data structures introduction

Data Structure

Introduction

v  Data Structure can be defined as the group of data elements which provides an efficient way of storing and organising data in the computer so that it can be used efficiently.

v  Some examples of Data Structures are arrays, Linked List, Stack, Queue, etc.

v  Data Structures are widely used in almost every aspect of Computer Science i.e. Operating System, Compiler Design, Artifical intelligence, Graphics and many more.

Basic Terminology

Data structures are the building blocks of any program or the software. Choosing the appropriate data structure for a program is the most difficult task for a programmer. Following terminology is used as far as data structures are concerned

Data: Data can be defined as an elementary value or the collection of values, for example, student's name and its id are the data about the student.

Group Items: Data items which have subordinate data items are called Group item, for example, name of a student can have first name and the last name.

Record: Record can be defined as the collection of various data items, for example, if we talk about the student entity, then its name, address, course and marks can be grouped together to form the record for the student.

File: A File is a collection of various records of one type of entity, for example, if there are 60 employees in the class, then there will be 20 records in the related file where each record contains the data about each employee.

Attribute and Entity: An entity represents the class of certain objects. it contains various attributes. Each attribute represents the particular property of that entity.

Field: Field is a single elementary unit of information representing the attribute of an entity.

Q) What are the steps required for the Data structures?

Ans)   The organization of data into fields, records and files may not be complex enough to maintain       and efficiently process certain collections of data. For this reason, data are also organized          into more complex types of structures. To learn about these data structures, we have to   follow these three steps:

1. Logical or mathematical description of the structure
2. Implementation of the structure on a computer
3. Quantitative analysis of the structure, which includes determining the amount of memory needed to store the structure and time required to process the structure.(Time and Space Complexity)

Need of Data Structures

As applications are getting complexed and amount of data is increasing day by day, there may arrise the following problems:

Processor speed: To handle very large amout of data, high speed processing is required, but as the data is growing day by day to the billions of files per entity, processor may fail to deal with that much amount of data.

Data Search: Consider an inventory size of 106 items in a store, If our application needs to search for a particular item, it needs to traverse 106 items every time, results in slowing down the search process.

Multiple requests: If thousands of users are searching the data simultaneously on a web server, then there are the chances that a very large server can be failed during that process

in order to solve the above problems, data structures are used. Data is organized to form a data structure in such a way that all items are not required to be searched and required data can be searched instantly.

Advantages of Data Structures

Efficiency: Efficiency of a program depends upon the choice of data structures. For example: suppose, we have some data and we need to perform the search for a perticular record. In that case, if we organize our data in an array, we will have to search sequentially element by element. hence, using array may not be very efficient here. There are better data structures which can make the search process efficient like ordered array, binary search tree or hash tables.

Reusability: Data structures are reusable, i.e. once we have implemented a particular data structure, we can use it at any other place. Implementation of data structures can be compiled into libraries which can be used by different clients.

Abstraction: Data structure is specified by the ADT which provides a level of abstraction. The client program uses the data structure through interface only, without getting into the implementation details.

Data Structure Classification

Linear Data Structures: 

• A data structure is called linear if all of its elements are arranged in the linear order.
• In linear data structures, the elements are stored in non-hierarchical way where each element has the successors and predecessors except the first and last element.

Types of Linear Data Structures are given below:

Arrays: 

• An array is a collection of similar type of data items and each data item is called an element of the array. 
• The data type of the element may be any valid data type like char, int, float or double.
• The elements of array share the same variable name but each one carries a different index number known as subscript. 
• The array can be one dimensional, two dimensional or multidimensional.
• The individual elements of the array age are:age[0], age[1], age[2], age[3],......... age[98], age[99].

Linked List: 

• Linked list is a linear data structure which is used to maintain a list in the memory. 
• It can be seen as the collection of nodes stored at non-contiguous memory locations. 
• Each node of the list contains a pointer to its adjacent node.

Stack: 

• Stack is a linear list in which insertion and deletions are allowed only at one end, called top.
• A stack is an abstract data type (ADT), can be implemented in most of the programming languages. 
• It is named as stack because it behaves like a real-world stack, for example: - piles of plates or deck of cards etc.

Queue: 

• Queue is a linear list in which elements can be inserted only at one end called rear and deleted only at the other end called front.
• It is an abstract data structure, similar to stack. 
• Queue is opened at both end therefore it follows First-In-First-Out (FIFO) methodology for storing the data items.

Non Linear Data Structures: 

• This data structure does not form a sequence i.e. each item or element is connected with two or more other items in a non-linear arrangement. 
• The data elements are not arranged in sequential structure.

Types of Non Linear Data Structures are given below:

Trees: 

• Trees are multilevel data structures with a hierarchical relationship among its elements known as nodes. 
• The bottommost nodes in the herierchy are called leaf node 
• while the topmost node is called root node. 
• Each node contains pointers to point adjacent nodes.
• Tree data structure is based on the parent-child relationship among the nodes. 
• Each node in the tree can have more than one children except the leaf nodes whereas each node can have atmost one parent except the root node. 
• Trees can be classfied into many categories which will be discussed later in this tutorial.

