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design and analysis of algorithm
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CHAPTER 4 Divide-and-conquer
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DESIGN AND ANALYSIS OF ALGORITHMSPrepared by
R.Cheran [M.Sc. computer science]
, SYLLABUS
UNIT -I: ALGORITHM AND ANALYSIS
What is an Algorithm? - Algorithm Specification- Performance Analysis-
Randomized Algorithms.
UNIT - II: DIVIDE AND CONQUER
General Method - Binary Search - Finding the Maximum and Minimum-
Merge Sort - Quick Sort - Selection Sort- Stassen‟s Matrix
Multiplications.
UNIT - III: THE GREEDY METHOD
The General Method - Knapsack Problem – Tree Vertex Splitting - Job
Sequencing with Deadlines - Minimum Cost Spanning Trees - Optimal
Storage on Tapes - Optimal Merge Pattern - Single Source Shortest Paths.
UNIT - IV: DYNAMIC POGRAMMING
The General Method – Multistage Graphs - All pair shortest path - String
Editing - 0/1 Knapsack – Reliability Design - The Traveling Salesperson
Problem
UNIT - V: TRAVERSAL, SEARCHING & BACKTRACKING
Techniques for Binary Trees- Techniques for Graphs - The General
Method - The 8-Queens Problem – Sum of Subsets- Graph Colouring-
Hamiltonian Cycles
, DESIGN AND ANALYSIS ALGORITHM
UNIT – I
.
ALGORITHM
Informal Definition:
An Algorithm is any well-defined computational procedure that takes some value
or set of values as Input and produces a set of values or some value as output. Thus algorithm is
a sequence of computational steps that transforms the i/p into the o/p.
Formal Definition:
An Algorithm is a finite set of instructions that, if followed, accomplishes a
particular task. In addition, all algorithms should satisfy the following criteria.
1. INPUT Zero or more quantities are externally supplied.
2. OUTPUT At least one quantity is produced.
3. DEFINITENESS Each instruction is clear and unambiguous.
4. FINITENESS If we trace out the instructions of an algorithm, then for all cases, the algorithm
terminates after a finite number of steps.
5. EFFECTIVENESS Every instruction must very basic so that it can be carried out, in principle, by a
person using only pencil & paper.
Issues or study of Algorithm:
How to device or design an algorithm creating and algorithm.
How to express an algorithm definiteness.
How to analysis an algorithm time and space complexity.
How to validate an algorithm fitness.
Testing the algorithm checking for error.
Algorithm Specification:
Algorithm can be described in three ways.
1. Natural language like English:
When this way is choused care should be taken,
we should ensure that each & every statement is definite.
2. Graphic representation called flowchart:
This method will work well when the algorithm
is small& simple.
3. Pseudo-code Method:
In this method, we should typically describe algorithms as program,
which resembles language like Pascal & algol.
DESIGN AND ANALYSIS ALGORITHM CHERAN
, DESIGN AND ANALYSIS ALGORITHM
Pseudo-Code Conventions:
1. Comments begin with // and continue until the end of line.
2. Blocks are indicated with matching braces {and}.
3. An identifier begins with a letter. The data types of variables are not explicitly declared.
4. Compound data types can be formed with records. Here is an example,
Node. Record
{
data type – 1 data-1;
.
.
.
data type – n data – n;
node * link;
}
Here link is a pointer to the record type node. Individual data items of a record
can be accessed with and period.
5. Assignment of values to variables is done using the assignment
statement. <Variable>:= <expression>;
6. There are two Boolean values TRUE and FALSE.
Logical AND, OR, NOT
OperatorsRelation <, <=,>,>=, =, !=
al Operators
7. The following looping statements are employed.
For, while and repeat-until
While Loop:
While < condition > do
{
<statement-1>
.
.
.
<statement-n>
}
For Loop:
DESIGN AND ANALYSIS ALGORITHM CHERAN
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