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
CSC-305
CSC-305 Design
Design
andand
Analysis
Analysis
of of
Algorithms
Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
2
 Basic Concerns
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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
Design and Analysis of Algorithms
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Fall-2014
Algorithm Basics
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 What is Algorithm? What do you think?
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Design and Analysis of Algorithms
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Fall-2014
Algorithm Basics
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 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 9th 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
CSC-305
Design and Analysis of Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
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 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.
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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.
Design and Analysis of Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
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 Five Distinct Areas in the Study of Algorithms
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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.
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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.
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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.
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Design and Analysis of Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
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 Algorithm and Data Structure
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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.
Design and Analysis of Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
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 Qualitative Aspects of Good Solutions (Algorithms)
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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
Design and Analysis of Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
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 Quantitative Aspects of Good Solutions (Algorithms)
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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
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A good algorithm must have three features: correctness, maintainability and
efficiency
Design and Analysis of Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
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 Correctness
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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?
Design and Analysis of Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
11
 Correctness
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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
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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?
Design and Analysis of Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
12
 Maintainability
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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?
Design and Analysis of Algorithms
BS(CS) -6
Fall-2014
Algorithm Basics
13
 Pseudo-code
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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:
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// 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
CSC-305
Design and Analysis of Algorithms
BS(CS) -6
Fall-2014