Instructor : Zuhair Qadir
Lecture # 1
Design & Analysis of Algorithms
CS3444 – Design & Analysis of Algorithms
16-September-2014
1
Instructor Introduction
• Education
MS Computer Sciences from LUMS 2011- 2013
BS Computer Engineering from UET, Lahore 2006-2010
• Industry Experience
• Systems Limited 2010-2012
Design & Analysis of Algorithms
• Zuhair Qadir
• Core Interests
• Computer Vision, Network Security and Algorithms
2
•
•
•
•
•
•
•
•
Course Overview: Goals & Objectives
Class Protocols
Outline of topics to be discussed in the course
Understanding a problem
Purpose of a Algorithms—setting the stage for Algo
concepts and principles
What is an Algorithm?
Reading Suggestions
Design & Analysis of Algorithms
Outline
3
Course Title
Design & Analysis of Algorithms
Course Code
CS3444
Credit Hours
3 credit hours
Instructor
Zuhair Qadir
Contact
Office
Office Hours
Sections
Course Website
Muhammad.Qadir@cs.uol.edu.pk
Room-102
Saturday 12:00pm – 2:00pm
BSCS – Section B
Design & Analysis of Algorithms
Course Information
www.zuhairqadir.info/UOL/ALGO/
4
Course Information
• Lectures
• There will be 2 lectures a week of one and a half hour each.
• Refer to the timetable for class timings/venue.
Design & Analysis of Algorithms
• No Lab
5
Course Objective
• We will study fundamental algorithms for solving a variety of
problems, including sorting, searching and graph algorithms. More
importantly, we will focus on general design and analysis techniques
that underlie these algorithms. For example, we will examine divideand-conquer, dynamic programming, greediness, and probabilistic
approaches. With an understanding of these techniques, you will be
prepared to design some of your own algorithms.
• We will learn techniques for analyzing time and space complexity of
algorithms and will use these to evaluate tradeoffs between
different algorithms. We will also see that problems can be
organized into a hierarchy that measures their inherent difficulty by
the efficiency of the best possible algorithm for solving them.
Design & Analysis of Algorithms
• Introduce the classic algorithms in various domains, and techniques
for designing efficient algorithms.
6
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Algorithm design
Algorithm analysis
Sorting Algorithms
Divide-and-conquer approach
Greedy approach
Graph algorithms
Graph searching
Minimum spanning tree
Shortest paths
Backtracking and its applications in games
String matching
Dynamic programming
Longest common subsequence
Theory of NP-completeness
Design & Analysis of Algorithms
Course Contents
7
Text Books
• Course Book
• Reference Books
• The Algorithm Design Manual - Steven S.
• Algorithms – Dasgupta, Papadimitriou, Vazirani
• Some relevant important material from internet as well
Design & Analysis of Algorithms
• Introduction to Algorithms, 3rd edition by Cormen, Leisersen,
Rivest and Stein.
8
Assessment
Weightage
Mid Term Exam
30%
Final Term Exam
40%
Assignments
10%
Quizzes
20%
Design & Analysis of Algorithms
Grading Policy
9
Class Honor Code
• Copying code from someone else’s screen or notes
• Providing your own written code to another student
• Letting another student type solutions for you on the machine you are working on, for assignment
submission
• Looking at someone else’s answer sheet during a quiz or an exam
• Downloading code from the internet or any other source and submitting portions of it as your own.
• Writing code, whether on a computer or a sheet of paper, for someone else’s assignment and
providing it to him or her.
• Emailing your own code to someone else.
• Debugging someone else’s code.
Some examples of what does not constitute cheating and plagiarism
• Answering questions on the web forum
• Discussing ideas with another student
• Helping other students understand concepts
If in doubt, discuss with your instructor.
• Try to come in class on time
Design & Analysis of Algorithms
We expect all UOL students to act honestly at all times. Cheating and plagiarism will not be tolerated.
Resorting to unfair means may result in an F in the course and Disciplinary Committee Case from UOL,
even for first-time offenders. Some examples of what constitutes cheating and plagiarism are listed
below, though this is not an exhaustive list:
10
Lecture # 1
Design & Analysis of Algorithms
Design & Analysis of
Algorithms
11
Introduction
• What are Algorithms ?
