This document discusses data structures and algorithms. It provides grading schemes for theory and lab components. It acknowledges reference sources used to prepare the lecture. Key points covered include: what data structures are and why they are important for organizing data efficiently; characteristics of good data structures like time and space complexity; definitions of algorithms and examples like searching and sorting; and algorithmic notations used to describe processes like linear and binary search of arrays.
This document discusses data structures and their role in organizing data efficiently for computer programs. It defines key concepts like abstract data types, algorithms, and problems. It also provides examples to illustrate selecting the appropriate data structure based on the operations and constraints of a problem. A banking application is used to demonstrate how hash tables are suitable because they allow extremely fast searching by account numbers while also supporting efficient insertion and deletion. B-trees are shown to be better than hash tables for a city database because they enable fast range queries in addition to exact searches. Overall, the document emphasizes that each data structure has costs and benefits, and a careful analysis is needed to determine the best structure for a given problem.
This document provides an introduction to data structures and algorithms. It defines key concepts such as data structures, abstract data types, abstraction, and algorithms. Data structures are used to organize data in memory to solve problems, while algorithms are the step-by-step processes used to manipulate data structures. Programs consist of both data structures and algorithms. The document also outlines properties that algorithms must have such as being finite, definite, sequential, feasible, correct, independent of language, complete, effective, and having specified input/output.
The document discusses data structures and their importance in organizing data efficiently for computer programs. It defines what a data structure is and how choosing the right one can improve a program's performance. Several examples are provided to illustrate how analyzing a problem's specific needs guides the selection of an optimal data structure.
The document discusses data structures and their importance in organizing data efficiently for computer programs. It defines what a data structure is and how choosing the right one can improve a program's performance. Several examples are provided to illustrate how analyzing a problem's specific needs guides the selection of an optimal data structure.
Introduction to Data structure and algorithm.pptxline24arts
This document discusses data structures and algorithms. It begins by outlining the key topics that will be covered, including explaining data structures, their operations and classifications, algorithm time complexity, and calculating time complexity. It then defines fundamental concepts like data, entities, records and files. The rest of the document provides examples of different data structures and algorithms, and analyzes their time complexities using Big O notation. It explains concepts like linear, logarithmic and quadratic time complexity through worked examples.
This document introduces key concepts related to data structures and algorithms. It defines objectives like introducing commonly used data structures and selecting the best one for a given problem. It describes how abstraction is used to model problems and define abstract data types independently of programming languages. Data structures provide a physical implementation of abstract data types by organizing data in memory. Algorithms manipulate data structures to transform their state and produce outputs. Properties like finiteness, definiteness, correctness, and efficiency are discussed for algorithms. Measuring an algorithm's theoretical efficiency using asymptotic analysis is introduced.
This document describes a parallel implementation of the Apriori algorithm for frequent itemset mining using MapReduce. The key steps are: (1) The Apriori algorithm is broken down into independent mapping tasks to count candidate itemset occurrences in parallel; (2) A MapReduce job is used for each iteration where the map function counts occurrences and the reduce function sums the counts; (3) Experimental results on real datasets show the approach achieves good speedup, scaleup, and can efficiently process large datasets in a distributed manner.
This document discusses data structures and their role in organizing data efficiently for computer programs. It defines key concepts like abstract data types, algorithms, and problems. It also provides examples to illustrate selecting the appropriate data structure based on the operations and constraints of a problem. A banking application is used to demonstrate how hash tables are suitable because they allow extremely fast searching by account numbers while also supporting efficient insertion and deletion. B-trees are shown to be better than hash tables for a city database because they enable fast range queries in addition to exact searches. Overall, the document emphasizes that each data structure has costs and benefits, and a careful analysis is needed to determine the best structure for a given problem.
This document provides an introduction to data structures and algorithms. It defines key concepts such as data structures, abstract data types, abstraction, and algorithms. Data structures are used to organize data in memory to solve problems, while algorithms are the step-by-step processes used to manipulate data structures. Programs consist of both data structures and algorithms. The document also outlines properties that algorithms must have such as being finite, definite, sequential, feasible, correct, independent of language, complete, effective, and having specified input/output.
The document discusses data structures and their importance in organizing data efficiently for computer programs. It defines what a data structure is and how choosing the right one can improve a program's performance. Several examples are provided to illustrate how analyzing a problem's specific needs guides the selection of an optimal data structure.
