CSCE 110 PROGRAMMING FUNDAMENTALS. Prof. Amr Goneid AUC

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1 CSCE 110 PROGRAMMING FUNDAMENTALS WITH C++ Prof. Amr Goneid AUC Part 13. Abstract Data Types (ADT s) Prof. amr Goneid, AUC 1

2 Data Modeling and ADTs Prof. Amr Goneid, AUC 2

3 Data Modeling and ADTs Data Modeling Abstract Data types (ADTs) A Classification of Abstract Structures Another Classification Special Data Structures Examples on Modeling Example ADT s Prof. Amr Goneid, AUC 3

4 1. Data Modeling Real-world applications need to be reduced to a small number of existing problems (topdown design) Real-world data need to be described in an abstract way in terms of fundamental structures Prof. Amr Goneid, AUC 4

5 Data Modeling The collection of data in some organization is called a Data Structure The sequences of operations to be done on the data are called Algorithms Prof. Amr Goneid, AUC 5

) An Algorithm is a procedure to do a certain task An

6 Data Modeling The word Algorithm comes from the name of Abu Ja afar Mohamed ibn Musa Al Khowarizmi (c. 825 A.D.) An Algorithm is a procedure to do a certain task An Algorithm is supposed to solve a general, wellspecified problem Prof. Amr Goneid, AUC 6

7 Data Modeling A real-world application is basically Data Structures + Algorithms Prof. Amr Goneid, AUC 7

8 Data Modeling Data and the Operations on that data are parts of an object that cannot be separated. These two faces of an object are linked. Neither can be carried out independently of the other. Prof. Amr Goneid, AUC 8

9 The Data Cone Real-world Data ADTs Data Structures Fundamental Data Types Prof. Amr Goneid, AUC 9

10 2. Abstract Data Types (ADTs) The most important attribute of data is its type. Type implies certain operation. It also prohibits other operations. For example, + - * / are allowed for types int and double, but the modulus (%) is allowed for int and prohibited for double. When a certain data organization + its operations are not available in the language, we build it as a new data type. To be useful to many applications, we build it as an Abstract Data Type. Prof. Amr Goneid, AUC 10

11 Abstract Data Types (ADTs) An ADT represents the logical or conceptual level of the data. It consists of: 1. A collection of data items in some Data Structure 2. Operations (algorithms) on the data items For example, a Stack supports retrieval in LIFO (Last In First Out) order. Basic operations are push and pop. It can be implemented using arrays (static or dynamic) or linked lists Prof. Amr Goneid, AUC 11

12 Abstract Data Types (ADTs) ADT (Abstract Data Type) is a description of a new data type together with operations on the data. An ADT can be used in one or more applications. The definition of the data type is separated from its implementation (Data Abstraction). (e.g. ADT Table can be implemented using a static array, a dynamic array or a linked list. Prof. amr Goneid, AUC 12

13 Using ADT s ADT ADT ADT ADT ADT Program Program Program Standard Types/Libraries User Built ADT s Prof. amr Goneid, AUC 13

14 ADT Definition The first step in creating an ADT is the process of Data Abstraction Data Abstraction provides a complete description of the following items independent of the way it will be implemented: A definition of the ADT. Elements or members of that ADT. Relationship between the members. The fundamental operations on the members. Prof. Amr Goneid, AUC 14

15 ADT Implementation Usually, an ADT can be implemented in different ways. To the applications, such implementation should be completely hidden. The Implementation part will describe: how the ADT will be implemented using native Data Structures or other pre-defined ADT s in C++. how the relationships and fundamental operations on the members will be implemented as C++ functions. In Object Oriented Programming, ADTs are created as Classes Prof. Amr Goneid, AUC 15

16 3. A Classification of Abstract Structures According to the relationship between members Data Structures Set Linear Tree Graph Prof. amr Goneid, AUC 16

17 Abstract Structures Sets: No relationship. Only that elements are members of the same set. Linear: Sequential, one-to-one relationship e.g Arrays, Strings and Streams Trees: Non-Linear, hierarchical one-to-many. Graph: Non-Linear, many-to-many. Arrays, Structs, pointers and standard Classes are used to model different ADT s. Prof. amr Goneid, AUC 17

