DATA STRUCTURE AND

ALGORITHM ANALYSIS

WHAT ARE DATA STRUCTURES

AND ALGORITHMS?

DATA STRUCTURE It is a way of storing data in a computer

so that it can be used efficiently. Is a collection of data objects and a set

of legal operations to be performed on them.

method of organizing large amounts of data

Filing cabinets with alphabetized folders

The correct choice of data structure allows major improvements in program efficiency.

ALGORITHM manipulate the data in these structures in

various ways, such as inserting anew data item, searching for a particular item, or sorting the items.

You can think of analgorithm as a recipe: a list of detailed instructions for carrying out an activity.

Step-by-step procedure used to solve a problem These steps should be capable of being

performed by a machine Must eventually stop and so produce an answer

WHAT SORTS OF PROBLEMS CAN YOU SOLVE WITH A KNOWLEDGE OF THESE TOPICS?

they’re useful into three categories:

- Real-world data storage- Programmer’s tools- Modeling

REAL-WORLD DATA STORAGE Some examples are a personnel record that

describes an actual human being, an inventory record that describes an existing car part or grocery item, and a financial transaction record.

A non-computer example of real-world data storage is a stack of index cards.(address book or home inventory)

PROGRAMMER’S TOOLS

Not all data storage structures are used to store real-world data.

Typically, real-world data is accessed more or less directly by a program’s user.

However, some data storage structures are not meant to be accessed by the user, but by the program itself.

A programmer uses such structures as tools to facilitate some other operation.

Stacks, queues, and priority queues are often used in this way.

REAL-WORLD MODELING

Some data structures directly model a real-world situation.

Stacks, queues, and priority queues are often used for this purpose.

A queue, for example, can model customers waiting in line at a bank, whereas a priority queue can model messages waiting to be transmitted over a local area network

OVERVIEW OF DATA STRUCTURE

OVERVIEW OF DATA STRUCTURE

OVERVIEW OF ALGORITHM Many of the algorithms apply directly to

specific data structures. For most data structures, you must know how

to do the following:● Insert a new data item.● Search for a specified item.● Delete a specified item.● traverse through all the items in a data structure

●Sorting● Recursion

ALGORITHM ANALYSIS

Analysis: How to predict an algorithm’s performance How well an algorithm scales up How to compare different algorithms for a problem

Data Structures How to efficiently store, access, manage data Data structures effect algorithm’s performance

EXAMPLE ALGORITHMS Two algorithms for computing the Factorial Which one is better?

int factorial (int n) { if (n <= 1) return 1; else return n * factorial(n-1);}

int factorial (int n) { if (n<=1) return 1; else { fact = 1; for (k=2; k<=n; k++) fact *= k; return fact; }}

EXAMPLES OF FAMOUS ALGORITHMS Constructions of Euclid Newton's root finding Fast Fourier Transform Compression (Huffman, Lempel-Ziv, GIF, MPEG) DES, RSA encryption Simplex algorithm for linear programming Shortest Path Algorithms (Dijkstra, Bellman-Ford) Error correcting codes (CDs, DVDs) TCP congestion control, IP routing Pattern matching (Genomics) Search Engines

ROLE OF ALGORITHMS IN MODERN WORLD Enormous amount of data

E-commerce (Amazon, Ebay) Network traffic (telecom billing, monitoring) Database transactions (Sales, inventory) Scientific measurements (astrophysics, geology) Sensor networks. RFID tags Bioinformatics (genome, protein bank)

Amazon hired first Chief Algorithms Officer (Udi Manber)

A REAL-WORLD PROBLEM Communication in the Internet Message (email, ftp) broken down into IP

packets. Sender/receiver identified by IP address. The packets are routed through the Internet

by special computers called Routers. Each packet is stamped with its destination

address, but not the route. Because the Internet topology and network

load is constantly changing, routers must discover routes dynamically.

What should the Routing Table look like?

HOW TO MEASURE ALGORITHM PERFORMANCE What metric should be used to judge

algorithms? Length of the program (lines of code) Ease of programming (bugs, maintenance) Memory required Running time

Running time is the dominant standard. Quantifiable and easy to compare Often the critical bottleneck

PRIMITIVE TYPESare data types provided by a

programming language as basic building blocks. Primitive types are also known as built-in types or basic types.

PRIMITIVE TYPESCharacter IntegerStringDoubleFloatArray

SPECIAL TYPES

IntegerIs used to refer a data type which

represents some finite subset of mathematical integers.

Also known as integral data types.

Integral Types:UnsignedSigned

Binary Coded DecimalIt is another representation of integer which is commonly used in mainframe financial applications and in database.

StringIs an ordered sequence of

symbols.

Binary string

Byte string

Are used to suggest strings in which the stored data does not represent text.

Double Double precision is a computer

numbering format that occupies two adjacent location in computer memory.

DoubleorDouble precision number

Defined to be an integer, fixed point, or floating point.

Floatdescribes a system for numerical

representation in which a string of digits (or bits) represents a real number.

The term floating point refers to the fact that the radix point (decimal point, or, more commonly in computers, binary point) can "float": that is, it can be placed anywhere relative to the significant digits of the number

ArrayIs a data structure consisting of a

group that are accessed by indexing.

Classification of ArrayFixed-sized arraysDynamic arrays

DIFFERENT ALGORITHMS FOR SAME PROBLEM

Devise an algorithm to find the solution to a number raised to a positive powereg 45or 10 3 ie number power

1 set answer to 12 Loop 1 to power times

2.1 answer becomes answer * number3 report answer

Notice the layout and numbering

FIND THE RESULT OF NUMBER POWER

1 Set answer to 12 Loop for 1 to 5 times

2.1 answer becomes answer * 2

3 Report answer

AnswerLoop

1 12 24 38 416 532 ?

2 5 3 4

1 Set answer to 12 Loop for 1 to 4 times

2.1 answer becomes answer * 3

3 Report answerAnswer

Loop1 13 29 327 481 ?