1. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Design and Analysis of Algorithms Khawaja Mohiuddin Assistant Professor, Department of Computer Sciences Bahria University, Karachi Campus, Contact: khawaja.mohiuddin@bimcs.edu.pk Lecture # 2 – Algorithm Basics

2. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 2  Basic Concerns  Computer programming is both an art and science  Elegance and beauty of expression on one hand  Accuracy, correctness, reliability and efficiency on the other hand  These concerns arise trying to balance the needs of two classes of people  The Programmers: who would like to be elegant and expressive, while delivering correctness and efficiency  The Users: who would like accuracy, reliability, correctness and efficiency in a program  In general, both are concerned with a good solution to a problem  A good solution is economical in the use of computing and human resources

3. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 3  What is Algorithm? What do you think?

4. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 4  Algorithm  The Concise Oxford Dictionary defines Algorithm (also “Algorism”) as: a process or a set of rules used for calculation or problem solving, especially with a computer  The word algorithm is derived by a distortion of the name Al-Khuwarizmi, a Persian Mathematician of 9 th Century A.D.  In Computer Science, algorithm has a special significance to mean “a precise method usable by a computer for the solution of a problem”  An algorithm is composed of a finite number of steps, each of which may require one or more operations. These operations must be unambiguous. This implies that each of these operations must be definite, clearly specifying what is meant to be done  All steps in the algorithm should be effective, that is, they should produce the desired result in a finite time frame  The algorithm should terminate after a finite number of operations. If the algorithm does not terminate in certain time limit, we do have a serious problem.  Thus, an algorithm should be definite, effective and finite

5. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 5  Program  A program is an expression of algorithm in a programming language e.g. C, C++, Java, FORTRAN etc.  Five Distinct Areas in the Study of Algorithms  To devise an algorithm: This is an activity where human intelligence is definitely required; some of the strategies used have a general applicability like dynamic programming, divide-and conquer, back-tracking, and so on.  To express an algorithm: An algorithm can be expressed in various ways: flow-chart, pseudo-code, program, and the like. Out of these only the program in certain programming languages are acceptable to a computer.

6. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 6  Five Distinct Areas in the Study of Algorithms  To validate an algorithm: This means that a program satisfies its precise specifications. This involves proving the correctness of an algorithm. Once an algorithm is shown to be correct, only then should the program coding begin. The program also has to be verified by testing, profiling and so on.  To analyze an algorithm: This field is called analysis of algorithms. It is concerned with the amount of computer time and storage that is required by the algorithm. This study allows us to compare valid algorithms for efficiency.  To test a program: Testing a program consists of two parts – debugging and profiling. Debugging can only point to the presence of errors and never their absence. Profiling is a process of executing a correctly working program with the appropriate data sets, and measuring the time and memory space it takes to execute various parts of the program.

7. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 7  Algorithm and Data Structure  An algorithm is a recipe for performing a certain task  A data structure is a way of arranging data to make solving a particular problem easier  A data structure could be a way of arranging values in an array, a linked list that connects items in a certain pattern, a tree, a graph, a network etc.  An algorithm does not necessarily need a data structure. For example, many of the numeric algorithms do not use data structures  On the other hand, there is a need to use some sort of algorithm to build the data structure.

8. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 8  Qualitative Aspects of Good Solutions (Algorithms)  They are simple yet powerful and general solutions  They can be easily understood by others which means that the implementation is clear and concise in the use of without being tricky  They can be easily modified if necessary  They give correct results for all clearly specified cases, including extreme cases  They are economical in the use of computer time, computer storage, and peripherals  They are properly documented, so that they can be used by others for their own applications  They are not dependent on any particular computer hardware or operating system on which they are run or implemented – system independence (portability)  They can be used as sub-procedures for other problems and applications  They are pleasing and satisfying to their designer – no patch-work solution

9. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 9  Quantitative Aspects of Good Solutions (Algorithms)  Quantitative measures are valuable as they provide a way of directly predicting and evaluating the performance of a good solution and comparing the relative performance of two or more solutions  More efficient solutions result in saving in computations, which results in saving in computer resource usage which in turn saves time and money  Algorithm Features  A good algorithm must have three features: correctness, maintainability and efficiency

10. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 10  Correctness  A program works correctly, outputting the expected behaviour and results in the complete range of data that is required to handle  One cannot demonstrate the correctness of the program by simply taking each of the possible input data, feeding it to the program, and showing that the result is correct.  Example: A boy sent to the market to buy a match box and asked to check the box for any moisture before buying it. The boy went on lighting one match-stick after another, till all were burnt. When asked why he did so, he replied “But then how can I be sure if the other matches will light?” Unfortunately, the computer programmers are in the same situation. How can they be sure that the program is correct without exhaustive testing?

11. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 11  Correctness  He could have argued that if the box had absorbed moisture, there was a good probability that all the match-sticks would be equally moist. So if he had tested any one of them, it should tell him about the whole box  Thus, he could have used limited testing plus proof instead of exhaustive testing  Efficiency  A program should be efficient, both in terms of execution time and the amount of resources like main memory it uses  However, the correctness requirement is fundamental, what will one do with a program that is very fast but does not give correct results?

12. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 12  Maintainability  If an algorithm isn’t maintainable, it is dangerous to use in a program. If an algorithm is simple, intuitive, and elegant, one can be confident that it is producing correct results, and one can fix it if it does not.  If the algorithm is intricate, confusing, and convoluted, one may have a lot of trouble implementing it, and one will have even more trouble fixing it if a bug arises.  If it is hard to understand, how can one know if it is producing correct results?

13. CSC-305 Design and Analysis of AlgorithmsBS(CS) -6 Fall-2014 Algorithm Basics 13  Pseudo-code  Pseudo-code is text that is a lot like a programming language but that is not really a programming language  The idea is to give the structure and details that would need to implement the algorithm in code without tying the algorithm to a particular programming language  The following snippet shows an example of pseudo-code for an algorithm that calculates the greatest common divisor (GCD) of two integers:  // Find the greatest common divisor of a and b. // GCD (a, b) = GCD(b, a Mod b). Integer: Gcd (Integer: a, Integer: b) While (b != 0) // Calculate the remainder. Integer: remainder = a Mod b // Calculate GCD (b, remainder). a = b b = remainder End While Return a // GCD (a, 0) is a. End Gcd