18 Sets Order of elements does not matter. Only that they are members of the same set ({1,3,4} is identical to {1,4,3}). Can be implemented using arrays or linked lists. Used in problems seeking: groups collection selection packaging Prof. Amr Goneid, AUC 18

19 Linear Structures Sequential, one-to-one relationship. Examples: Tables, Stacks, Queues, Strings and Permutations. Can be implemented using arrays and linked lists (structs and pointers). Used in problems dealing with: Searching, Sorting, stacking, waiting lines. Text processing, character sequences, patterns Arrangements, ordering, tours, sequences. Prof. Amr Goneid, AUC 19

20 Trees Non-Linear, hierarchical one-to-many. Examples: Binary Trees, Binary Search Trees (BST) Can be implemented using arrays, structs and pointers Used in problems dealing with: Searching Hierarchy Ancestor/descendant relationship Classification Prof. Amr Goneid, AUC 20

21 Graphs Non-Linear, many-to-many. Can be implemented using arrays or linked lists Used to model a variety of problems dealing with: Networks Circuits Web Relationship Paths Prof. Amr Goneid, AUC 21

22 4. Another Classification of Abstract Structures According to their functions Special Abstract Structures Containers Dictionaries Priority Queues Disjoint Sets Graphs Strings Geometric DS Prof. Amr Goneid, AUC 22

23 Containers Permit storage and retrieval of data items independent of content (access by location only). Support two basic operations: Put (x,c): Insert item x in container C Get (C): Retrieve next item from C. Prof. Amr Goneid, AUC 23

24 Containers Examples: Stacks: Last-In-First-Out (LIFO) structures Queues: First-In-First-Out (FIFO) structures Tables: Retrieval by position. Prof. Amr Goneid, AUC 24

25 Dictionaries A form of container that permits access by content. Support the following main operations: Insert (D,x): Insert item x in dictionary D Delete (D,x): Delete item x from D Search (D,k): search for key k in D Prof. Amr Goneid, AUC 25

search Binary Search Trees (BST): fast support of all dictionary operations.

26 Dictionaries Examples: Unsorted arrays and Linked Lists: permit linear search Sorted arrays: permit Binary search Ordered Lists: permit linear search Binary Search Trees (BST): fast support of all dictionary operations. Hash Tables: Fast retrieval by hashing key to a position. Prof. Amr Goneid, AUC 26

27 Priority Queues Allow processing items according to a certain order (Priority) Support the following main operations: Insert (Q,x): Insert item x in priority queue Q Remove (Q): Return and remove item with Highest/Lowest Priority Prof. Amr Goneid, AUC 27

28 Priority Queues Examples: Heaps and Partially Ordered Trees (POT) Major DS in HeapSort Prof. Amr Goneid, AUC 28

29 Disjoint Sets Disjoint sets are collections of elements with no common elements between the sets. A set can be identified by a parent node and children nodes. Prof. Amr Goneid, AUC 29

30 Disjoint Sets Support the following main operations: Find (i): Find Parent (set) containing node (i) Union (i,j): make set (i) the child of set (j) Examples: Representation of disjoint collections of data Representation of Trees, Forests and Graphs Prof. Amr Goneid, AUC 30

31 Graphs Can be used to represent any relationship and a wide variety of structures. Prof. Amr Goneid, AUC 31

32 Graphs Can be used to represent any relationship and a wide variety of structures. Well-known graph algorithms are the basis for many applications. Examples of such algorithms are: Minimum Spanning Trees Graph traversal (Depth-First and Breadth-First) Shortest Path Algorithms Prof. Amr Goneid, AUC 32

33 5. Special Data Structures Strings: Typically represented as arrays of characters. Various operations support pattern matching and string editing Prof. Amr Goneid, AUC 33

34 Special Data Structures Geometric Data Structures: Represent collections of data points and regions. Data points can represent segments. Segments can represent polygons that can represent regions. Prof. Amr Goneid, AUC 34

35 6. Examples on Modeling Problem: In Encryption problems, we need to do arithmetic on very large integers (e.g. 300 digits or more) ADTs: List Data Structures: 1-D array or Linked List Prof. Amr Goneid, AUC 35