The document discusses data structures and their importance in organizing data efficiently for computer programs. It defines what a data structure is and how choosing the right one can improve a program's performance. Several examples are provided to illustrate how analyzing a problem's specific needs guides the selection of an optimal data structure.
Introduction to Data structure and algorithm.pptxline24arts
This document discusses data structures and algorithms. It begins by outlining the key topics that will be covered, including explaining data structures, their operations and classifications, algorithm time complexity, and calculating time complexity. It then defines fundamental concepts like data, entities, records and files. The rest of the document provides examples of different data structures and algorithms, and analyzes their time complexities using Big O notation. It explains concepts like linear, logarithmic and quadratic time complexity through worked examples.
This document introduces key concepts related to data structures and algorithms. It defines objectives like introducing commonly used data structures and selecting the best one for a given problem. It describes how abstraction is used to model problems and define abstract data types independently of programming languages. Data structures provide a physical implementation of abstract data types by organizing data in memory. Algorithms manipulate data structures to transform their state and produce outputs. Properties like finiteness, definiteness, correctness, and efficiency are discussed for algorithms. Measuring an algorithm's theoretical efficiency using asymptotic analysis is introduced.
This document describes a parallel implementation of the Apriori algorithm for frequent itemset mining using MapReduce. The key steps are: (1) The Apriori algorithm is broken down into independent mapping tasks to count candidate itemset occurrences in parallel; (2) A MapReduce job is used for each iteration where the map function counts occurrences and the reduce function sums the counts; (3) Experimental results on real datasets show the approach achieves good speedup, scaleup, and can efficiently process large datasets in a distributed manner.
The document discusses algorithms and data structures. It begins by introducing common data structures like arrays, stacks, queues, trees, and hash tables. It then explains that data structures allow for organizing data in a way that can be efficiently processed and accessed. The document concludes by stating that the choice of data structure depends on effectively representing real-world relationships while allowing simple processing of the data.
This document provides an introduction to data structures and algorithms. It defines data structures as organized ways to store and access data to enable efficient operations. Common data structures include linked lists, trees, graphs, and stacks and queues. The document also defines algorithms as step-by-step instructions to solve problems and discusses ways to analyze their time and space complexity, such as using Big O notation. Specific algorithms covered include bubble sort, insertion sort, and quicksort.
The document provides an introduction to data structures and algorithms analysis. It discusses that a program consists of organizing data in a structure and a sequence of steps or algorithm to solve a problem. A data structure is how data is organized in memory and an algorithm is the step-by-step process. It describes abstraction as focusing on relevant problem properties to define entities called abstract data types that specify what can be stored and operations performed. Algorithms transform data structures from one state to another and are analyzed based on their time and space complexity.
The document discusses algorithms and data structures. It defines an algorithm as a step-by-step procedure for solving a problem using a computer in a finite number of steps. It categorizes common types of algorithms as search, sort, insert, update, and delete algorithms. The document also defines a data structure as a way to store and organize data for efficient use. It distinguishes between linear and non-linear as well as static and dynamic data structures. Finally, it discusses algorithm design strategies like divide and conquer, merge sort, and dynamic programming.
This document provides an overview of an introductory course on algorithms and data structures. It discusses key topics that will be covered including introduction to algorithms, complexity analysis, algorithm design strategies like divide and conquer, and data structures. Specific examples of algorithms and data structures are provided like sorting, searching, linked lists, stacks, queues, trees and graphs. Implementation tools for algorithms like pseudo code and flowcharts are also introduced.
This document provides an introduction to data structures and algorithms. It discusses why they are important for programming and problem solving. It defines key concepts like abstract data types, data structures, algorithms, and algorithm analysis. It also covers different ways of classifying data structures and analyzing the time and space complexity of algorithms. The goal is to help students understand fundamental concepts around organizing data and designing efficient computational procedures.
The document discusses data structures and algorithms. It defines data structures and different types including primitive and non-primitive structures. It describes operations on data structures like traversing, searching, insertion and deletion. It also defines concepts like abstract data types, asymptotic analysis, and different algorithm analysis methods. Examples provided include linear search algorithm and binary search algorithm in pseudocode and C code.
