofthelistwillbethenodeprevioustotheheadnode.Letusassumewewanttoprintthecontentsofthenodesstartingwiththeheadnode.Printitscontents,movetothenextnodeandcontinueprintingtillwereachtheheadnodeagain.
TimeComplexity:O(n),forscanningthecompletelistofsizen.SpaceComplexity:O(1),fortemporaryvariable.
InsertingaNodeattheEndofaCircularLinkedList
Letusaddanodecontainingdata,at theendofa list (circular list)headedbyhead.Thenewnodewillbeplacedjustafterthetailnode(whichisthelastnodeofthelist),whichmeansitwillhavetobeinsertedinbetweenthetailnodeandthefirstnode.
• Createanewnodeandinitiallykeepitsnextpointerpointingtoitself.
• Updatethenextpointerofthenewnodewiththeheadnodeandalsotraversethelisttothetail.Thatmeansinacircularlistweshouldstopatthenodewhosenextnodeishead.
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