No matter which programming language you program in if you want to be able to build scalable systems, it is important to learn data structures and algorithms.

Our tutorials on Data structure and algorithms or DSA in short, teach all the basic concepts with examples and code in C, C++, Java, and Python.

 If you are willing to set up your environment for C programming language, you need the following two tools available on your computer, (a) Text Editor, and (b) The C Compiler.

Before starting my video I hope you have already subscribed to my channel, if not then subscribe now and press the bell icon to stay updated with our upcoming exciting videos.

Text Editor

This will be used to type your program. Examples of few editors include Windows Notepad, OS Edit command, Brief, Epsilon, EMACS, and vim or VI.

The name and the version of the text editor can vary on different operating systems. For example, Notepad will be used on Windows, and vim or vi can be used on Windows as well as Linux or UNIX.

The files you create with your editor are called source files and contain program source code. The source files for C programs are typically named with the extension ".c".

Before starting your programming, make sure you have one text editor in place and you have enough experience to write a computer program, save it in a file, compile it, and finally execute it.

The C Compiler

The source code written in the source file is the human-readable source for your program. It needs to be "compiled", to turn into machine language so that your CPU can actually execute the program as per the given instructions.

This C programming language compiler will be used to compile your source code into a final executable program. We assume you have the basic knowledge about a programming language compiler.

The most frequently used and free available compiler is GNU C/C++ compiler. Otherwise, you can have compilers either from HP or Solaris if you have respective Operating Systems (OS).

The following section guides you on how to install GNU C/C++ the compiler on various Operating Systems. We are mentioning C/C++ together because the GNU GCC compiler works for both C and C++ programming languages.

Installation on UNIX/Linux

If you are using Linux or UNIX, then check whether GCC is installed on your system by entering the following command from the command line –

If you have GNU compiler installed on your machine, then it should print a message such as the following -

If GCC is not installed, then you will have to install it yourself using the detailed instructions available at https://gcc.gnu.org/install/

This tutorial has been written based on Linux and all the given examples have been compiled on Cent OS flavor of the Linux system

Installation on Mac OS

If you use Mac OS X, the easiest way to obtain GCC is to download the Xcode development environment from Apple's website and follow the simple installation instructions. Once you have Xcode setup, you will be able to use the GNU compiler for C/C++.

Xcode is currently available at developer.apple.com/technologies/tools/

Installation on Windows

To install GCC on Windows, you need to install MinGW. To install MinGW, go to the MinGW homepage, www.mingw.org, and follow the link to the MinGW download page. Download the latest version of the MinGW installation program, which should be named MinGW<version>.exe.

While installing MinGW, at a minimum, you must install GCC-core, GCC-g++, Binutils, and the MinGW runtime, but you may wish to install more.

Add the bin subdirectory of your MinGW installation to your PATH environment variable, so that you can specify these tools on the command line by their simple names.

When the installation is complete, you will be able to run GCC, g++, ar, ranlib, dlltool, and several other GNU tools from the Windows command line.

 Algorithm is a step-by-step procedure, which defines a set of instructions to be executed in a certain order to get the desired output. Algorithms are generally created independent of underlying languages, i.e., an algorithm can be implemented in more than one programming language.

Before starting my video I hope you have already subscribed to my channel, if not then subscribe now and press the bell icon to stay updated with our upcoming exciting videos.

From the data structure point of view, the following are some important categories of algorithms -

·         Search - Algorithm to search an item in a data structure.

·         Sort - Algorithm to sort items in a certain order.

·         Insert - Algorithm to insert an item in a data structure.

·         Update - Algorithm to update an existing item in a data structure.

·         Delete - Algorithm to delete an existing item from a data structure.

Characteristics of an Algorithm

Not all procedures can be called an algorithm. An algorithm should have the following characteristics -

·         Unambiguous - Algorithm should be clear and unambiguous. Each of its steps (or phases), and their inputs/outputs should be clear and must lead to only one meaning.

·         Input - An algorithm should have 0 or more well-defined inputs.

·         Output - An algorithm should have 1 or more well-defined outputs and should match the desired output.

·         Finiteness - Algorithms must terminate after a finite number of steps.

·         Feasibility - Should be feasible with the available resources.

·         Independent - An algorithm should have step-by-step directions, which should be independent of any programming code.

How to Write an Algorithm?

There are no well-defined standards for writing algorithms. Rather, it is a problem and resource-dependent. Algorithms are never written to support a particular programming code.

