Welcome to CIS 068 !

1. Welcome to CIS 068 ! Lesson 10: Data Structures CIS 068

2. Overview • Description, Usage and Java-Implementation of • Collections • Lists • Sets • Hashing CIS 068

3. Definition • Data Structures • Definition (www.nist.gov): • “An organization of information, usually in memory, for better algorithmefficiency, such as queue, stack, linked list, heap, dictionary, and tree, or conceptual unity, such as the name and address of a person.” CIS 068

4. Efficiency • “An organization of information …for better algorithmefficiency...”: • Isn’t the efficiency of an algorithm defined by the order of magnitude O( )? CIS 068

5. Efficiency • Yes, but it is dependent on its implementation. CIS 068

6. Introduction • Data structures define the structure of a collection of data types, i.e. primitive data types or objects • The structure provides different ways to access the data • Different tasks need different ways to access the data • Different tasks need different data structures CIS 068

7. Introduction • Typical properties of different structures: • fixed length / variable length • access by index / access by iteration • duplicate elements allowed / not allowed CIS 068

8. Examples • Tasks: • Read 300 integers • Read an unknown number of integers • Read 5th element of sorted collection • Read next element of sorted collection • Merge element at 5th position into collection • Check if object is in collection CIS 068

9. Examples • Although you can invent any datastructure you want, there are ‘classic structures‘, providing: • Coverage of most (classic) problems • Analysis of efficience • Basic implementation in modern languages, like JAVA CIS 068

10. Data Structures in JAVA • Let‘s see what JAVA has to offer: CIS 068

11. The Collection Hierarchy • Collection: top interface, specifying requirements for all collections CIS 068

12. Collection Interface CIS 068

13. Collection Interface ! CIS 068

14. Iterator Interface • Purpose: • Sequential access to collection elements • Note: the so far used technique of sequentially accessing elements by sequentially indexing is not reasonable in general (why ?) ! • Methods: CIS 068

15. Iterator Interface • Iterator points ‘between‘ the elements of collection: 1 2 3 4 5 first position, hasNext() = true, remove() throws error Returned element Current position (after 2 calls to next() ), remove() deletes element 2 Position after next() hasNext() = false CIS 068

16. Iterator Interface Usage Typical usage of iterator: CIS 068

17. Back to Collections AbstractCollection CIS 068

18. AbstractCollection • Facilitates implementation of Collection interface • Providing a skeletal implementation • Implementation of a concrete class: • Provide data structure (e.g. array) • Provide access to data structure CIS 068

19. AbstractCollection • Concrete class must provide implementation of Iterator • To maintain ‘abstract character‘ of data in AbstractClass implemented (non abstract) methods use Iterator-methods to access data myCollection AbstractCollection implements Iterator; int[ ] data; Iterator iterator(){ return this; } hasNext(){ … } … add(){ Iterator i=iterator(); … } Clear(){ Iterator i=iterator(); … } CIS 068

20. Back to Collections List Interface CIS 068

21. List Interface • Extends the Collection Interface • Adds methods to insert and retrieve objects by their position (index) • Note: Collection Interface could NOT specify the position • A new Iterator, the ListIterator, is introduced • ListIterator extends Iterator, allowing for bidirectional traversal (previousIndex()...) CIS 068

22. List Interface Incorporates index ! A new Iterator Type (can move forward and backward) CIS 068

23. Example: Selection-Sorting a List Part 1: call to selection sort Actual implementation of List does not matter ! Call to SelectionSort Use only Iterator-properties of ListIterator (upcasting) CIS 068

24. Example: Selection-Sorting a List Part 2: Selection sort access at index ‘fill‘ Inner loop swap CIS 068

25. Back to Collections AbstractList: ...again the implementation of some methods... Note: Still ABSTRACT ! CIS 068

26. Concrete Lists ArrayList and Vector: at last concrete implementations ! CIS 068

27. ArrayList and Vector • Vector: • For compatibility reasons (only) • Use ArrayList • ArrayList: • Underlying DataStructure is Array • List-Properties add advantage over Array: • Size can grow and shrink • Elements can be inserted and removed in the middle CIS 068

28. An Alternative Implementation (1) CIS 068

29. An Alternative Implementation (2) CIS 068

30. An Alternative Implementation (3) CIS 068

31. Collections • The underlying array-datastructure has • advantages for index-based access • disadvantages for insertion / removal of middle elements (copy), insertion/removal with O(n) • Alternative: linked lists CIS 068

32. Linked List • Flexible structure, providing • Insertion and removal from any place in O(1), compared to O(n) for array-based list • Sequential access • Random access at O(n), compared to O(1) for array-based list CIS 068

33. Linked List • List of dynamically allocated nodes • Nodes arranged into a linked structure • Data Structure ‘node‘ must provide • Data itself (example: the bead-body) • A possible link to another node (ex.: the link) Children’s pop-beads as an example for a linked list CIS 068

34. Linked List New node Old node next next (null) CIS 068

35. Connecting Nodes creating the nodes connecting CIS 068

36. Inserting Nodes r • p.link = r • r.link = q • q can be accessed by p.link.link CIS 068

37. Removing Nodes p q CIS 068

38. Traversing a List (null) CIS 068

39. Double Linked Lists Single linked list Double linked list (null) (null) data data data (null) successor successor successor predecessor predecessor predecessor (null) CIS 068

40. Back to Collections AbstractSequentialList and LinkedList CIS 068

41. LinkedList An implementation example: See textbook CIS 068

42. Sets Example task: Examine, collection contains object o Solution using a List: -> O(n) operation ! CIS 068

43. Sets • Comparison to List: • Set is designed to overcome the limitation of O(n) • Contains unique elements • contains() / remove() operate in O(1) or O(log n) • No get() method, no index-access... • ...but iterator can (still) be used to traverse set CIS 068

44. Back to Collections Interface Set CIS 068

45. Hashing How can method ‘contain()‘ be implemented to be an O(1) operation ? http://ciips.ee.uwa.edu.au/~morris/Year2/PLDS210/hash_tables.html CIS 068

46. Hashing • How can method ‘contain()‘ be implemented to be an O(1) operation ? • Idea: • Retrieving an object of an array can be done in O(1) if the index is known • Determine the index to store and retrieve an object by the object itself ! CIS 068

47. Hashing • Determine the index ... by the object itself: • Example: • Store Strings “Apu“, “Bob“, “Daria“ as Set. • Define function H: String -> integer: • Take first character, A=1, B=2,... • Store names in String array at position H(name) CIS 068

48. Hashing Apu: first character: A H(A) = 1 Bob: first character: B H(B) = 2 Daria: first character: D H(D) = 4 ... CIS 068

49. Hashing • The Function H(o) is called the HashCode of the object o • Properties of a hashcode function: • If a.equals(b) then H(a) = H(b) • BUT NOT NECESSARILY VICE VERSA: • H(a) = H(b) does NOT guarantee a.equals(b) ! • If H() has ‘sufficient variation‘, then it is most likely, that different objects have different hashcodes CIS 068

50. Hashing • Additionally an array is needed, that has sufficient space to contain at least all elements. • The hashcode may not address an index outside the array, this can easily be achieved by: • H1(o) = H(o) % n • % = modulo-function, n = array length • The larger the array, the more variates H1() ! CIS 068