Data Abstractions

1. Data Abstractions Shyh-Kang Jeng Department of Electrical Engineering/ Graduate Institute of Communication Engineering National Taiwan University

2. Data Structures • Conceptual organization of data • Basic data structures • Homogeneous array • List • Stack • Queue • Tree

3. List • A collection of entries that appear in a sequential order • Examples • Class enrollment lists • “things-to-do” lists • Dictionaries • Sentences • Appear in both static and dynamic forms

4. Stacks • A list in which all insertions and deletions are performed at the same end • A last-in, first-out (LIFO) structures • Push and pop Top B A C

5. Queue • A list in which all insertions are performed at one end while all deletions are made at the other • A first-in, first-out (FIFO) structure • Head (front) and tail (rear)

6. Organization Chart

7. File Structure of Windows

8. Trees

9. Trees • Nodes • Root • Terminal (leaf) • Parent, children, siblings • Subtrees • Depth

10. Data Abstraction • Explores ways in which users can be shielded from the details of actual data storage (memory cells and address) and be allowed to access information as though it were stored in a more convenient form – Concept of abstraction • The term user can be either human or a software module

11. Static vs. Dynamic Structures • Static structures • Shape and size of the structure do not change over time • Easier to manage • Dynamic structures • Either shape or size of the structure changes over time • Must deal with adding and deleting data entries as well as finding the memory space required by a growing data structure

12. Pointers • A memory cell (or perhaps a block of memory cells) that contains the address of another memory cell • Examples • Program counter as an instruction pointer • URL • Many programming languages include pointers as a primitive data type • Allow the declaration, allocation, and manipulation of pointers • Used to create dynamic data structures

13. Use of Pointers

14. Stack and Heap Space Heap Storage Stack Storage

15. Homogeneous Arrays

16. Two-Dimensional Array

17. Storage of a 2-D Array • Row major order vs. column major order • Finding an entry in the th row and th column of a -column 2-D array stored in row major order Address polynomial

18. Mini Review • Show how the array below would be arranged in main memory when stored in row major order

19. Answer • 5 3 7 4 2 8 1 9 6

20. Mini Review • Give a formula for finding the entry in the th row and th column of a 2-D array stored in column major order • In C, C++, and Java, indices of arrays start at 0 rather than 1. In this case what address polynomial is used by the translator to convert references of the form Array[i][j] into memory address?

21. Answers

22. Storing lists • Contiguous list = list stored in a homogeneous array • Linked list = list in which each node points to the next one • Head pointer = pointer to first entry in list • NIL pointer = non-pointer value used to indicate end of list

23. Contiguous Lists

24. Contiguous List • Convenient storage structure when implementing static lists • Inconvenient in dynamic cases • Delete a name • Move entries to keep the list in the same order • Add a name • Move the entire list to obtain an available block of contiguous cells large enough for the expanded list

25. Linked List

26. Deleting an Entry

27. Inserting an Entry

28. A Stack in Memory

29. Operations on Queues

30. Circular Queues (1)

31. Circular Queues (2)

32. Mini Review • Using paper and pencil, keep a record of the circular queue during the following scenario. Assume that the block reserved for the queue can contain only four entries. • Insert entries A, B, C • Remove two entries • Insert entries D, E • Remove an entry • Insert entry F • Remove an entry

33. H T H T B C A B C H T T H H T H T C C D E C D E D T H H T E F D E F Answer

34. Storing a binary tree • Linked structure • Each node = data cell + two child pointers • Accessed through a pointer to root node • Mapped to a contiguous array • A[1] = root node • A[2],A[3] = children of A[1] • A[4],A[5],A[6],A[7] = children of A[2] and A[3] • …

35. Binary Tree Node

36. Linked Storage System

37. Storage without Pointers

38. Inefficient Storage

39. Mini Review • Draw a diagram representing how the tree below appears in memory when stored using the left and right child pointers. • Draw another diagram showing how the tree would appear in contiguous storage. y z x w

40. Y X Z W Answer Y Z NIL NIL X NIL W NIL NIL

41. Manipulating data structures • Ideally, a data structure should be manipulated solely by pre-defined procedures. • Example: A stack typically needs at least push and pop procedures. • The data structure along with these procedures constitutes a complete abstract tool.

42. Printing a Linked List

43. Binary Tree Package • Search for the presence of an entry • Use the binary search algorithm • Print the list in order • Insert a new entry

44. Ordered Tree

45. Search the Binary Tree

46. Search Binary Tree

47. Printing a Binary Tree

48. Mini Review • Draw a binary tree to store the list R, S, T, U, V, W, X, Y, and Z for future searching

49. Answer V Y T X Z U S W R

50. Printing a Tree in Order