1. Advance Analysis of Algorithms
Lecture # 1
MS(Computer Science)
Semester 1
Fall 2017
Advance Analysis of Algorithms

2. Course Information Course Title Course Blog Grading Policy
Advanc Analysis of Algorithms
Credit Hours 03
Course Blog
Grading Policy
Mid Term Examination = 25 Marks
Final Term Examination = 50 Marks
Attendance Marks = 10 Marks
Sessional Marks = 15 Marks

3. Course Information Reference Books Other Books
Approximation Algorithms by Vijay V. Vazirni, Springer, 2004.
Introduction to Algorithms by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, 2nd edition, published by MIT Press, 2001
Algorithms and Theory of Computation Handbook, by Mikhail J. Atallah Contributor Mikhail J. Atallah, CRC Press, 1998.
Other Books
Introduction to Design & Analysis Computer Algorithm 3rd, Sara Baase, Allen Van Geleder, Adisor-Wesley 2000.
Algorithms, Richard Johnsonbaugh, Marcus Schaefer, Prentice Hall, 2004
Introduction to The Design and Analysis of Algorithms 2nd Edition Anany Levitin, Adison-Wesley, 2007.

4. Course Information Supporting Material Class Assessment Tools
Lecture Slides & Notes
Research Articles
Class Assessment Tools
Assignments
Presentations
Research Articles Reading
Research Paper Writing

5. Course Information Course Objective
Design and Analysis of Modern Algorithms
Different variants
Efficiency
Accuracy
Comparing Efficiencies
Motivation Thinking New Algorithms
Advanced Designing Techniques
Real World Research Problems will be taken as example.
Major focus of the subject is to Study Algorithms in Research Perspective.

6. Course Information Expected Results
On successful completion of this courses, students will be able to
Understand, analyze algorithms
Argue and prove correctness of algorithms
Analyze Time and Space Complexity of Algorithms
Understand algorithm design approaches
Use of graph theory in Problem Solving
Understand advance analysis and design topics.
Easily analyze existing algorithms and able to propose more efficient and effective algorithm for any real life research problem / situation.

7. Course Objectives
This course introduces students to the analysis and design of computer algorithms. Upon completion of this course, students will be able to do the following:
Analyze the asymptotic performance of algorithms.
Demonstrate a familiarity with major algorithms and data structures.
Apply important algorithmic design paradigms and methods of analysis.
Synthesize efficient algorithms in common engineering design situations.

8. Course Outline
Preliminaries : different types of algorithms, analyzing methodologies,
notations, proof techniques and limits.
Asymptotic Notation : different notations and their examples, standard
notations and their common functions.
Analysis of Algorithms : analyzing control structures, using barometer
instruction, amortization, and different examples for analysis and solving
recurrences.
Structures: use of arrays, stacks, queues, records, pointers, lists, graphs,
trees, hash tables, heaps and binomial heaps.
Searching/Sorting Algorithms : Various searching and sorting algorithms and
their comparisons.

9. Course Outline

10. Algorithms ABU JAFAR MUHAMMAD IBN MUSU AL-KHOWARIZMI:
Abu Ja'far Muhammad ibn Musa Al-Khwarizmi
[Born: about 780 in Baghdad (now in Iraq). Died: about 850]
An algorithm, named after the ninth century scholar Abu Jafar Muhammad Ibn Musu Al-Khowarizmi.

11. Algorithm Informal Definition
What is an Algorithms ?

12. Algorithm Concepts What is Data Structure?
A data structure is a systematic way of organizing and accessing data. Some basic data structure as follows.
 Array
 Link List
 Stacks
 Queues
 Trees
What is Program?
Program is an implementation of an algorithm in some programming language.
Data structure + Algorithm = Program

13. Design & Analysis of Algorithms
The “design” pertains to
i. The description of algorithm at an abstract level by means of a pseudo language, and
ii. Proof of correctness that is, the algorithm solves the given problem in all cases.
2. The “analysis” deals with performance evaluation (complexity analysis).

14. Problem, Solution and Tools
A computer does not solve problems; it's just a tool that I can use to implement my plan for solving the problem.
A computer program is a set of instructions for a computer. These instructions describe the steps that the computer must follow to implement a plan.
An algorithm is a plan for solving a problem.
A person must design an algorithm.
A person must translate an algorithm into a computer program.
Algorithm Development Process
Understand the problem
Design an algorithm and proper data structures
Analyze the algorithm
Code the algorithm

15. What is a good algorithm?
Good algorithm is an efficient algorithm.
What does efficient means?
Efficient is something, which has small running time and takes (spaced used) less memory.
 We would be spending more time on analyzing the running time of an algorithm.
 We will also spend some time on analyzing the space. Efficiency of algorithms is as a function of input size.

16. How to Calculate Running Time
analyze running time in the
best case (usually useless)
worst case (we focus on the worst case running time)
average case (very useful but often difficult to determine)

17. Theoretical Analysis of Running Time
Uses a pseudo-code description of the algorithm instead of an implementation
Characterizes running time as a function of the input size, n
Takes into account all possible inputs
Allows us to evaluate the speed of an algorithm independent of the hardware/software environment

18. Pseudocode Example: find max element of an array
In this course, we will mostly use pseudocode to describe an algorithm
Pseudocode is a high- level description of an algorithm
More structured than English prose
Less detailed than a program
Preferred notation for describing algorithms
Hides program design issues
Algorithm arrayMax(A, n)
Input: array A of n integers
Output: maximum element of A
currentMax  A[0]
for i  1 to n  1 do
if A[i]  currentMax then
currentMax  A[i]
return currentMax

19. Pseudocode Details Algorithm arrayMax(A, n)
Input: array A of n integers
Output: maximum element of A
currentMax  A[0]
for i  1 to n  1 do
if A[i]  currentMax then
currentMax  A[i]
return currentMax
Control flow
if … then … [else …]
while … do …
repeat … until …
for … do …
Indentation replaces braces
Method declaration
Algorithm method (arg, arg…)
Input …
Output …

20. Pseudocode Details Method call Return value Expressions
Algorithm arrayMax(A, n)
Input: array A of n integers
Output: maximum element of A
currentMax  A[0]
for i  1 to n  1 do
if A[i]  currentMax then
currentMax  A[i]
return currentMax
Method call
var.method (arg [, arg…])
Return value
return expression
Expressions
Assignment (like  in Java)
Equality testing (like  in Java)
n2 superscripts and other mathematical formatting allowed

21. Primitive Operations
For theoretical analysis, we will count primitive or basic operations, which are simple computations performed by an algorithm
Basic operations are:
Identifiable in pseudocode
Largely independent from the programming language
Exact definition not important (we will see why later)
Assumed to take a constant amount of time

22. Primitive Operations Examples of primitive operations:
Evaluating an expression x2+ey
Assigning a value to a variable cnt  cnt+1
Indexing into an array A[5]
Calling a method mySort(A,n)
Returning from a method return(cnt)

23. Real-World Applications
Hardware design: VLSI chips
Compilers
Computer graphics: movies, video games
Routing messages in the Internet
Searching the Web
Distributed file sharing
Computer aided design and manufacturing
Security: e-commerce, voting machines
Multimedia: CD player, DVD, MP3, JPG, HDTV
DNA sequencing, protein folding
and many more!

24. Some Important Problem Types
Sorting
a set of items
Searching
among a set of items
String processing
text, bit strings, gene sequences
Graphs
model objects and their relationships
Combinatorial
find desired permutation, combination or subset
Geometric
graphics, imaging, robotics
Numerical
continuous math: solving equations, evaluating functions

25. Algorithm Design Techniques
Brute Force & Exhaustive Search
follow definition / try all possibilities
Divide & Conquer
break problem into distinct subproblems
Transformation
convert problem to another one
Dynamic Programming
break problem into overlapping subproblems
Greedy
repeatedly do what is best now
Iterative Improvement
repeatedly improve current solution
Randomization
use random numbers

26. FURTHER DISCUSSION
NEXT WEEK …………….