Data may be organized in many different ways; the logical or mathematical model of a particular organization of data is called "Data Structure". The choice of a particular data model depends on two considerations:
It must be rich enough in structure to reflect the actual relationships of the data in the real world.
The structure should be simple enough that one can effectively process the data when necessary.
Data Structure Operations
The particular data structure that one chooses for a given situation depends largely on the nature of specific operations to be performed.
The following are the four major operations associated with any data structure:
i. Traversing : Accessing each record exactly once so that certain items in the record may be processed.
ii. Searching : Finding the location of the record with a given key value, or finding the locations of all records which satisfy one or more conditions.
iii. Inserting : Adding a new record to the structure.
iv. Deleting : Removing a record from the structure.
Primitive and Composite Data Types
Primitive Data Types are Basic data types of any language. In most computers these are native to the machine's hardware.
Some Primitive data types are:
Integer
Bca ii dfs u-1 introduction to data structureRai University
This document provides an introduction to data structures. It defines data structures as a way of organizing and storing data in a computer so it can be used efficiently. There are two main types: primitive data structures like integers and characters that are directly operated on by the CPU, and non-primitive structures like arrays and linked lists that are more complex. Key aspects of data structures covered include operations, properties, performance analysis using time and space complexity, and examples of linear structures like arrays and non-linear structures like trees. Common algorithms are analyzed based on their asymptotic worst-case running times.
Chapter 1 Introduction to Data Structures and Algorithms.pdfAxmedcarb
Data structures provide an efficient way to store and organize data in a computer so that it can be used efficiently. They allow programmers to handle data in an enhanced way, improving software performance. There are linear data structures like arrays and linked lists, and non-linear structures like trees and graphs. Common operations on data structures include insertion, deletion, searching, sorting, and merging. Asymptotic analysis is used to define the time complexity of algorithms in the average, best, and worst cases.
Mca ii dfs u-1 introduction to data structureRai University
This document provides an introduction to data structures. It defines data structures as a way of organizing and storing data in a computer so that it can be used efficiently. The document discusses different types of data structures including primitive, non-primitive, linear and non-linear structures. It provides examples of various data structures like arrays, linked lists, stacks, queues and trees. It also covers important concepts like time complexity, space complexity and Big O notation for analyzing algorithms. Common operations on data structures like search, insert and delete are also explained.
Rajat Kumar submitted a project report for partial fulfillment of his B.Tech degree in computer science from Lovely Professional University. The project involved developing a snake game where the player moves a snake to eat fruit without touching itself or the border, which ends the game. The report provided background on data structures, algorithms, common data structures like stacks and queues, and algorithm design techniques like recursion, dynamic programming, and backtracking. It concluded that data structures are important tools that enable efficient information storage, data management, and algorithm design.
This document describes a course on data structures and algorithms. The course covers fundamental algorithms like sorting and searching as well as data structures including arrays, linked lists, stacks, queues, trees, and graphs. Students will learn to analyze algorithms for efficiency, apply techniques like recursion and induction, and complete programming assignments implementing various data structures and algorithms. The course aims to enhance students' skills in algorithm design, implementation, and complexity analysis. It is worth 4 credits and has prerequisites in computer programming. Student work will be graded based on assignments, exams, attendance, and a final exam.
This document provides an overview of a Data Structures course. The course will cover basic data structures and algorithms used in software development. Students will learn about common data structures like lists, stacks, and queues; analyze the runtime of algorithms; and practice implementing data structures. The goal is for students to understand which data structures are appropriate for different problems and be able to justify design decisions. Key concepts covered include abstract data types, asymptotic analysis to evaluate algorithms, and the tradeoffs involved in choosing different data structure implementations.
This document provides an introduction to the CSE 326: Data Structures course. It discusses the following key points in 3 sentences or less:
The course will cover common data structures and algorithms, how to choose the appropriate data structure for different needs, and how to justify design decisions through formal reasoning. It aims to help students become better developers by understanding fundamental data structures and when to apply them. The document provides examples of stacks and queues to illustrate abstract data types, data structures, and their implementations in different programming languages.
This document provides an introduction to the CSE 326: Data Structures course. It discusses the following key points in 3 sentences or less:
The course will cover common data structures and algorithms, how to choose the appropriate data structure for different needs, and how to justify design decisions through formal reasoning. It aims to help students become better developers by understanding fundamental data structures and when to apply them. The document provides examples of stacks and queues to illustrate abstract data types, data structures, and their implementations in different programming languages.