$Select whole or fractions of the objects such that the total weight does not exceed (m) and the total price is maximum ADTs: List Data Structures: 1-D array or Linked$

36 Examples on Modeling Problem: (Knapsack Problem) We have (n) objects each with a weight and a price and a container with maximum capacity (m). Select whole or fractions of the objects such that the total weight does not exceed (m) and the total price is maximum ADTs: List Data Structures: 1-D array or Linked List Prof. Amr Goneid, AUC 36

37 Examples on Modeling Problem: (Chess Games) 8-Queens problem, Knight s Tour problem, etc ADTs: Board ADT Data Structures: 2-D array Prof. Amr Goneid, AUC 37

38 Examples on Modeling Problem: (Dictionary) We would like to build and use a small dictionary of words that translates from language (A) to language (B) ADTs: Key Table or List Data Structures: 1-D array or linked list Prof. Amr Goneid, AUC 38

39 Examples on Modeling Problem: (Small and fast Directory) We would like to build and use a small and fast directory to check username and pass word logins ADTs: Hash Table Data Structures: 1-D array Prof. Amr Goneid, AUC 39

40 Examples on Modeling Problem: (Large and fast Directory) We would like to build and use a large and fast telephone directory. ADTs: Binary Search Tree Data Structures: Linked Structure (Nodes) Prof. Amr Goneid, AUC 40

41 Examples on Modeling Problems: Evaluation of arithmetic expressions The Hanoi Towers game ADTs: Stack Data Structures: 1-D array or Linked List Prof. Amr Goneid, AUC 41

42 Examples on Modeling Problem: We would like to simulate the waiting process for airplanes to land in an airport. ADTs: Queue Data Structures: 1-D array or Linked List Prof. Amr Goneid, AUC 42

43 Examples on Modeling Problem: Sorting a set of elements Selection of the k th smallest (largest) element ADTs: Priority Queue Data Structures: 1-D array Prof. Amr Goneid, AUC 43

44 Examples on Modeling Problem: ADTs: Graph Find the shortest path between a source and a destination Find the exit in a Maze Data Structures: 2-D array or Linked list Prof. Amr Goneid, AUC 44

45 Examples on Modeling Problem: Find a wiring scheme for electrical power with minimum cost of wiring ADTs: Graph Priority Queue Disjoint Sets Data Structures: 1-D arrays, 2-D array, Linked list Prof. Amr Goneid, AUC 45

46 7. Examples ADT s: The Array as an ADT Abstraction: A homogenous sequence of elements with a fixed size that allows direct access to its elements. Elements (members): Any type, but all elements must be of the same type Relationship: Linear (One-To-one). Ordered storage with direct access. Fundamental Operations: create array store an element in the array at a given position (direct access) retrieve an element from a given position (direct access) Prof. amr Goneid, AUC 46

47 Examples on ADT s: ADT rational Abstraction: A rational number (fraction) is a rational representation of two integers (x,y). Elements or Members: A numerator (x) and a denominator (y), both are integers. (y) cannot be zero Relationship: The representation is equivalent to x / y Prof. amr Goneid, AUC 47

48 ADT rational (continued) Fundamental Operations: Read a fraction from keyboard Display a fraction on the screen Add Fractions f = f1 + f2 (e.g. ½ + ¼ = ¾) Subtract Fractions f = f1 f2 (e.g. ½ - 1/3 = 1/6) Multiply Fractions f = f1 * f2 (e.g. ½ * ¾ = 3/8) Divide Fractions f = f1 / f2 (e.g. 1/5 / ¼ = 4/5) Reduce Fractions (e.g. 2/6 = 1/3) Prof. amr Goneid, AUC 48

CSCE 210/2201 Data Structures and Algorithms. Prof. Amr Goneid

CSCE 210/2201 Data Structures and Algorithms. Prof. Amr Goneid CSCE 20/220 Data Structures and Algorithms Prof. Amr Goneid Fall 208 / Spring 209 CSCE 20/220 DATA STRUCTURES AND ALGORITHMS Prof. Amr Goneid Instructor: Prof. Amr Goneid E-mail: goneid@aucegypt.edu Office: