Chapter 8 Data Abstractions

2 Chapter 8: Data Abstractions 8.1 Data Structure Fundamentals 8.2 Implementing Data Structures 8.3 A Short Case Study 8.4 Customized Data Types 8.5 Classes and Objects 8.6 Pointers in Machine Language

3 Basic Data Structures Homogeneous array Heterogeneous array List Stack Queue Tree

4 Figure 8.1 Lists, stacks, and queues

5 Terminology for lists List = collection of data whose entries are arranged sequentially Head = beginning of the list Tail = end of the list

6 Terminology for stacks Stack = a list in which entries are removed and inserted only at the head LIFO = last-in-first-out Top = head of list Bottom or base = tail of list Pop = remove entry from the top Push = insert entry at the top

7 Terminology for queues Queue = a list in which entries are removed at the head and are inserted at the tail FIFO = first-in-first-out

8 Terminology for a tree Tree = a collection of data whose entries have a hierarchical organization Node = an entry in a tree Binary tree = tree in which every node has at most two children Depth = number of nodes in longest path from root to leaf

9 Terminology for a tree (continued) Root node = the node at the top Terminal or leaf node = a node at the bottom Parent of a node = the node immediately above the specified node Child of a node = a node immediately below the specified node Ancestor = parent, parent of parent, etc. Descendent = child, child of child, etc. Siblings = nodes sharing a common parent

10 Figure 8.1 An example of an organization chart

11 Figure 8.2 Tree terminology

12 Basic data structures Homogeneous array is an array of entries of the same type. List The unique feature of arrays is that their size and shape are constant. For the group with dynamic population (members join/leave), lists structure employs the concept of a pointer to accommodate such variations on membership.

13 Nature of data structures Static: size of data structure does not change Dynamic: size of data structure can change Pointer: Main memory location of an data item A is identified by its numeric address, which value can be saved in another memory location P. Such P is called a pointer to the data item A. The program counter is indeed the instruction pointer. URLs(Uniform resource Locator) used to link hypertext contents are also like the pointers.

14 Figure 8.3 Novels arranged by title but linked according to authorship

15 1.Give examples of each of the following structures in daily life: List Stack Queue Tree 2.Suppose a tree has four nodes A,B,C,and D. If A and C are siblings and D ’ s parent is A, which nodes are leaf Nodes? Which is root node?

16 Storing homogeneous arrays Requires enough contiguous memory to hold all data Int readings [24]; reading[4] <- 67; Two dimensional arrays Row-major order: each row is stored together Address polynomial: A[r,c] = (r-1)(# columns) + (c-1) Column-major order: each column is stored together

17 Figure 8.4 The array of temperature readings stored in memory starting at address x

18 Figure 8.5 A two-dimensional array with four rows and five columns stored in row major order

19 Figure 8.7 Storing the heterogeneous array Employee

20 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

21 Figure 8.6 Names stored in memory as a contiguous list

22 Figure 8.7 The structure of a linked list

23 Figure 8.8 Deleting an entry from a linked list

24 Figure 8.9 Inserting an entry into a linked list

25 Storing stacks and queues Can use same mechanisms as for lists Circular queue = homogeneous array where the first array entry is treated as immediately following the last array entry Prevents a queue from crawling out of its allotted storage space

26 Figure 8.10 A stack in memory

27 Figure 8.11 A queue implementation with head and tail pointers. Note how the queue crawls through memory as entries are inserted and removed.

28 Problems with Pointers Pointers in Queue may grow out of the region of the specified memory region In Java to advance pointer redirect Next to the next list entry In C Assign Next the value Next +1 What is the problem in C?

29 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] …

30 Figure 8.12 The structure of a node in a binary tree

31 Figure 8.13 The conceptual and actual organization of a binary tree using a linked storage system

32 Figure 8.14 A tree stored without pointers

33 Figure 8.15 A sparse, unbalanced tree shown in its conceptual form and as it would be stored without pointers

34 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.