This document provides information about getting fully solved assignments from an assignment help service. It includes contact information for the service via email or phone call. It also provides a sample assignment question from the subject of Data Structure and Algorithm for BCA semester 2. The sample assignment includes 6 questions ranging from explaining common data structure operations and algorithms like insertion sort to defining concepts like NP-completeness, queues, and the greedy method strategy. Students are encouraged to contact the provided email or phone number to receive solved assignments.
Bsc cs ii dfs u-1 introduction to data structureRai University
This document provides an introduction to data structures. It defines data structures as a way of organizing and storing data in a computer so it can be used efficiently. The document discusses different types of data structures including primitive, non-primitive, linear and non-linear structures. It provides examples of common data structures like arrays, linked lists, stacks, queues and trees. It also covers important concepts like time and space complexity analysis and Big O notation for analyzing algorithm efficiency.
Data Structures and Algorithm - Module 1.pptxEllenGrace9
This document provides an introduction to data structures and algorithms from instructor Ellen Grace Porras. It defines data structures as ways of organizing data to allow for efficient operations. Linear data structures like arrays, stacks, and queues arrange elements sequentially, while non-linear structures like trees and graphs have hierarchical relationships. The document discusses characteristics of good data structures and algorithms, provides examples of common algorithms, and distinguishes between linear and non-linear data structures. It aims to explain the fundamentals of data structures and algorithms.
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In the ever-evolving landscape of cybersecurity, safeguarding sensitive data and critical systems has become paramount. As cyber threats grow in sophistication, organizations are constantly seeking innovative methods to fortify their defenses. Multi-Factor Authentication (MFA) stands out as a potent tool within the security arsenal, particularly when integrated with Privileged Access Management (PAM).
Privileged access management encompasses the methods, protocols, and tools employed to regulate and monitor access to privileged accounts within an organization. These accounts wield elevated privileges, enabling users to execute vital operations such as system configuration, access to sensitive data, and management of network infrastructure. However, if these privileges fall into the wrong hands, they pose a significant security risk. MFA adds an additional layer of protection by requiring users to provide multiple forms of verification before gaining access to a system or application. Key components of MFA in PAM include biometric verification, passwords, security tokens, and one-time passcodes. Deploying MFA within a PAM environment necessitates meticulous planning and consideration of various factors to ensure robust security.
The document discusses algorithms and data structures. It begins by introducing common data structures like arrays, stacks, queues, trees, and hash tables. It then explains that data structures allow for organizing data in a way that can be efficiently processed and accessed. The document concludes by stating that the choice of data structure depends on effectively representing real-world relationships while allowing simple processing of the data.
This document provides an introduction to data structures and algorithms. It defines data structures as organized ways to store and access data to enable efficient operations. Common data structures include linked lists, trees, graphs, and stacks and queues. The document also defines algorithms as step-by-step instructions to solve problems and discusses ways to analyze their time and space complexity, such as using Big O notation. Specific algorithms covered include bubble sort, insertion sort, and quicksort.
The document provides an introduction to data structures and algorithms analysis. It discusses that a program consists of organizing data in a structure and a sequence of steps or algorithm to solve a problem. A data structure is how data is organized in memory and an algorithm is the step-by-step process. It describes abstraction as focusing on relevant problem properties to define entities called abstract data types that specify what can be stored and operations performed. Algorithms transform data structures from one state to another and are analyzed based on their time and space complexity.
The document discusses algorithms and data structures. It defines an algorithm as a step-by-step procedure for solving a problem using a computer in a finite number of steps. It categorizes common types of algorithms as search, sort, insert, update, and delete algorithms. The document also defines a data structure as a way to store and organize data for efficient use. It distinguishes between linear and non-linear as well as static and dynamic data structures. Finally, it discusses algorithm design strategies like divide and conquer, merge sort, and dynamic programming.
This document provides an overview of an introductory course on algorithms and data structures. It discusses key topics that will be covered including introduction to algorithms, complexity analysis, algorithm design strategies like divide and conquer, and data structures. Specific examples of algorithms and data structures are provided like sorting, searching, linked lists, stacks, queues, trees and graphs. Implementation tools for algorithms like pseudo code and flowcharts are also introduced.
