ds 1 Introduction to Data Structures.ppt

Introduction to Data Structures

Introduction
• Data means value or set of values . Data items refers to a single unit of values.
• Data is represented in the from of text/numbers/figures/ tables/graphs/pictures etc.
A computer Language is incomplete without data.
• Information is derived from data, such as:
per capita income, Average Population of the states , price index ,etc.
Data
Method to
Process data
I
N
F
O
R
M
A
T
I
O
N

Introduction
• In a month we everyday get the newspaper then at the end we can calculate the
bill from the data of the cost of newspaper we daily receive.
• Data about some persons in a group:
• Distance between the two stations:
A 100 km B
Information Details Data
Name Satish
Gender Male
Age 32
Phone 987680987

Introduction
• From the score of an individual cricket player we can draw following information:
• Total Runs Scored
• Highest score
• Average
• Strike rate
• No. of Sixes
• No. of fours
• This information helps the planners/analysts/to make decisions.
• Info. In Computer: A computer is an electronic device that manipulates the
information presented in the form of data.
• Data: Data is nothing but a collection of numbers, alphabets and symbols
combined to represent information.
• Entity: An entity possesses some attributes and some values can be allocated to it.
E.g. student entity in a college.

Overview of Data Structures
• Data Structures are a method of representing of logical relationships between
individual data elements related to the solution of a given problem.
• A data structure is a structured set of variables associated with one another in
different ways, co-operatively defining the components in the system and capable
of being operated upon in the program.
• Data structures are the basis of the programming tools. The choice of data
structures should provide the following:
1. The data structure should satisfactorily represent the relationship between the
data elements.
2. The data structure should be easy so that the programmer can easily process the
data.

Classification of Data Structures
• Linear: The values are arranged in a linear fashion. E.g. Arrays, Linked Lists, Stacks,
Queues etc.
• Non-Linear: The values are not arranged in an order. E.g. Tree, Graph, Table etc.
• Homogeneous: Here all the values stored are of same type e.g. arrays
• Non- Homogeneous: Here all the values stored are of different type e.g. structures and
classes.
• Dynamic:A dynamic data structure is one that can grow or shrink as needed to contain
the data you want stored. That is, you can allocate new storage when it's needed and
discard that storage when you're done with it. E.g. pointers, or references
• Static:They're essentially fixed-size and often use much space E.g. Array

Basic Notations
• Mathematical Notations and Functions:
1. Floor and Ceiling
2. Remainder Function
3. Integer and Absolute Value
4. Summation Symbol
5. Factorial Function
6. Permutations
7. Exponents and Logarithms:
am =a.a.a…a (m times) a0 =1

C++ Program of sum of two numbers
#include<iostream>
Using namespace std;
Main()
{
int a,b,sum;
cout<<“enter a and b”;
cin>> a>>b;
sum=a+b;
cout<<“sum of a and b is “;
cout<<sum;
}

Sum of N numbers
Part 1
#include<iostream>
Using namespace std;
Main()
{
int sum=0;
For(int i=0;i<n;i++)
{
Part 2
cin>>i;
sum=sum +i;
cout<<“sum of n numbers is “;
cout<<sum;
}

Basic Notations
Algorithmic Notations:
Finite step by step list of well-defined instructions for solving a particular problem.
Formal presentation of the Algorithm consists of two parts:
1. A paragraph that tells the purpose of an algorithm. Identifies the variables which occur in the algorithm
and lists the input data.
2. The list of the steps that is to be executed.
Some conventions used in Algorithms:
 Identifying Number (Algorithm 2: )
 Steps, Control and Exit ( All statements are numbered, Go to and Exit)
 Comments (The comments are to be given to understand the meaning)
 Variable Names (capital letters are used for variable names)
 Assignment Statement (Max:=DATA[1])
 Input and output (Read: variable names, Write: Messages and/or variable names)
 Procedure

Basic Notations
Control Structures:
1. Sequential Logic or Sequential Flow
2. Selection Logic or Conditional Flow
• If (condition) , then:
-----
[Endif]
• If (condition) , then:
-----
Else :
-------
[ Endif]

• Multiple If (condition), then : -----
Elseif : -----
Else :
------
[Endif]
3. Iteration Logic (Repetitive Flow)
• for loop =>
Repeat for K=I to N:
[Module] [End of Loop]

• While loop=>
Repeat while K<= N:
(logic)
[end of while loop]

Types of Data Structures
• Arrays:
1. Linear data Structure
2. All elements stored at contiguous memory locations
3. Every element is identified by an index (Logical Address)
4. At the same time every element is identified by a physical address (Physical
Address)
5. We can have 2 D and 3D arrays also but stored in memory in a linear way.

• Stack:
– Only the top item can be accessed
– Can only extract one item at a time
• A stack is a data structure with the property that only the top element of the stack
is accessible
• The stack’s storage policy is Last-In, First-Out
• Only the top element of a stack is visible, therefore the number of operations
performed by a stack are few
• Need the ability to
– Inspect the top element
– Retrieve the top element
– Push a new element on the stack
– Test for an empty stack

• Queue:
• Stores a set of elements in a particular order
• Stack principle: FIRST IN FIRST OUT
• = FIFO
• It means: the first element inserted is the first one to be removed
• Real life examples
– Waiting in line
– Waiting on hold for tech support
• Applications related to Computer Science
– Threads
– Job scheduling (e.g. Round-Robin algorithm for CPU allocation)

Linked Lists
• A linked list is a series of connected nodes
• Each node contains at least
– A piece of data (any type)
– Pointer to the next node in the list
• Head: pointer to the first node
• The last node points to NULL
A 
Head
B C
A
data pointer
node

• Linked List:
1. Linear data structure.
2. Primarily used when the elements are to stored at non-contiguous locations.
1. Linked list is able to grow in size as needed.
2. Does not require the shifting of items during insertions and deletions.

