Understanding Algorithms in Computer Science

1. Chapter 1: An Introduction to Computer Science Invitation to Computer Science, C++ Version, Third Edition

2. Objectives In this chapter, you will learn about: • The definition of algorithm • The definition of computer science • Overiew of the course Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

3. What is an Algorithm? • An algorithm is a • well-orderedcollection of • unambiguousand • effectively computableoperations that, when executed, • produces a result and • halts in a finite amount of time. Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

4. Example of Algorithm • An algorithm is a list that looks like • STEP 1: Do something • STEP 2: Do something • STEP 3: Do something • . . • . . • . . • STEP N: Stop, you are finished Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

5. The Formal Definition of an Algorithm • Algorithm • A well-ordered collection of unambiguous and effectively computable operations that, when executed, produces a result and halts in a finite amount of time Example: Make Pasta • Boil two quarts of water • Add ½ lb of pasta in the water • Strain the water • Add the sauce Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

6. The Formal Definition of an Algorithm (continued) • Unambiguous operation • An operation that can be understood and carried out directly by the computing agent without needing to be further simplified or explained • Ex. • Boil some water (ambiguous) • Boil 2 quarts of water (unambiguous) • An operation that is unambiguous is called a primitive operation (or just a primitive) • Q. - What are the primitives of a computer? • A. - Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

7. The Formal Definition of an Algorithm (continued) • Effectively computable • Computational process exists that allows computing agent to complete that operation successfully • Note that a given collection of operations may be an algorithm with respect to one computing agent, but not with respect to another computing agent!! • Example of not effectively computable operations: • Write all the real numbers between 0 and 1. Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

8. The Formal Definition of an Algorithm (continued) • The result of the algorithm must be produced after the execution of a finite number of operations • i.e. Can the user of the algorithm observe a result produced by the algorithm? • A result can be a sign, a sound, an alarm, a number, a message of error, ect… Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

9. The Formal Definition of an Algorithm (continued) • It halts in a finite amount of time. • Infinite loop • The algorithm has no provisions to terminate • A common error in the designing of algorithms • Do not confuse, "not finite" with "very, very large". • Q. - Is this loop “finite” or “very, very large”? Step 1. Write the number 1 on the board. Step 2. Add 1 to the number you just wrote and write the result on the board Step 3. Repeat Step 2. Step 4. Stop. Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

10. The Importance of Algorithmic Problem Solving • Algorithmic solutions can be: • Encoded into some appropriate language • Given to a computing agent to execute • The computing agent • Would mechanically follow these instructions and successfully complete the task specified • Would not have to understand • Creative processes that went into discovery of solution • Principles and concepts that underlie the problem Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

11. Which of those is an algorithm? • Write all the possible numbers on a paper. • Fill 1 cup of sugar. Mix it to 3 cups of milk. • Think of a number. Add 20 to it. • Either wet your hair or lather your hair. Then rinse your hair. • If your hair are dirty, wet your hair; lather your hair; rinse your hair; else go back to study. Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

12. Common misconceptions about Computer Science Misconception 1 • Computer science is the study of computers Misconception 2 • Computer science is the study of how to write computer programs Misconception 3 • Computer science is the study of the uses and applications of computers and software Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

13. The Definition of Computer Science • Computer science is the study of algorithms including • 1. Their formal and mathematical properties • 2. Their hardware realizations • 3. Their linguistic realizations • 4. Their applications Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

14. 1. Their formal and mathematical properties • It is not enough to design an algorithm to solve a problem. • We must worry about some additional properties of an algorithm: • How efficient is it? • What kinds of resources must be used to execute it? • How does it compare to other algorithms that solve the same problem? Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

15. 2. Their hardware realizations • Computing entities are required to execute algorithms • Computing entities are not necessarily machines! • However our interest will lie with algorithms that execute on computing entities called "computers". • How are computer constructed? • The emphasis of the course will be on the logicalconstruction of a computer, not the physical construction. Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

16. 3. Their linguistic realizations • Which language do we use to code the algorithms? • We will start with one linguistic realization, called pseudocodeand later will look at possible different realizations in various programming languages. • In particular we will do some introductory programming in C++. Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

17. 4. Their applications • What are some of the many important and popular applications of computers in current use including: • numerical problem solving • information retrieval • graphics • networking • artificial intelligence • telecommunications • modeling and simulation Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

18. Overview of the course • 1. The algorithmic foundations of computer science. (Ch 1-3) • 2. The hardware world. (Ch 4-5) • 3. The virtual machine. (Ch 6-7) • 4. The software world. (Ch 8-11) • 5. Applications. (Ch 12-14) • 6. Social issues. (Ch 15) • Note these correspond to the levels of the pyramid on the cover of your text. • Each level addresses one aspect of the definition of computer science • Computer science/Algorithms Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

19. Figure 1.9 Organization of the Text into a Six-Layer Hierarchy Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

20. Summary • Computer science is the study of algorithms • An algorithm is a well-ordered collection of unambiguous and effectively computable operations that, when executed, produces a result and halts in a finite amount of time • If we can specify an algorithm to solve a problem, then we can automate its solution • Computers developed from mechanical calculating devices to modern electronic marvels of miniaturization Invitation to Computer Science, C++ Version, Third Edition - Modified by A. Guercio

21. BE SURE TO CHECK THE CLASS WEBSITE DAILY FOR YOUR: Reading assignments Homework assignments Other materials related to this course http://www.personal.edu/~aguercioa/Spring06/CS10051-600.html