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Chap 3 Linked Lists Vocabulary Linear List Linked List Retrieval Traversal Node Circularly Linked Lists Doubly Linked Lists Multilinked Lists 线性表 链表 检索 遍历 结点 循环链表 双向链表 多重链表 3.1 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 Unordered Ordered Restricted 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. list 10 data 25 10 20 30 Inserted Data Insertion 20 25 30 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. list blue Delete element identified search green Deletion red blue green red yellow yellow Retrieval: List retrieval requires that data be located in a list and presented to the calling module without changing the contents of the list. Retrieved element identified by search list cat dog Retrieval cat dog zebra goldfish goldfish dog zebra 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 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. pHead data link data link data link A linked list with a head pointer: pHead pHead An empty linked list Nodes: The elements in a linked list are called nodes. 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: metadata dataType key field1 <…> field2 <…> … fieldN <…> End dataType List count head Head structure link Data node structure Node count <integer> data <datatype> head <pointer> link <pointer> End List data <keyType> End Node 3.3 Linked List Algorithms Create List: it receives the head structure and initializes the metadata for the list. The pseudocode algorithms: Algorithm createList(ref list <metadata>) Initializes metadata for a linked list. list ? ? count head (a) before create list.head = null list.count = 0 list 0 count head (b) after create Pre list is metadata structure passed by reference Post metadata initialized 1 list.head = null 2 list.count = 0 3 return End createList 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 list insert at beginning insert in middle insert at end Insert into empty list: 0 head count (a) before add pNew->link = list.head List.head = pNew 75 pNew Set link to null pointer Point list to first node 75 1 head count (b) after add pNew Insert at beginning: Before add 1 count 75 head pNew 39 pNew->link = list.head List.head = pNew After add 1 count 75 head pNew 39 Logically,inserting into an empty list is the same as inserting at the beginning of a list. Insert in middle: Before add 2 count 39 75 head pPre pNew 52 pNew->link = pPre->link pPre->link = pNew After add 3 count 39 75 head pPre pNew 52 Insert at end: Before add 39 3 count 52 75 head pPre 134 pNew pNew->link = pPre->link pPre->link = pNew After add 3 count 39 52 pPre pNew 75 head 134 Insert node algorithm: Algorithm insertNode (ref list val pPre val dataIn 1 allocate(pNew) 2 if (memory overflow) 1 return false 3 end if 4 pNew->data=dataIn 5 if (pPre null) < metadata >, <node pointer>, <dataType>) 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 1 pNew-.link =list.head 2 list.head = new Post 1 pNew->link = pPre->link data have been inserted in sequence 2 pPre->link = pNew Return 7 end if 8 list.count = list.count+1 true if successful , false is memory overflow 9 Return ture 6 else end insertNode 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: Before delete 3 count 39 75 134 head pLoc pPre list.head = pLoc->link recycle(pLoc) After delete 2 count (Recyled) head pLoc pPre 75 134 General delete case: Before delete 3 count 39 75 pPre pLoc 134 head pPre->link = pLoc->link recycle(pLoc) After delete 3 count 39 (Recycled) head pPre pLoc 134 Delete node algorithm: Algorithm insertNode (ref list val pPre <node pointer>, val pLoc <node pointer>, ref dataOut 1 Dataout = pLoc->data 2 if (pPre null) 1 list.head = pLoc->link 3 < metadata >, else 1 pPre->link = pLoc->link <dataType>) 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 4 end if 5 list.count = list.count - 1 6 recycle(pLoc) dataIn is variable to received deleted data 7 Return Post end deleteNode data have been deleted and returned to caller Search list: it is used by several algorithms to Searches list and passes back address of node containing target andor its logical locate data in a list. When we insert or delete predecessor. retrieve data from a list, wePre need to search the list and find the data. List is metadata structure to a valid Algorithm searchList (val list <metadata> ref pPre <node pointer> ref pLoc <node pointer> ref target <key type> list 6 else pPre is pointer to predecessor node 1 pointer if (target variable equal pLoc->data.key) pLoc is for current node 1 found = true target2iselse the being sought 3 Post 1 found = false pLoc point to first node with equal pLoc = list.head end if /greater 3key Loop (pLoc not null AND target > pLoc->data.key) -or7 null end if if targer > key of last node pPre to largest node smaller 1 pPre =pLoc 8 points return found than key 2 pLoc = pLoc->link -or-end nullsearchList if targer < key of first node 4 end loop 5 If (pLoc null) 1 2 pPre = null 1 found = false 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. algorithm retrieveNode (val list val key < metadata >, <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 Empty list: Algorithm emtpyList (val list <metadata>) 1 return (list.count equal to zero) End emptyList Full list: 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 List count: 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 Count N 5 10 pos • 15 head 20 moredata = getNext (list, o, dataout) Loop (moredata true) process(dataout) moredata = getNext (list, o, dataout) End loop … 95 100 Algorithm getNext ( ref list <metatype>, val fromWhere <Boolean>, ref dataOut 1 <datatype> ) 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 deleted Return 3.4 Processing A Linked list LinkedList createList destroyList (+) getData addNode (+) removeNode printList searchList getNext menu searchList insertNode deleteNode Algorithm buildLinkedList 1 Print (welcome to exploring linked lists.) 2 CrateList (list) 3 Loop (option not to quit) 1 option = menu () This program builds a linked list that can be modified or printed by the user. 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 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) Display a menu and read user option. Pre Nothing Return Valid choice 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 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. NotAdd added.) data to a linked list 3 Else Pre 1 success = insertNode (list, pPre, dataIn)List is metadata structure to a valid list 2 if (success false) dataIn are data to be inserted into list 1 print (Error: Out of memory. Program quitting.) 2 abort algorithm 3 end if 4 Return End addNode Post Data have been inserted into list in key sequence Algorithm removeNode (ref list val key <metadata>, <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 1 <metadata> ) If (emptyList (list)) 1 print (No data in list.) 2 Else 1 print (**** Begin Data Print ****) 2 count = 0 This algorithm traverses a linked list and prints the key in each node. Pre List is metadata structure to a valid list 3 moreData = getNext (list, 0, dataPtr)Post 4 loop (moreData true) All key have been printed 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 3.5 List Applications Append Lists: list1 5 count pos head 5 10 15 20 25 7 12 17 22 27 list2 5 count pos head Before Append list1 5 count pos head 5 10 15 20 25 7 12 17 22 27 list2 5 count pos head 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 val file <metadata>, <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 val numLists 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 <metadata>, <integer>) 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 3.6 Complex Linked List Structures Circularly Linked Lists:In this structure, the last node’s link points to the first node of the list. N count pos rear link 5 10 95 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. List B count head rear 5 B F 10 B: Backward pointer Doubly F B 95 F: Forward pointer Linked List Insertion: –Follow the basic patter. –Need to connect both the forward and backward pointers. F 0 pNew 1 20 20 After Insert into null list or before first node Before 3 2 pPre 40 20 pNew 20 30 40 30 After Before Insert between two nodes Algorithm insertDbl (ref list 1 <metadata>, 6 if (pPre->fore null) val dataIn <dataType>) 1 list.rear = pNew If (full list) 7 else 1 return 0 1 pSucc->back = pNew 2 End if 8 end if 3 Found = searchList (list, Pre, pSucc, dataIn.key) 9 pFore->fore = pNew 4 If (not found) 10 list.count = list.count + 1 1 allocate (pNew) 11 return (1) 2 pNew->data = dataIn 5 End if 3 if (pPre is null) 6 Return (2) 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 End insertDbl Doubly Linked List deletion: pPred pDlt pSucc 3 25 75 50 Before delete 3 25 75 50 (Recycled) After deleting 50 Algorithm deleteDbl ( ref list val pDlt 1 <metadata>, <node pointer>) 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. President link 3 Pres rear Spouse link Sp rear Washington 1789 Cutis Admas,J 1779 Smith Jefferson 1801 Skelton Multilinked List Insert: Build Multilinked insert getData Build Node Insert Pres Insert Spouse Search Pres Search Spouse Multilinked List Delete: – The major variation for multilinked list delete: need to reconnect 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 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 deleted 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.