This document provides an introduction to data structures and algorithms. It discusses why they are important for programming and problem solving. It defines key concepts like abstract data types, data structures, algorithms, and algorithm analysis. It also covers different ways of classifying data structures and analyzing the time and space complexity of algorithms. The goal is to help students understand fundamental concepts around organizing data and designing efficient computational procedures.
The document discusses data structures and algorithms. It defines data structures and different types including primitive and non-primitive structures. It describes operations on data structures like traversing, searching, insertion and deletion. It also defines concepts like abstract data types, asymptotic analysis, and different algorithm analysis methods. Examples provided include linear search algorithm and binary search algorithm in pseudocode and C code.
Data may be organized in many different ways; the logical or mathematical model of a particular organization of data is called "Data Structure". The choice of a particular data model depends on two considerations:
It must be rich enough in structure to reflect the actual relationships of the data in the real world.
The structure should be simple enough that one can effectively process the data when necessary.
Data Structure Operations
The particular data structure that one chooses for a given situation depends largely on the nature of specific operations to be performed.
The following are the four major operations associated with any data structure:
i. Traversing : Accessing each record exactly once so that certain items in the record may be processed.
ii. Searching : Finding the location of the record with a given key value, or finding the locations of all records which satisfy one or more conditions.
iii. Inserting : Adding a new record to the structure.
iv. Deleting : Removing a record from the structure.
Primitive and Composite Data Types
Primitive Data Types are Basic data types of any language. In most computers these are native to the machine's hardware.
Some Primitive data types are:
Integer
Bca ii dfs u-1 introduction to data structureRai University
This document provides an introduction to data structures. It defines data structures as a way of organizing and storing data in a computer so it can be used efficiently. There are two main types: primitive data structures like integers and characters that are directly operated on by the CPU, and non-primitive structures like arrays and linked lists that are more complex. Key aspects of data structures covered include operations, properties, performance analysis using time and space complexity, and examples of linear structures like arrays and non-linear structures like trees. Common algorithms are analyzed based on their asymptotic worst-case running times.
Chapter 1 Introduction to Data Structures and Algorithms.pdfAxmedcarb
Data structures provide an efficient way to store and organize data in a computer so that it can be used efficiently. They allow programmers to handle data in an enhanced way, improving software performance. There are linear data structures like arrays and linked lists, and non-linear structures like trees and graphs. Common operations on data structures include insertion, deletion, searching, sorting, and merging. Asymptotic analysis is used to define the time complexity of algorithms in the average, best, and worst cases.
Mca ii dfs u-1 introduction to data structureRai University
This document provides an introduction to data structures. It defines data structures as a way of organizing and storing data in a computer so that it can be used efficiently. The document discusses different types of data structures including primitive, non-primitive, linear and non-linear structures. It provides examples of various data structures like arrays, linked lists, stacks, queues and trees. It also covers important concepts like time complexity, space complexity and Big O notation for analyzing algorithms. Common operations on data structures like search, insert and delete are also explained.
Rajat Kumar submitted a project report for partial fulfillment of his B.Tech degree in computer science from Lovely Professional University. The project involved developing a snake game where the player moves a snake to eat fruit without touching itself or the border, which ends the game. The report provided background on data structures, algorithms, common data structures like stacks and queues, and algorithm design techniques like recursion, dynamic programming, and backtracking. It concluded that data structures are important tools that enable efficient information storage, data management, and algorithm design.
This document describes a course on data structures and algorithms. The course covers fundamental algorithms like sorting and searching as well as data structures including arrays, linked lists, stacks, queues, trees, and graphs. Students will learn to analyze algorithms for efficiency, apply techniques like recursion and induction, and complete programming assignments implementing various data structures and algorithms. The course aims to enhance students' skills in algorithm design, implementation, and complexity analysis. It is worth 4 credits and has prerequisites in computer programming. Student work will be graded based on assignments, exams, attendance, and a final exam.
This document provides an overview of a Data Structures course. The course will cover basic data structures and algorithms used in software development. Students will learn about common data structures like lists, stacks, and queues; analyze the runtime of algorithms; and practice implementing data structures. The goal is for students to understand which data structures are appropriate for different problems and be able to justify design decisions. Key concepts covered include abstract data types, asymptotic analysis to evaluate algorithms, and the tradeoffs involved in choosing different data structure implementations.