Graphs: 

• Graphs can be defined as the pictorial representation of the set of elements (represented by vertices) connected by the links known as edges.
•  A graph is different from tree in the sense that a graph can have cycle while the tree can not have the one.

Operations on data structure

1) Traversing: Every data structure contains the set of data elements. Traversing the data structure means visiting each element of the data structure in order to perform some specific operation like searching or sorting.

Example: If we need to calculate the average of the marks obtained by a student in 6 different subject, we need to traverse the complete array of marks and calculate the total sum, then we will devide that sum by the number of subjects i.e. 6, in order to find the average.

2) Insertion: Insertion can be defined as the process of adding the elements to the data structure at any location.

If the size of data structure is n then we can only insert n-1 data elements into it.

3) Deletion:The process of removing an element from the data structure is called Deletion. We can delete an element from the data structure at any random location.

If we try to delete an element from an empty data structure then underflow occurs.

4) Searching: The process of finding the location of an element within the data structure is called Searching. There are two algorithms to perform searching, Linear Search and Binary Search. We will discuss each one of them later in this tutorial.

5) Sorting: The process of arranging the data structure in a specific order is known as Sorting. There are many algorithms that can be used to perform sorting, for example, insertion sort, selection sort, bubble sort, etc.

6) Merging: When two lists List A and List B of size M and N respectively, of similar type of elements, clubbed or joined to produce the third list, List C of size (M+N), then this process is called merging

Algorithm

An algorithm is a procedure having well defined steps for solving a particular problem. Algorithm is finite set of logic or instructions, written in order for accomplish the certain predefined task. It is not the complete program or code, it is just a solution (logic) of a problem, which can be represented either as an informal description using a Flowchart or Pseudo code.

The major categories of algorithms are given below:

• Sort: Algorithm developed for sorting the items in certain order.
• Search: Algorithm developed for searching the items inside a data structure.
• Delete: Algorithm developed for deleting the existing element from the data structure.
• Insert: Algorithm developed for inserting an item inside a data structure.
• Update: Algorithm developed for updating the existing element inside a data structure.

The performance of algorithm is measured on the basis of following properties:

• Time complexity: It is a way of representing the amount of time needed by a program to run to the completion.
• Space complexity: It is the amount of memory space required by an algorithm, during a course of its execution. Space complexity is required in situations when limited memory is available and for the multi user system.

Each algorithm must have:

• Specification: Description of the computational procedure.
• Pre-conditions: The condition(s) on input.
• Body of the Algorithm: A sequence of clear and unambiguous instructions.
• Post-conditions: The condition(s) on output.

Example: Design an algorithm to multiply the two numbers x and y and display the result in z.

• Step 1 START
• Step 2 declare three integers x, y & z
• Step 3 define values of x & y
• Step 4 multiply values of x & y
• Step 5 store the output of step 4 in z
• Step 6 print z
• Step 7 STOP

. Alternatively the algorithm can be written as ?

• Step 1 START MULTIPLY
• Step 2 get values of x & y
• Step 3 z← x * y
• Step 4 display z
• Step 5 STOP

Characteristics of an Algorithm

An algorithm must follow the mentioned below characteristics:

• Input: An algorithm must have 0 or well defined inputs.
• Output: An algorithm must have 1 or well defined outputs, and should match with the desired output.
• Feasibility: An algorithm must be terminated after the finite number of steps.
• Independent: An algorithm must have step-by-step directions which is independent of any programming code.
• Unambiguous: An algorithm must be unambiguous and clear. Each of their steps and input/outputs must be clear and lead to only one meaning.

Q) what is an Algorithm and explain its notations?

Ans)

                An algorithm is a step by step list of well-defined instructions for solving a particular problem. Mainly the algorithm consists of two parts namely first part is a paragraph which tells the purpose of the algorithm and identifies the variables which occur in the algorithm and lists the input data. The second part of the algorithm consists of the list of steps that is to be executed. The following are the certain conventions that are used in algorithm.

Algorithm notations:

1. Identifying number: each algorithm is assigned an identifying number as follows; Algorithm 4.3 refers to the third algorithm in chapter 4.

2. Steps, Control, Exit: The steps of the algorithm are executed one after the other, beginning with step1. Control may be transferred to step  n of the algorithm by the statement “Go to step n.” The algorithm is completed when the statement “Exit” is encountered.

3. Comments: each step may contain a comment in brackets which indicates the main purpose of the step. The comment will usually appear at the beginning or the end of the step. In algorithm, Comments will be represented as “ [ ] ”.

4. Variable names: In algorithm, variable names will be in capital letters. Even though lowercase letters will also be used for accompanying mathematical description and analysis.  

5. Assignment statement: In algorithm, assignment statement means “dots-equal operator”. It will be appears as “ : = ”.

6. Input and output: Data may be input and assigned to variables by means of a Read statement with the following form:

Read: Variable names.

                                Similarly data in variables may be output by means of a Write or Print statement with the following form:

                                                                Write: Messages and/or variable names.

 Procedures: The term “Procedure” will be used for an independent algorithm module which solves a particular problem. Generally the word “algorithm” will be reserved for the solution of general problems and the term “procedure” will also be used to describe a certain type of sub algorithm.