1. 1 Linked Lists Gordon College Prof. Brinton

2. 2 Linked List Basics Why use? 1.Efficient insertion or deletion into middle of list. (Arrays are not efficient at doing this.) 2.Dynamic creation Any drawbacks? Yes, linked lists take up extra space - remember the pointers.

3. 3 The Linked List Node Contains 2 items: –Payload for linked list entries –Pointer(s) to surrounding links class Node { public: Node(int p) {next=NULL; item=p; }; int item; Node* next; }; Note: the node class can either be private within the Linked list class or it can stand on its own.

4. 4 Linked List Class class LinkedList { public: LinkedList() { first=NULL; mySize=0; }; const int size() {return mySize; }; void insert(int p, int pos ); void display(ostream & out); void erase(int value); private: class Node { public: Node(int p) {next=NULL; item=p; }; int item; Node* next; }; int mySize; Node * first; };

5. 5 Inserting a new node Steps: 1.Find location within list 2.Create new node with payload and pointer to current node’s next 3.Assign address of new node to current node’s next Note: order is essential

6. 6 Inserting a new node Exception cases: begin and end of list Begin Case: 1.Create new node 2.Assign address found in first to current node’s next 3.Place address of new node in first End case: 1.Create new node 2.Put NULL in new node’s next 3.Assign address of new node to next of last node

7. 7 Deleting a node Steps 1.Find the node to delete (keep finger on previous node) 2.Assign next address in previous node to next address of node to delete 3.Delete current node

8. 8 Deleting a node Exception cases: begin and end of list Begin: 1.Assign address of current next to first 2.Delete current node End: 1.Place NULL in previous node’s next 2.Delete current node

9. 9 Order of Magnitude How many operations does it take? 1.Inserting at front of list - O(1) 2.Deleting at front of list - O(1) 3.Inserting at the back of list - O(n) 4.Deleting at the back of list - O(n) What happens if we add a pointer called Back that points to the last node? Inserting at the back of the list is now O(1) How about deleting at the back?

10. 10 Order of Magnitude The list is still a Singly Linked List. In order to delete at the end of a list, we still must have a pointer to the predecessor to back. Therefore O(n): 1.Walk to the end of the list (keep finger on previous node) 2.Assign next address in previous node to NULL 3.Delete current node

11. 11 Singly LL with back pointer Problems: –Insert on an empty list - must update both pointers –Erase on one node - must update both pointers

12. 12 Doubly Linked Lists New Node structure: class Node { public: Node(int p) { next=NULL; prev=NULL; item=p; }; int item; Node* prev; Node* next; };

13. 13 Doubly Linked Lists Inserting a node at a position 1.Find place to insert: current node 2.Set new node’s prev pointer to current node’s prev pointer 3.Set new node’s next pointer to current node 4.Set previous node’s next to new pointer 5.Set current node’s previous to new node

14. 14 Doubly Linked Lists Removing a node at a position 1.Find node to remove: current node 2.Set previous node’s next to current’s next 3.Set next node’s (successor) prev to current node’s prev 4.Delete current

15. 15 Doubly Linked Lists Exceptions: first and last node. Order of Magnitude: O(1) insert and remove at either end. Note: also search time can be quicker if you know which end to begin searching.

16. 16 What’s a Head Node? Consider simple linked lists –First node is different from others –Only node that is directly accessible –Has no predecessor Thus insertions and deletions must consider two cases –First node or not first node –The algorithm is different for each

17. 17 Linked Lists with Head Nodes Dual algorithms can be reduced to one –Create a "dummy" head node –Serves as predecessor holding actual first element Thus even an empty list has a head node

18. 18 Linked Lists with Head Nodes For insertion at beginning of list –Head node is predecessor for new node newptr->next = predptr->next; predptr->next = newptr;

19. 19 Linked Lists with Head Nodes For deleting first element from a list with a head node –Head node is the predecessor predptr->next = ptr->next; delete ptr;

20. 20 Circular Linked Lists Set the link in last node to point to first node –Each node now has both predecessor and successor –Insertions, deletions now easier Special consideration required for insertion to empty list, deletion from single item list

21. 21 Circular Linked Lists Traversal algorithm must be adjusted: if (first != NULL) // list not empty { ptr = first; do { // process ptr->data ptr = ptr->next; } while (ptr != first); } How must this be different?

22. 22 Circular Linked Lists Traversal if (first!=NULL) { ptr = first; //process ptr->data ptr = ptr->next; while (ptr != first) { //process ptr->data ptr = ptr->next; } if (first!=NULL) { ptr = first; do { //process ptr->data ptr = ptr->next; } while (ptr != first); }

23. 23 Circular Linked Lists Traversal with Head Node ptr = first->next; while (ptr != first) { //process ptr->data ptr = ptr->next; }

24. 24 Polynomial Representation x 2 - 4x + 7 Consider a polynomial of degree n –Can be represented by an array For a sparse polynomial this is not efficient 5

25. 25 Polynomial Representation x 2 - 4x + 7 We could represent a polynomial by a list of ordered pairs –{ (coef, exponent) … } Fixed capacity of array still problematic –Wasted space for sparse polynomial

26. 26 Linked Implementation of Sparse Polynomials Linked list of these ordered pairs provides an appropriate solution –Each node has form shown Now whether sparse or well populated, the polynomial is represented efficiently ( with head nodes )

27. 27 Linked Implementation of Sparse Polynomials How would this class look?

