Anna University Regulation 2017 Design and Analysis of Algorithms Text : Introduction to Design and Analysis of Algorithms by Anany Levitin

1. The Design and
Analysis of
Algorithms
by Anany Levitin

2. 2
CHAPTER 1: INTRODUCTIONCHAPTER 1: INTRODUCTION
 What is an Algorithm
 Steps in Designing and Implementing
an Algorithm
 Important Problem Types
 Fundamental Data Structures

3. 3
ALGORITHM
 A sequence of unambiguous
instructions for solving a problem,
i.e. for obtaining the required
output for any legitimate input in
a finite amount of time

4. Notation of the Algorithm
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5. 5
Special Features of Algorithms
 Non-ambiguity
 Range of inputs
 The same algorithm can be represented
in different ways
 Several algorithms for solving the
same problem
 Different algorithms with different
speeds

6. Find the GCD(m,n)
Method 1: Descriptive Algorithm
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7. GCD using Euclid’s Method
gcd(m,n)=gcd(n,m nod n)
Find:
1. GCD(124,12)
2. GCD(160,15)
3. GCD(338,22)
4. GCD(150,8)
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8. Find the GCD(m,n)
Method 2:
Descriptive Algorithm
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9. Find the GCD(m,n)
Method 2: Pseudocode Representation
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10. Find the set of all Prime
numbers
Method 1: Middle School Level
Find Set of ALL Prime Numbers within 25
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11. Find the set of all Prime
numbers
Method 2: Sieve of Erathosthenes
Find Set of ALL Prime Numbers within 25
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12. Fundamentals of Algorithmic Problem Solving /
Algorithm Design & Analysis Process
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What does it mean to understand
the problem?
 What are the problem objects?
 What are the operations applied to the objects?
Deciding on computational
means
 How the objects would be represented?
 How the operations would be implemented?

14. 14
Design an algorithm
• Build a computational model of the
solving process
Prove correctness
• Correct output for every legitimate input
in finite time
• Based on correct math formula
• By induction

15. 15
Analyze the algorithm
Efficiency: time and space
Simplicity:
Generality: range of inputs, special cases
Optimality: no other algorithm can do better
Coding
How the objects and operations in the
algorithm are represented in the chosen
programming language?

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Important problem types
 Sorting
 Searching
 String processing
 Graph problems
 Combinatorial problems
 Geometric problems
 Numerical problems

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Fundamental data structures
Linear data structures
 Array
 Linked list
 Stack
 Queue
Operations: search, delete, insert
Implementation: static, dynamic

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Non-linear data structures
 Graphs
 Trees : connected graph without cycles
Rooted trees
 Ordered trees
Binary trees
Graph representation: adjacency lists,
adjacency matrix
Tree representation: as graphs; binary nodes
Fundamental data structures

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Fundamental data structures
Sets, Bags, Dictionaries
 Set: unordered collection of distinct elements
Operations: membership, union, intersection
Representation: bit string; linear structure
 Bag: unordered collection,
elements may be repeated
 Dictionary: a bag with operations search, add,
delete

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Conclusion
 Algorithm classification
By types of problems
By design technique
 Design techniques
a general approach to solving problems

21. Check if you are Clear with:
 Definition of Algorithm
 Notation of Algorithm
 Examples: GCD and Prime
 Fundamentals of Algorithms / Process of
Design & Analysis of Algorithms
 Types of Problems
 Fundamental Data Structures
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22. Have a GREAT Day..!!!
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