ds and algorithims

7/30/2019 DS and Algorithims

1/17

Data Structures&

Algorithms

Dr Ravi Prakash Gorthi

Aug-Dec, 2010


2/17

Data Structures & Algorithms

Topics

1. Why Study DS & Algorithms?

2. Abstract Data Types

3. Arrays and Linked Lists

4. Stacks & Queues

5. Trees & Graphs

6. Sorting and Searching

7. Complexity of Algorithms


3/17

Why Study DS & Algorithms?

Let consider an example:

Many business companies NEED daily / weekly data on

sales or revenue sorted in different ways;Example: A Company needs daily data of:

1. Product-wise sales (first sort sales data according to the

product-type, sum the sales per product and sort in thedescending-order of sales)

2. Region-wise sales (similar to the above)

3. Sales-person-wise sales (similar to the above)The sorting software module has to sort a few million

records sometime between 2 to 4am in the night.


4/17

Sorting A Set of Records

Region Code Sales-

Person-

Code

Product-

Code

Qty-Sold Unit-Price Special-

Discount

Offered

North-India N-001 P-1045 5000 99.00 1%

North-India N-001 P-2022 900 49.00 0%

North-India N-112 P-1025 15000 56.00 3%

South-India S-005 P-1025 18000 56.00 3%

South-India S-212 P-3033 300 230.00 2%

West-India W-109 P-1025 25000 56.00 3%

West-India W-119 P-1045 900 99.00 2%

East-India E-112 P-1025 12000 56.00 3%

East-India E-112 P-1045 300 99.00 1%

Consider An Indian FMCG Company:

From the above records, you have region-wise, sales-person-wise, product-wise,total revenues!


5/17

Sorting A Set of RecordsConsider An Indian FMCG Company:

Product-Code Total-

Revenues

P-1025 78L

P-1045 74L

P-2022 71L

P-3082 68L

Region-Code Total-

Revenues

West-India 450L

North-India 437L

South-India 412L

East-India 373L

Sales-Person-

Code

Total-

RevenuesS-125 135L

N-109 132L

W-212 128L

S-218 121L


6/17

Sorting A Set of RecordsConsider An Indian FMCG Company:

Product-Code Total-

Revenues

P-1025 78L

P-1045 32L

P-2022 31L

P-3082 30L

Region-Code Total-

Revenues

West-India 38L

South-India 9L

North-India 7.5L

East-India 6L

Sales-Person-

Code

Total-

Revenues

W-109 12.5L

W-212 10l

W-178 8l

W-218 7.5L


7/17

Why Study DS & Algorithms?

An inefficient sorting algorithm will take 10 hours to sort

1 million records on the latest supercomputer

whereas an efficient sorting algorithm will take 10mins.

Efficient algorithms require very appropriate data-structures.

Thus, there is a need to study a variety of data-structures

and their usage in efficient algorithms.


8/17

Algorithms

What is an algorithm?A step-by-step procedure, which is unambiguous and

machine executable

Solves a given problem correctly and guarantees to give theright answer(s) in finite time (in other words, an algorithm isa provably correct method to solve the given problem)

Finite in lengthTakes afinite number of valid input(s) of finite length, takesa finite time to solve the given problem for the given inputsand produces afinite number of correct output(s) of finite

length (and produces an appropriate error message forinvalid input(s))

Initially described in pseudo-English but can be programmedusing one of the formal computer programming languages

on any computing platform


9/17

Algorithms

An example to illustrate

Suppose the goal is to find the solution (values of x, y & z), ifany, of the following system of linear equations:

The algorithm is as follows:

Eliminatexfrom all equations below L1 And then, eliminate yfrom all equations below L2 This will give a value for z (if the equations are solvable)

Then, using back-substitution, each unknown variable is solved for.


10/17

Algorithms

An example to illustrate

In the example, xis eliminated from L2 by adding to L2.

xis then eliminated from L3 by adding L1 to L3. The result is:


11/17

AlgorithmsAn example to illustrate

Now yis eliminated from L3 by adding 4L2 to L3:

The result is:

Then, z can be substituted into L2, which can then be solved toobtain

Next, z and ycan be substituted into L1, which can be solved toobtain


12/17

Algorithms

Why to design and develop algorithms?

1. A mechanism to solve a problem (e.g. Gauss EliminationMethod is a mechanism to solve Linear Simultaneous

Equations)

2. A mechanism to automate the process of solving a given

problem repeatedly on a computing platform on different

sets of inputs


13/17

Algorithms

Why to analyze algorithms?

1. Any correct solution to a given problem is NOT the end-of

research endeavor

2. The time and memory-space taken by an algorithm are of

critical importance to both the computer scientists and IT

industry professionals

3. If there are more than one algorithm to solve a given

problem, these algorithms can be compared along the

dimensions of time and memory-space complexities

4. It is at times possible to find a better algorithm to a givenproblem which takes less time and consumes less memory-

space; sometimes, there is a trade-off and one can choose

the best-fit algorithm for a given situation


14/17

Algorithms

Why to analyze algorithms?

1. The complexity of an algorithm is typically analyzed along

the dimensions of

1. Time taken

2. Memory-space taken

to solve a typical average type instance / the worst-case

instance / the best-case instance of the given problem

2. The time or memory-space taken by a digital computer to

solve an instance of the problem (a given set of inputs

define an instance of the problem) using a particularalgorithm does NOT offer any definitive views on the

complexity of an algorithm

3. A theory & notation on the Order of Complexity wasinvented as a means to compare algorithms


15/17

Algorithms

Design and selection of Data Structures has a major

impact on the Complexity of an algorithm


16/17

Characteristics of a Good S/W Program

1. Reliable

2. Efficient / Scalable

3. Readable / Maintainable / Extensible

4. Portable


17/17

Assignments of Class # 1

1. Send a write-up on who invented calculus and why it

was invented?

2. Write a Computer Program that reads three integersas input and determines whether these three

integers constitute the sides of a triangle or not.

3. Who invented Quick-Sort algorithm?

Send your C language based program to my email-id:

[email protected]

ds and algorithims

Documents