28. 28 Linked Implementation of Sparse Polynomials class Polynomial { public: Polynomial() { first=NULL; mySize=0; }; const int size() {return mySize; }; void insert(int p, int pos ); void display(ostream & out); void erase(int value); private: class Term { public: int coef; unsigned expo; }; class Node { public: Node(int co, int ex) {next=NULL; data.coef=co; data.expo = ex; }; Term Data; Node* next; }; … };

29. 29 Addition Operator Requires temporary pointers for each polynomial (the addends and the resulting sum)

30. 30 Addition Operator As traversal takes place –Compare exponents –If different, node with smaller exponent and its coefficient attached to result polynomial –If exponents same, coefficients added, new corresponding node attached to result polynomial

31. 31 Doubly-Linked Lists Bidirectional lists –Nodes have data part, forward and backward link Facilitates both forward and backward traversal –Requires pointers to both first and last nodes

32. 32 Doubly-Linked Lists To insert a new node –Set forward and backward links to point to predecessor and successor

33. 33 Doubly-Linked Lists To insert a new node –Set forward and backward links to point to predecessor and successor –Then reset forward link of predecessor, backward link of successor

34. 34 Doubly-Linked Lists To delete a node –Reset forward link of predecessor, backward link of successor –Then delete removed node

35. 35 The STL list Class Template A sequential container –Optimized for insertion and erasure at arbitrary points in the sequence. –Implemented as a circular doubly-linked list with head node.

36. 36 Comparing List With Other Containers Note : list does not support direct access –does not have the subscript operator [ ]. PropertyArray vector deque list Direct/random access ( [] )  (exclnt)  (good)X Sequential access  Insert/delete at front  (poor)  Insert/delete in middle  Insert/delete at end  Overheadlowestlowlow/mediumhigh

37. 37 list Iterators list 's iterator is "weaker" than that for vector.  vector : random access iterators  list : bidirectional iterators Operations in common  ++Move iterator to next element (like ptr = ptr-> next )  --Move iterator to preceding element (like ptr = ptr-> prev )  *dereferencing operator (like ptr-> data )

38. 38 list Iterators Operators in common  =assignment (for same type iterators) it1 = it2 makes it1 positioned at same element as it2  == and != (for same type iterators) checks whether iterators are positioned at the same element

39. 39 Example: Internet Addresses Consider a program that stores IP addresses of users who make a connection with a certain computer –We store the connections in an AddressCounter object –Tracks unique IP addresses and how many times that IP connected

40. 40 The STL list Class Template Node structure struct list_node { pointer next, prev; T data; }

41. 41 The STL list Class Template But it's allocation/deallocation scheme is complex –Does not simply use new and delete operations. Using the heap manager is inefficient for large numbers of allocation/deallocations –Thus it does it's own memory management.

42. 42 The STL list Memory Management When a node is allocated 1.If there is a node on the free list, allocate it. This is maintained as a linked stack 2.If the free list is empty: a)Call the heap manager to allocate a block of memory (a "buffer", typically 4K) b)Carve it up into pieces of size required for a node of a list.

43. 43 The STL list Memory Management When a node is deallocated –Push it onto the free list. When all lists of this type T have been destroyed –Return it to the heap

44. 44 Case Study: Large-Integer Arithmetic Recall that numeric representation of numbers in computer memory places limits on their size –32 bit integers, two's complement max 2147483647 We will design a BigInt class –Process integers of any size –For simplicity, nonnegative integers only

45. 45 BigInt Design First step : select a storage structure –We choose a linked list –Each node sores a block of up to 3 consecutive digits –Doubly linked list for traversing in both directions

46. 46 BigInt Design Input in blocks of 3 integers, separated by spaces –As each new block entered, node added at end Output is traversal, left to right

47. 47 BigInt Design Addition adds the groupings right to left –Keeping track of carry digits

48. 48 Multiply-Ordered Lists Ordered linked list –Nodes arranged so data items are in ascending/descending order Straightforward when based on one data field –However, sometimes necessary to maintain links with a different ordering Possible solution –Separate ordered linked lists – but wastes space

49. 49 Multiply-Ordered Lists Better approach –Single list –Multiple links

50. 50 Sparse Matrices Usual storage is 2D array or 2D vector If only a few nonzero entries –Can waste space Stored more efficiently with linked structure –Similar to sparse polynomials –Each row is a linked list –Store only nonzero entries for the row

51. 51 For we represent with Sparse Matrices A =

52. 52 Sparse Matrices This still may waste space –Consider if many rows were all zeros Alternative implementation –Single linked list –Each node has row, column, entry, link Resulting list

53. 53 Sparse Matrices However … this loses direct access to rows Could replace array of pointers with –Linked list of row head nodes –Each contains pointer to non empty row list

54. 54 Sparse Matrices If columnwise processing is desired –Use orthogonal list –Each node stores row, column, value, pointer to row successor, pointer to column successor

55. 55 Sparse Matrices Note the resulting representation of the matrix A =

56. 56 Generalized Lists Examples so far have had atomic elements –The nodes are not themselves lists Consider a linked list of strings –The strings themselves can be linked lists of characters This is an example of a generalized list

57. 57 Generalized Lists Commonly represented as linked lists where –Nodes have a tag field along with data and link Tag used to indicate whether data field holds –Atom –Pointer to a list

58. 58 Generalized Lists Lists can be shared –To represent (2, (4,6), (4,6)) For polynomials in two variables P(x,y) = 3 + 7x + 14y 2 + 25y 7 – 7x 2 y 7 + 18x 6 y 7