35 Figure 8.16 A procedure for printing a linked list

36 What condition indicates a linked list is empty? What about Stack and Queue?

37 A Case Study Store the letters in a binary tree 1.The middle of the entry the root node 2.The middle of the remaining first half of the list the root ’ s left child 3. The middle of the remaining second half of the list the root ’ s right child A,B,C,D,E,F,G,H,I,J,K,L,M Then 3 operations to be performed Search for the presence of an entry Print the list in alphabetical order Insert a new entry

38 Figure 8.17 The letters A through M arranged in an ordered tree

39 Figure 8.18 The binary search as it would appear if the list were implemented as a linked binary tree

40 Figure 8.19 The successively smaller trees considered by the procedure in Figure 8.18 when searching for the letter J

41 Figure 8.20 Printing a search tree in alphabetical order

42 Figure 8.21 A procedure for printing the data in a binary tree

43 Figure 8.22 Inserting the entry M into the list B, E, G, H, J, K, N, P stored as a tree

44 Figure 8.23 A procedure for inserting a new entry in a list stored as a binary tree

45 Non-recursive way for serach procedure BinarySearch (Tree, TargetValue) CurrentPointer ¬  root pointer of Tree; *The node pointed to by CurrentPointer will be called the current node* Found ¬  false; while (Found is false and CurrentPointer is not NIL) do (Perform the activity associated with the appropriate case below:

46 Non-recursive way for serach case 1, TargetValue = current node: (Found ¬  true) case 2, TargetValue < current node: (CurrentPointer ¬  current node's left child pointer) case 3, TargetValue > current node: (CurrentPointer ¬  current node's right child pointer) ) if (Found = false) then (declare the search a failure) else (declare the search a success)

47 Customized data types User-defined data type = template for a heterogeneous structure define type EmployeeType to be { char Name[8]; Int Age ; real SkillRating; } EmployeeType DistManager; DistManager.name=John; DistManager.age=30;

48 Customized data types Abstract data type = user-defined data type with methods for access and manipulation define type StackType to be {int StackEntries[20]; int StackPointer = 0; Procedure push(value) {StackEnties[StackPointer]=value; Stackpointer++;} Procedure pop ….. } StackType Stackone; Stackone.push(25);

49 Customized data types What should be considered when building an abstract data type for a list. 1 insert, delete, find the entry 2. Ways of implementing a list — Contiguous or linked list 3. The choice of either way is invisible to users

50 Customized data types Class and Objects Class = abstract data type with extra features Characteristics can be inherited Contents can be encapsulated Constructor methods to initialize new objects

51 Figure 8.24 A stack of integers implemented in Java and C#

52 Pointers in machine language Immediate addressing: instruction contains the data to be accessed Direct addressing: instruction contains the address of the data to be accessed Indirect addressing: instruction contains the location of the address of the data to be accessed

53 Figure 8.25 Our first attempt at expanding the machine language in Appendix C to take advantage of pointers DRXY — load register R with contents of the memory cells whose address is found at address XY Need to change Stack pointer(load to register,-1,then load)

54 Figure 8.26 Loading a register from a memory cell that is located by means of a pointer stored in a register DR0S — load register R with the contents of the memory cells Pointed by register S

55 Figure 8.26 Loading a register from a memory cell that is located by means of a pointer stored in a register DR0S — load register R with the contents of the memory cells Pointed by register S Write a complete machine language routine to perform a Pop operation. Assume stack pointer is in register F And Top of the stack is to be pooped into register 5.

56 Push operation ER0S — store the contents of register R in the memory cells Pointed by register S DRXS:load register R with the data pointed by the value in register S plus the value X EX: If register F contained 0x04, then DE2F will Load register E with the content of the memory cell at address ?. The value of register F remains ? What advantage of this instruction has when used in linked list data structure? Each entry has two memory cells(data+pointer) DR0S can be used to retrieve the data DR1S can be used to retrieve the pointer