As we know that all programming languages share basic code constructs like loops (do, for, while), flow-control (if-else), etc. These common constructs can be used to write an algorithm.

We write algorithms in a step-by-step manner, but it is not always the case. Algorithm writing is a process and is executed after the problem domain is well-defined. That is, we should know the problem domain, for which we are designing a solution.

Example

Let's try to learn algorithm-writing by using an example.

Problem - Design an algorithm to add two numbers and display the result.

Algorithms tell the programmers how to code the program. Alternatively, the algorithm can be written as -

In the design and analysis of algorithms, usually, the second method is used to describe an algorithm. It makes it easy for the analyst to analyze the algorithm ignoring all unwanted definitions. He can observe what operations are being used and how the process is flowing.

Writing step numbers is optional.

We design an algorithm to get a solution to a given problem. A problem can be solved in more than one way.

Hence, many solution algorithms can be derived for a given problem. The next step is to analyze those proposed solution algorithms and implement the best suitable solution.

Algorithm Analysis

The efficiency of an algorithm can be analyzed at two different stages, before implementation, and after implementation. They are the following -

• A Priori Analysis - This is a theoretical analysis of an algorithm. The efficiency of an algorithm is measured by assuming that all other factors, for example, processor speed, are constant and have no effect on the implementation.
• A Posterior Analysis - This is an empirical analysis of an algorithm. The selected algorithm is implemented using a programming language. This is then executed on the target computer machine. In this analysis, actual statistics like running time and space required, are collected.

We shall learn about a priori algorithm analysis. Algorithm analysis deals with the execution or running time of various operations involved. The running time of an operation can be defined as the number of computer instructions executed per operation. Algorithm Complexity

Suppose X is an algorithm and n is the size of input data, the time and space used by the algorithm X are the two main factors, which decide the efficiency of X.

• Time Factor - Time is measured by counting the number of key operations such as comparisons in the sorting algorithm.
• Space Factor - Space is measured by counting the maximum memory space required by the algorithm.

The complexity of an algorithm f(n) gives the running time and/or the storage space required by the algorithm in terms of n as the size of input data.

Space Complexity

The space complexity of an algorithm represents the amount of memory space required by the algorithm in its life cycle. The space required by an algorithm is equal to the sum of the following two components -

A fixed part is a space required to store certain data and variables that are independent of the size of the problem. For example, simple variables and constants used, program size, etc.

A variable part is a space required by variables, whose size depends on the size of the problem. For example, dynamic memory allocation, recursion stack space, etc.

Space complexity S(P) of any algorithm P is S(P) = C + SP(I), where is the fixed part and S(I) is the variable part of the algorithm, which depends on instance characteristic I.

Following is a simple example that tries to explain the concept -

Here we have three variables A, B, and C, and one constant. Hence S(P) = 1 + 3. Now, space depends on data types of given variables and constant types and it will be multiplied accordingly.

Time Complexity

The time complexity of an algorithm represents the amount of time required by the algorithm to run to completion. Time requirements can be defined as a numerical function T(n), where T(n) can be measured as the number of steps, provided each step consumes constant time.

For example, the addition of two n-bit integers takes n steps. Consequently, the total computational time is T(n) = c*n, where c is the time taken for the addition of two bits. Here, we observe that T(n) grows linearly as the input size increases.

Asymptotic analysis of an algorithm refers to defining the mathematical boundation/framing of its run-time performance. Using asymptotic analysis, we can very well conclude the best case, average case, and worst-case scenario of an algorithm.

Asymptotic analysis is input bound i.e. if there's no input to the algorithm, it is concluded to work in a constant time. Other than the "input" all other factors are considered constant.

Asymptotic analysis refers to computing the running time of any operation in mathematical units of computation. For example, the running time of one operation is computed as f(n) and maybe for another operation, it is computed as g(n²). This means the first operation running time will increase linearly with the increase in n and the running time of the second operation will increase exponentially when n increases. Similarly, the running time of both operations will be nearly the same if n is significantly small.

Usually, the time required by an algorithm falls under three types

• Best Case - Minimum time required for program execution.
• Average Case - Average time required for program execution.
• Worst Case - The maximum time required for program execution.

Asymptotic Notations

Following are the commonly used asymptotic notations to calculate the running time complexity of an algorithm.

O Notation

Ω Notation

Θ Notation

Big Oh Notation, O

The notation O(n) is the formal way to express the upper bound of an algorithm's running time. It measures the worst-case time complexity or the longest amount of time an algorithm can possibly take to complete. 