• An algorithm is the thing which stays the same whether the
program is in C++ running on a PC in New York or is in Android
running on a Smartphone in Lahore!
• An algorithm has to solve a general, specified problem. An
algorithmic problem is specified by describing the set of
instances/input it must work on and what desired properties the
output must have.
Design & Analysis of Algorithms
• Algorithms are the ideas behind computer programs.
12
Introduction
• Naïve Definition:
• An algorithm is a set of instructions to be followed to solve a
problem.
an algorithm is a complete set of rules that transform the
input into the output in a finite number of steps.
• Characterisics of an Algorithm
• There can be more than one solution (more than one algorithm)
to solve a given problem.
• An algorithm can be implemented using different programming
languages on different platforms.
• An algorithm should correctly solve the problem.
• e.g., for sorting, this means even if (1) the input is already sorted,
or (2) it contains repeated elements.
• Once we have a correct algorithm for a problem, we have to
determine the efficiency of that algorithm.
Design & Analysis of Algorithms
• Concrete Definition:
13
Introduction
• Key features of Algorithms:
• Algorithms are judged not only by how well they solve a problem,
but also by how effectively they use resources like time and
space.
Design & Analysis of Algorithms
• Algorithms are recipes for solving computational problems.
14
Aspects of studying algorithms:
1. Designing algorithms:
• putting the pieces of the puzzles together,
• choosing data structures,
• selecting the basic approaches to the solution of the
problem,
•
The most popular design strategies are divide&conquer, greedy,
dynamic prog., backtracking, and branch&bound.
2. Expressing and implementing the algorithm
Concerns are:
• clearness
• conciseness
• Effectiveness
• etc.
Design & Analysis of Algorithms
Design & Analysis of Algorithms
15
Design & Analysis of Algorithms
3. Analyzing the algorithm
4. Compare UB and LB to see if your solution is good enough
Analyzing the algorithm gives us the upper bound to solve the problem
Analyzing the problem gives us the lower bound to solve the problem
5. Validate the algorithm
We show that the algorithm computes the correct answer for all possible
legal (or given) inputs. In contrast with the verification it is concerned
with the external things. “are you building the right thing ?”
Design & Analysis of Algorithms
Algorithm analysis is assessing the time and space resources required
by an algorithm as a function of the size of the problem, without
actually implementing the algorithm.
16
Design & Analysis of Algorithms
6. Verifying the algorithm (or program)
7. Testing algorithms
There are two phases;
 Debugging: The process of executing programs on sample
data sets to determine if faulty results occur, and if so, to
correct them.
“Debugging can only point to the presence of errors, but not to
their absence”

Profiling: the process of executing a correct program on
various data sets and measuring the time (and space) it takes
to compute the results.
Design & Analysis of Algorithms
An algorithm is said to be correct (verified) if, for every input
instance, it halts with the correct output. In contrast with
validation it is concerned with the internal things. “are you
building it right?”
17
Algorithmic Performance
• Instructions take time.
• How fast does the algorithm perform?
• What affects its runtime?
• Space
• Data structures take space
• What kind of data structures can be used?
• How does choice of data structure affect the runtime?
• We will focus on time:
• How to estimate the time required for an algorithm
• How to reduce the time required
Design & Analysis of Algorithms
There are two aspects of algorithmic performance:
• Time
18
Algorithmic Analysis
• How do we compare the time efficiency of two
algorithms that solve the same problem?
Naïve Approach: implement these algorithms in
a programming language (i.e., C++), and run
them to compare their time requirements.
Design & Analysis of Algorithms
• Analysis of Algorithms is the area of computer
science that provides tools to analyze the
efficiency of different methods of solutions.
19
Sorting
• Input : 6, 3, 1, 8, 2, 4
Design & Analysis of Algorithms
• How to Sort ?
20
Bubble Sort
• Input : 6, 3, 1, 8, 2, 4
Design & Analysis of Algorithms
• Sort ?
21
Readings for Today
• Google:
• Google Search Engine Algorithm
• Why do we need algorithms ? Why analysis is important ?
Design & Analysis of Algorithms
• History of Algorithms , inventor of algorithms
22