Terminology for a Tree
• Tree: A collection of data whose entries have a hierarchical organization
• Node: An entry in a tree
• Root node: The node at the top
• Terminal or leaf node: A node at the bottom
• Parent: The node immediately above a specified node
• Child: A node immediately below a specified node
• Ancestor: Parent, parent of parent, etc.
• Descendent: Child, child of child, etc.
• Siblings: Nodes sharing a common parent
• Binary tree: A tree in which every node has at most two children
• Depth: The number of nodes in longest path from root to leaf

Graph
• A graph is a pair (V, E), where
– V is a set of nodes, called vertices
– E is a collection of pairs of vertices, called edges
– Vertices and edges are positions and store elements
• Example:
– A vertex represents an airport and stores the three-letter airport code
– An edge represents a flight route between two airports and stores the
mileage of the route
21
Graphs
ORD
PVD
MIA
DFW
SFO
LAX
LGA
HNL

Edge Types
• Directed edge
– ordered pair of vertices (u,v)
– first vertex u is the origin
– second vertex v is the destination
– e.g., a flight
• Undirected edge
– unordered pair of vertices (u,v)
– e.g., a flight route
• Directed graph
– all the edges are directed
– e.g., route network
• Undirected graph
– all the edges are undirected
– e.g., flight network
22
Graphs
ORD PVD
flight
AA 1206
ORD PVD
849
miles

Applications
• Electronic circuits
– Printed circuit board
– Integrated circuit
• Transportation networks
– Highway network
– Flight network
• Computer networks
– Local area network
– Internet
– Web
• Databases
– Entity-relationship diagram
23
Graphs
John
David
Paul
brown.edu
cox.net
cs.brown.edu
att.net
qwest.net
math.brown.edu
cslab1b
cslab1a

Complexity Analysis
and
Time Space Trade-off

Algorithm
• A clearly specified set of instructions to solve a problem.
• Characteristics:
– Input: Zero or more quantities are externally supplied
– Definiteness: Each instruction is clear and unambiguous
– Finiteness: The algorithm terminates in a finite number of steps.
– Effectiveness: Each instruction must be primitive and feasible
– Output: At least one quantity is produced

Need for analysis
• To determine resource consumption
– CPU time
– Memory space
• Compare different methods for solving the same problem
before actually implementing them and running the
programs.
• To find an efficient algorithm

Complexity
• A measure of the performance of an algorithm
• An algorithm’s performance depends on
– internal factors
– external factors

External Factors
• Speed of the computer on which it is run
• Quality of the compiler
• Size of the input to the algorithm

Internal Factor
30
The algorithm’s efficiency, in terms of:
• Time required to run
• Space (memory storage)required to run
Note:
Complexity measures the internal factors (usually more interested in time than
space)

Two ways of finding complexity
• Experimental study
• Theoretical Analysis

Experimental study
• Write a program implementing the algorithm
• Run the program with inputs of varying size and
composition
• Get an accurate measure of the actual running time
Use a method like System.currentTimeMillis()
• Plot the results

Example
 a. Sum=0;
for(i=0;i<N;i++)
for(j=0;j<i;j++)
Sum++;

Example graph
Time in millisec

Limitations of Experiments
• It is necessary to implement the algorithm, which may be
difficult
• Results may not be indicative of the running time on other
inputs not included in the experiment.
• In order to compare two algorithms, the same hardware and
software environments must be used
• Experimental data though important is not sufficient

Theoretical Analysis
• Uses a high-level description of the algorithm instead of an
implementation
• Characterizes running time as a function of the input size, n.
• Takes into account all possible inputs
• Allows us to evaluate the speed of an algorithm independent of
the hardware/software environment

Space Complexity
• The space needed by an algorithm is the sum of a fixed part and
a variable part
• The fixed part includes space for
– Instructions
– Simple variables
– Fixed size component variables
– Space for constants
– Etc..

Cont…
• The variable part includes space for
– Component variables whose size is dependant on the
particular problem instance being solved
– Recursion stack space
– Etc..

Time Complexity
• The time complexity of a problem is
– the number of steps that it takes to solve an instance of the problem as a
function of the size of the input (usually measured in bits), using the most
efficient algorithm.
• The exact number of steps will depend on exactly what machine or language
is being used.
• To avoid that problem, the Asymptotic notation is generally used.

Time Space Trade-off
• In computer science, a space-time or time-memory trade off is a situation
where the memory use can be reduced at the cost of slower program
execution (or, vice versa, the computation time can be reduced at the cost of
increased memory use). As the relative costs of CPU cycles, RAM space, and
hard drive space change — hard drive space has for some time been getting
cheaper at a much faster rate than other components of computers-the
appropriate choices for space-time tradeoffs have changed radically. Often,
by exploiting a space-time tradeoff, a program can be made to run much
faster.

Types of Time Space Trade-off
• Lookup tables v. recalculation
The most common situation is an algorithm involving a lookup table: an
implementation can include the entire table, which reduces computing time,
but increases the amount of memory needed, or it can compute table entries
as needed, increasing computing time, but reducing memory requirements.
• Compressed v. uncompressed data
A space-time trade off can be applied to the problem of data storage. If data is
stored uncompressed, it takes more space but less time than if the data were
stored compressed (since compressing the data reduces the amount of space it
takes, but it takes time to run the decompression algorithm). Depending on
the particular instance of the problem, either way is practical.

ds 1 Introduction to Data Structures.ppt

More Related Content

Similar to ds 1 Introduction to Data Structures.ppt (20)

Recently uploaded (20)

ds 1 Introduction to Data Structures.ppt