This document provides an introduction to the CSE 326: Data Structures course. It discusses the following key points in 3 sentences or less:
The course will cover common data structures and algorithms, how to choose the appropriate data structure for different needs, and how to justify design decisions through formal reasoning. It aims to help students become better developers by understanding fundamental data structures and when to apply them. The document provides examples of stacks and queues to illustrate abstract data types, data structures, and their implementations in different programming languages.
This document provides an introduction to the CSE 326: Data Structures course. It discusses the following key points in 3 sentences or less:
The course will cover common data structures and algorithms, how to choose the appropriate data structure for different needs, and how to justify design decisions through formal reasoning. It aims to help students become better developers by understanding fundamental data structures and when to apply them. The document provides examples of stacks and queues to illustrate abstract data types, data structures, and their implementations in different programming languages.
This document provides information about getting fully solved assignments from an assignment help service. It includes contact information for the service via email or phone call. It also provides a sample assignment question from the subject of Data Structure and Algorithm for BCA semester 2. The sample assignment includes 6 questions ranging from explaining common data structure operations and algorithms like insertion sort to defining concepts like NP-completeness, queues, and the greedy method strategy. Students are encouraged to contact the provided email or phone number to receive solved assignments.
Bsc cs ii dfs u-1 introduction to data structureRai University
This document provides an introduction to data structures. It defines data structures as a way of organizing and storing data in a computer so it can be used efficiently. The document discusses different types of data structures including primitive, non-primitive, linear and non-linear structures. It provides examples of common data structures like arrays, linked lists, stacks, queues and trees. It also covers important concepts like time and space complexity analysis and Big O notation for analyzing algorithm efficiency.
Data Structures and Algorithm - Module 1.pptxEllenGrace9
This document provides an introduction to data structures and algorithms from instructor Ellen Grace Porras. It defines data structures as ways of organizing data to allow for efficient operations. Linear data structures like arrays, stacks, and queues arrange elements sequentially, while non-linear structures like trees and graphs have hierarchical relationships. The document discusses characteristics of good data structures and algorithms, provides examples of common algorithms, and distinguishes between linear and non-linear data structures. It aims to explain the fundamentals of data structures and algorithms.
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2. Grading Theory
Mid Term 25%
Final 50%
Programming Assignments 10%
Surprise Quiz's 05%
Project 10%
3. Grading Lab
Mid Term 25%
Final 50%
Programming Project 20%
Presentation and viva voca 05%
4. Acknowledgement
This Lecture has been prepared from your Reference Course Book titled as
“Data Structure” by Schaum Series.
Other source includes tutorialpoint page and google pages
4
5. What is Data Structures
Data Structures are the programmatic way of storing data so that
data can be used efficiently.
Almost every enterprise application uses various types of data
structures in one or the other way.
5
6. Why to Learn Data Structure and
Algorithms?
As applications are getting complex and data rich, there are three
common problems that applications face now-a-days.
1. Data Search
2. Processor speed
3. Multiple requests
6
7. Why to Learn Data Structure and
Algorithms?
Data Search − Consider an inventory of 1 million(106) items of a
store. If the application is to search an item, it has to search an item
in 1 million(106) items every time slowing down the search. As data
grows, search will become slower.
7
8. Why to Learn Data Structure and
Algorithms?
Processor speed − Processor speed although being very high, falls
limited if the data grows to billion records.
Multiple requests − As thousands of users can search data
simultaneously on a web server, even the fast server fails while
searching the data.
8
9. Why to Learn Data Structure and
Algorithms?
To solve these mentioned problems, data structures come to rescue.
Data can be organized in a data structure in such a way that all items
may not be required to be searched, and the required data can be
searched almost instantly.
9
10. Data Structure: Foundation terms
Interface − Each data structure has an interface. Interface represents
the set of operations that a data structure supports. An interface only
provides the list of supported operations, type of parameters they can
accept and return type of these operations.
10
11. Data Structure: Foundation terms
Implementation − Implementation provides the internal
representation of a data structure.
Implementation also provides the definition of the algorithms used in
the operations of the data structure.
11
12. Characteristics of a Data Structure
1. Correctness − Data structure implementation
should implement its interface correctly.
2. Time Complexity − Running time or the execution
time of operations of data structure must be as
small as possible.
