Chapter 5: Algorithms

Transcription

1 Chapter 5 Algorithms By: J. Brookshear Modified by: Yacoub Sabatin, BEng, MSc Chapter 5: Algorithms 5.1 The Concept of an Algorithm 5.2 Algorithm Representation 5.3 Algorithm Discovery 5.4 Iterative Structures 5.5 Recursive Structures 5.6 Efficiency and Correctness 2005 Pearson Addison-Wesley. & 2014 Yacoub Sabatin. All rights reserved 2 1

2 Algorithm: definition Before a computer can perform a task, it must be given an algorithm telling it precisely what to do. An algorithm is an ordered set of unambiguous, executable steps that defines a terminating process. Requirements of an algorithm must comply with these definition Pearson Addison-Wesley. & 2014 Yacoub Sabatin. All rights reserved 3 Algorithms: levels of abstraction Problem = motivation for algorithm Algorithm = procedure to solve the problem Often one of many possibilities Representation = description of algorithm sufficient to communicate it to the desired audience Always one of many possibilities (algebraic, oral, flowchart, electronic ckt, comp prog) Distinguish between: Algorithm: abstract, conceptual Its representation 4 2

3 Figure 5.2 Folding a bird from a square piece of paper 5 Figure 5.3 Origami primitives 2005 Pearson Addison-Wesley. & 2014 Yacoub Sabatin. All rights reserved 6 3

4 Pseudocode primitives Assignment name expression Conditional selection if condition then action Repeated execution Procedure while condition do activity procedure name (generic names) 7 Figure 5.4 The procedure Greetings in pseudocode 8 4

5 Figure 5.6 The sequential search algorithm in pseudocode 9 Problem solving steps 1. Understand the problem. 2. Get an idea how an algorithmic procedure might solve the problem. 3. Formulate the algorithm and represent it as a program. 4. Evaluate the program for accuracy and its potential as a tool for solving other problems. 10 5

6 Techniques for getting a foot in the door Work the problem backwards Solve an easier related problem Relax some of the problem constraints Solve pieces of the problem first = bottom up methodology Stepwise refinement = top-down methodology Popular technique because it produces modular programs 11 Sample problem Person A is charged with the task of determining the ages of B s three children. B tells A that the product of the children s ages is 36. A replies that another clue is required. B tells A the sum of the children s ages. A replies that another clue is needed. B tells A that the oldest child plays the piano. A tells B the ages of the three children. How old are the three children? 12 6

7 Figure Figure 5.7 Components of repetitive control 14 7

8 Figure 5.8 The while loop structure 15 Figure 5.9 The repeat loop structure 16 8

9 Figure 5.10 Sorting the list Fred, Alex, Diana, Byron, and Carol alphabetically Insertion Sort: Sort the list within itself. Take a sublist, then sort it alphabetically. Details, textbook, p Figure 5.11 The insertion sort algorithm expressed in pseudocode Insertion Sort: Sort the list within itself. Take a sublist, then sort it alphabetically. Details, textbook, p

10 Figure 5.12 Applying our strategy to search a list for the entry John 19 Figure 5.13 A first draft of the binary search technique 20 10

11 Figure 5.14 The binary search algorithm in pseudocode 21 Figure

12 Figure Figure

13 Software efficiency Measured as number of instructions executed Θ notation for efficiency classes Example: insertion sort is Θ(n 2 ) Best, worst, and average case 25 Figure 5.18 Applying the insertion sort in a worst-case situation 26 13

14 Figure 5.19 Graph of the worst-case analysis of the insertion sort algorithm 27 Figure 5.20 Graph of the worst-case analysis of the binary search algorithm 28 14

15 Software verification Proof of correctness Assertions Testing Preconditions Loop invariants 29 Example problem: Chain separating A traveler has a gold chain of seven links. He must stay at an isolated hotel for seven nights. The rent each night consists of one link from the chain. What is the fewest number of links that must be cut so that the traveler can pay the hotel one link of the chain each morning without paying for lodging in advance? 30 15

16 Figure 5.21 Separating the chain using only three cuts 31 Figure 5.22 Solving the problem with only one cut 32 16

17 Figure 5.23 The assertions associated with a typical while structure 33 Chapter 6 Programming Languages By: J. Brookshear Modified by: Yacoub Sabatin, BEng, MSc 17

18 Chapter 6: Programming Languages 6.1 Historical Perspective 6.2 Traditional Programming Concepts 6.3 Procedural Units 6.4 Language Implementation 6.5 Object Oriented Programming 6.6 Programming Concurrent Activities 6.7 Declarative Programming 35 Figure 6.1 Generations of programming languages 36 18

