Pre Requirements for Advanced Algorithms

1. CSCI 4140 Advanced Algorithms
Dr. Zahid Khan
CUSSA Instructor

2. Outlines
 About the course
Objectives
Contents
Course Materials
Exams & Evaluations
 Introduction to Data Structure
 Basic Data Structures
 Introduction to Algorithm
 Summary
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3. About the course
 Analyze the asymptotic performance of algorithms.
 Write rigorous correctness proofs for 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.
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4. About the course
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 See the syllabus
◦ Uploaded to the course portal

5. About the course
Introduction to Algorithms
3rd edition, Thomas H Cormen Charles E,
Leiserson Ronald L Rivest Clifford Stein,
MIT press.
• Lecture slides and programing examples
will also be shared after very class
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6. About the course
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Assessments Quantity Percentage
Quizzes 5 20%
Projects 2 20%
Mid-Terms 2 30%
Final Exam 1 30%

7. About the course
 Regular Lectures:
Sunday, Monday, Tuesday, Wednesday, Thursday, Friday,
Saturday: 09:00 AM to 10:50AM
 Consultation Hours:
You can send me an email at any time.
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8. Introduction
 Definition
 Basic Data Structures
 Choosing a Data Structure
◦ Examples
 Data Structure operations
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9. Definition
◦ A data structure is a way to store and organize data
in order to facilitate access and modifications
◦ No single data structure works well for all purposes,
and so it is important to know the strengths and
limitations of several of them
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10. Basic Data Structures
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Basic Data Structures
Linear Data Structures Non-Linear Data Structures
Arrays LinkedLists Stacks Queues Trees Graphs Hash Tables

11. What data structure to use?
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array
Linked list
tree
queue
stack

12. Choosing a Data Structures
 The choice of particular data model
depends on two consideration:
◦ It must be rich enough in structure to mirror the actual
relationships of data in the real world
◦ The structure should be simple enough that one can
effectively process the data when necessary
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13. Basic data structures
 Linear structures
◦ Array: Fixed-size
◦ Linked-list: Variable-size
◦ Stack: Add to top and remove from top
◦ Queue: Add to back and remove from front
◦ Priority queue: Add anywhere, remove having highest priority
 Hash tables: Unordered lists which use a ‘hash function’ to insert
and search
 Tree: A branching structure with no loops
 Graph: A Graph consist of a set of vertices V and a set of edges E
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14. Arrays
 Linear array : A list of a
finite number n of
similar data elements
referenced respectively
by a set of n
consecutive numbers
 Also known as one
dimensional arrays
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STUDENT
Usman Saleem
Usama Arshad
Nasir Fida
Tayyab Ahmad
Abdullah
Musa Ahmad
1
2
3
4
5
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15. Arrays
 Multidimensional arrays
◦ Each elements is referenced
by two subscripts
◦ For example, weekly sales
record of a chain of 28
stores, each having 4 depts
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16. Linked List
 Suppose a firm maintains
a file, as shown here
 This file could be stored
in the computer by two
columns of nine names
 However, there is
redundant information in
such a scheme,
especially if we have
hundreds of names 16
Customer Salesperson
Adams Smith
Brown Ray
Clark Jones
Evans Smith
Farmer Jones
Drew Jones
Geller Ray
Hill Smith
Infeld Ray
1
2
3
4
5
6
7
8
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17. Alternate representation
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Salesperson
Jones
Ray
Smith
Customer Pointer
Adams 3
Brown 2
Clark 1
Evans 2
Farmer 3
Farmer 1
Geller 2
Hill 3
Infeld 2
1
2
3
4
5
6
7
8
9
3
2
1
An integer used as a pointer
requires less space than a name:
hence this representation saves
space.

18. Alternate representation
(cont.)
 Now suppose the firm wants the list of
customers for a given salesperson
◦ Using the data representation in last slide,
search is to be carried out through the
entire file ( not a good solution)
 Any Solution?
◦ Arrows to point the other way
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19. Another representation
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Salesperson Pointer
Jones 3, 6
Ray 2, 4, 7, 9
Smith 1, 5, 8
 Can you think of any disadvantage associated with this scheme ?
◦ Set of pointers will change as customers are added and deleted,
because each salesperson may have many pointers

20. Still another representation
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Customer Pointer
Adams 5
Brown 4
Clark 6
Evans 7
Farmer 8
Farmer 0
Geller 9
Hill 0
Infeld 0
1
2
3
4
5
6
7
8
9
Salesperson Pointers
Jones 3
Ray 2
Smith 1 3
2
1
Now we can easily insert and
delete customers
This
representation
is an example
of linked list

21. Hierarchical relationship
 Data frequently contain a hierarchical relationship between
various elements
 Data structure used to reflect such kind of relationship is called a
rooted tree graph or simply a tree.
 For example, an employee personal record may contain the
following data items:
◦ Social security number,
◦ Name,
◦ Address,
◦ Age,
◦ Salary,
◦ Dependents
 However Name is composed of subitems,
◦ Last,
◦ First
◦ MI (middle initial)
 Similarly we have address item
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22. Trees
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22
City Province Country
Area
Street
Address
Name
Last First MI
CNIC # Age Salary Dependent
Employee

23. Example
 Consider the following algebraic
expression
◦ (2x+y)(a-7b)3
◦ How can we represent such a data
structure?
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24. Tree
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*
+
y
*
x
2
^
3
-
a *
7 b
(2x+y)(a-7b)3

25. Other data structures
 Stack (LIFO)
◦ E.g., stack of dishes
 Queue (FIFO)
◦ E.g., line of people waiting at bus stand
 Graph
◦ Sometimes relationship between pairs of
data elements is not hierarchical.
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26. Stacks
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2132
123
123
123
123
123
123
546
45
543
3
3
2544
IN
OUT

27. Queue
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2132
123
123
123
123
123
3
3
2544
33
IN
OUT

28. The Need for Data Structures
 Goal: to organize data
 Criteria: to facilitate efficient
◦ storage of data
◦ retrieval of data
◦ manipulation of data
 Design Issue:
◦ select and design appropriate data types.
(This is the real essence of OOP.)
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29. After Class Dicussion (Self Test)
 Differentiate static and dynamic data structure.
 Why Data structure is necessory?
 What are the limitations of algorithms?
 How the efficiency of an algorithm can be measured ?
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30. Q/A
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