3. Space Complexity − Memory usage of a data
structure operation should be as little as possible.
12
13. What is an Algorithm?
The word algorithm comes from the name of a Persian author, Abu Ja’far
Mohammed ibn Musa al Khowarizmi (c. 825 A.O.) who wrote a textbook on
mathematics.
An examination of the latest edition of Webster's dictionary defines its
meaning as "any special method of solving a certain kind of problem.
13
14. Definition of “Algorithm”
An Algorithm, intuitively speaking, is a finite step-by-step list of well
defined instructions for solving a particular problem.
An algorithm is a clearly specified set of simple instructions to be
followed to solve a problem.
14
15. Definition of “Algorithm”
Algorithms are generally created independent of underlying languages,
i.e. an algorithm can be implemented in more than one programming
language.
15
16. Definition of “Algorithm”
From the data structure point of view, following
are some important categories of algorithms −
1. Search − Algorithm to search an item in a data
structure.
2. Sort − Algorithm to sort items in a certain order.
3. Insert − Algorithm to insert item in a data structure.
4. Update − Algorithm to update an existing item in a data
structure.
5. Delete − Algorithm to delete an existing item from a
data structure.
16
17. Properties or Constraints
For example, each operation must be definite, meaning that it must
be perfectly clear what should be done.
Directions such as "compute 5/0" or "add 6 or 7 to x" are not permitted
because it is not clear what the result is or which of the two possibilities
should be done.
17
18. Properties or Constraints
Another important property each operation should have is that it be
effective; each step must be such that it can, at least in principle, be
done by a person using pencil and paper in a finite amount of time.
Arithmetic operations on integer is an effective while on some real
numbers its not……
18
19. Properties or Constraints
An algorithm produces one or more outputs and may have zero or
more inputs which are externally supplied.
Another important criterion we will assume about algorithms is that
they terminate after a finite number of operations.
19
20. Algorithmic Notations
In coming slides you will learn the format that is used to present
algorithms throughout this course. This is best describes by means of an
example.
Example: An array DATA of numerical values is in memory. We want to
find the location LOC and the value MAX of the largest element of DATA.
20
21. Algorithmic Notations
Initially begin with LOC = 1 and MAX = DATA
[1]. Then compare MAX with each successive
element DATA[K] of DATA.
If DATA[K] exceeds MAX then update LOC and
MAX so that LOC = K and MAX = DATA [K].
The final values appearing in LOC and MAX give
the location and value of the largest element
of DATA. 21
25. Algorithmic Notations: The Solution of the
Quadratic Equation
The quantity D = b2 – 4ac is called the
discriminant of the equation. If D is negative,
then there are no real solutions.
If D = 0, then there is only one (double) real
solution , x = -b/2a
If D is positive, the formula gives the two
distinct real solutions.
27. Algorithmic Notations: Linear Search
Suppose a linear array DATA contains n elements,
and suppose a specific ITEM of information is given.
We want either to find the location LOC of item in
the array DATA, or to send some message, such as
LOC = 0, to indicate that ITEM is not in the DATA.
The linear search algorithm solves this problem by
comparing ITEM, one by one, with each element in
DATA. That is we compare ITEM with DATA[1],
DATA[2], and so on, until we find LOC such that ITEM
= DATA [LOC].
Algorithm 2.4
29. Algorithmic Notations: Binary Search
During each stage of binary search algorithm our search
for ITEM is reduced to a segment of elements of DATA
The BEG and END denote respectively the beginning and
end location of segment under consideration. Where
BEG = 1 or LB and END = n or UB
The Algorithm compares ITEM with the middle element
DATA[MID] of segment where MID is obtained by
MID = INT (BEG + END ) /2
30. Algorithmic Notations: Binary Search
If DATA [MID] = ITEM then search is successful and we
set LOC = MID, otherwise a new segment of DATA is
obtained as follow
A) If ITEM < DATA [MID] then ITEM can appear on left
side of segment
DATA [BEG] , DATA [BEG+1] … DATA[MID -1]
B) If ITEM > DATA [MID] then ITEM can appear in right half of the
segment
DATA [MID] , DATA [MID+1] … DATA[END]
31. Algorithmic Notations: Binary Search
• If ITEM is not in DATA then eventually we obtain
END < BEG
• This condition signals that the search is unsuccessful, and in such case we assign LOC =
NULL.
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