19 Second-generation: Assembly language A mnemonic system for representing programs Mnemonic names for op-codes Names for all registers Identifiers = descriptive names for memory locations, chosen by the programmer The machine language considered as the firstgeneration, ex. Instruction Set (similar to what s in chapter 2) 37 Assembly language characteristics One-to-one correspondence between machine instructions and assembly instructions Programmer must think like the machine Inherently machine-dependent Converted to machine language by a program called an assembler 38 19

20 Assembly language example Machine language 156C 166D CE C000 Assembly language LD R5, Price LD R6, ShippingCharge ADDI R0, R5 R6 ST R0, TotalCost HLT 39 Third generation language Uses high-level primitives Similar to our pseudo-code in Chapter 5 Machine independent (mostly) Examples: C, Basic, FORTRAN, COBOL Each primitive corresponds to a short sequence of machine language instructions Converted to machine language by a program called a compiler Some languages are interpreted i.e. require Interpreter, ex. Basic

21 Figure 6.2 The evolution of programming paradigms 41 Figure 6.3 A function for checkbook balancing constructed from simpler functions 42 21

22 Figure 6.4 The composition of a typical imperative program or program unit 43 Figure 6.5 Variable declarations in C, C++, C#, and Java 44 22

23 Figure 6.6 A two-dimensional array with two rows and nine columns 45 Figure 6.7 Declaration of heterogeneous array 46 23

24 Figure 6.8 Control structures and their representations in C, C++, C#, and Java 47 Figure 6.9 The for loop structure and its representation in C++, C#, and Java 48 24

25 Figure 6.10 The flow of control involving a procedure 49 Figure 6.11 The procedure ProjectPopulation written in the programming language C 50 25

26 Figure 6.12 Executing the procedure Demo and passing parameters by value 51 Figure 6.13 Executing the procedure Demo and passing parameters by reference 52 26

27 Figure 6.14 The function CylinderVolume written in the programming language C 53 Figure 6.21 The complete program preparation process 54 27

28 Figure 6.15 The translation process Lexical Analysis: The process of recognizing which strings of symbols represent a single entity. Analyzer reads the source symbol by symbol & identify which group of symbols are related. Parser: Views program in terms of lexical units (tokens) rather than individual symbols, to form a statement in the language. Code Generation: Machine-language constructing to implement the statements recognized by the parser. 55 Figure 6.16 A syntax diagram of our if-then-else pseudocode statement 56 28

29 Figure 6.17 Syntax diagrams describing the structure of a simple algebraic expression 57 Figure 6.18 The parse tree for the string x + y x z based on the syntax diagrams in Figure

30 Figure 6.19 Two distinct parse trees for the statement if B1 then if B2 then S1 else S2 59 Figure 6.20 An object-oriented approach to the translation process 60 30

31 Objects and Classes Object = active program unit containing both data and procedures Class = a template for all objects of the same type (blueprint) An Object is often called an instance of the class. 61 Components of an object Instance variable = variable within an object Method = function or procedure within an object Can manipulate the object s instance variables Constructor = special method to initialize a new object instance 62 31

32 Encapsulation Encapsulation = a way of restricting access to the internal components of an object Private Public 63 Additional object-oriented concepts Inheritance: allows new classes to be defined in terms of previously defined classes Polymorphism: allows method calls to be interpreted by the object that receives the call 64 32

33 Figure 6.22 The structure of a class describing a laser weapon in a computer game 65 Figure 6.23 A class with a constructor 66 33

34 Figure 6.24 Our LaserClass definition using encapsulation as it would appear in a Java or C# program 67 Programming concurrent activities Parallel or concurrent processing = simultaneous execution of multiple processes True concurrent processing requires multiple CPUs Can be simulated using time-sharing with a single CPU 68 34

35 Figure 6.25 Spawning processes 69 Interaction between processes Mutual exclusion = a method for ensuring that data can be accessed by only one process at a time Monitor = a data item augmented with the ability to control access to itself 70 35

36 Declarative programming Resolution = combining two or more statements to produce a new, logically equivalent statement Example: (P OR Q) AND (R OR Q) resolves to (P OR R) Resolvent = a new statement deduced by resolution Clause form = statement whose elementary components are connected by the Boolean operation OR Unification = assigning a value to a variable in a statement 71 Figure 6.26 Resolving the statements (P OR Q) and (R OR Q) to produce (P OR R) 72 36

37 Figure 6.27 Resolving the statements (P OR Q), (R OR Q), R, and P 73 Prolog Fact = predicatename(arguments). Example: parent(bill, mary). Rule = conclusion :- premise. :- means if Example: wise(x) :- old(x). Example: faster(x,z) :- faster(x,y), faster(y,z). All statements must be fact or rules