Omega Notation, Ω

The notation (n) is the formal way to express the lower bound of an algorithm's running time. It measures the best case time complexity or the best amount of time an algorithm can possibly take to complete.

Theta Notation, Θ

The notation  (n) is a formal way to express both the lower bound and the upper bound of an algorithm's running time. It is represented as follows –

Common Asymptotic Notations

Following is a list of some common asymptotic notations –

 This chapter explains the basic terms related to a data structure.

Data Definition

Data Definition defines a particular data with the following characteristics.

Atomic - Definition should define a single concept.

Traceable - Definition should be able to be mapped to some data element.

Accurate - Definition should be unambiguous.

Clear and Concise - Definition should be understandable.

Data Object

Data Object represents an object having data.

Data Type

A data type is a way to classify various types of data such as integer, string, etc. which determines the values that can be used with the corresponding type of data, the type of operations that can be performed on the corresponding type of data. There are two data types -

• Built-in Data Type
• Derived Data Type

Built-in Data Type

Those data types for which a language has built-in support are known as Built-in Datatypes. For example, most of the languages provide the following built-in data types.

• Integers
• Boolean (true, false)
• Floating (Decimal numbers)
• Character and Strings

Derived Data Type

Those data types which are implementation-independent as they can be implemented in one or the other way are known as derived data types. These data types are normally built by the combination of primary or built-in data types and associated operations on them.

For example -

·         List

·         Array

·         Files

List derived into two types:

• Linear Lists
• Non-Linear Lists

Examples of Linear lists are Stacks & Queues.

& Example of Non-Linear Lists is Trees and Graphs.

Basic Operations

The data in the data structures are processed by certain operations. The particular data structure was chosen largely depends on the frequency of the operation that needs to be performed on the data structure.

• Traversing
• Searching
• Insertion
• Deletion
• Sorting
• Merging

 An array is a container that can hold a fixed number of items and these items should be of the same type. Most of the data structures make use of arrays to implement their algorithms. Following are the important terms to understand the concept of Array.

• Element - Each item stored in an array is called an element.
• Index - Each location of an element in an array has a numerical index, which is used to identify the element.

Array Representation

Arrays can be declared in various ways in different languages. For illustration, let's take C array declaration.

As per the above illustration, the following are the important points to be considered.

• Index starts with 0.
• Array length is 10 which means it can store 10 elements.
• Each element can be accessed via its index. For example, we can fetch an element at index 6 as 9.

Basic Operations

Following are the basic operations supported by an array.

Traverse - print all the array elements one by one.

Insertion - Adds an element at the given index.

Deletion - Deletes an element at the given index.

Search - Searches an element using the given index or by the value.

Update - Updates an element at the given index.

In C, when an array is initialized with size, then it assigns default values to its elements in the following order.

Insertion Operation

Insert operation is to insert one or more data elements into an array. Based on the requirement, a new element can be added at the beginning, end, or any given index of an array.

Here, we see a practical implementation of insertion the operation, where we add data at the end of the array

Algorithm

Let Array be a linear unordered array of MAX elements.

Example

Result

Let LA be a Linear Array (unordered) with N elements and K is a positive integer such that K<=N? 

Following is the algorithm where ITEM is inserted into the K^th position of LA -

Example

Following is the implementation of the above algorithm

When we compile and execute the above program, it produces the following result -

Output

The original array elements are:

Deletion Operation

Deletion refers to removing an existing element from the array and re-organizing all elements of an array.

Algorithm

Consider LA is a linear array with N elements and K is a positive integer such that K<=N.

Following is the algorithm to delete an element available at the k^th position of LA.

Example

Following is the implementation of the above algorithm -

When we compile and execute the above program, it produces the following result -

 Output

Search Operation

You can perform a search for an array element based on its value or its index.

Algorithm

Consider LA is a linear array with N elements and K is a positive integer such that K<=N.

Following is the algorithm to find an element with a value of ITEM using sequential search.

Example

Following is the implementation of the above algorithm -

When we compile and execute the above program, it produces the following result -

Output

Update Operation

Update operation refers to updating an existing element from the array at a given index.

Algorithm

Consider LA is a linear array with N elements and K is a positive integer such that K<=N.

Following is the algorithm to update an element available at the K^th position of LA.

Example

Following is the implementation of the above algorithm

When we compile and execute the above program, it produces the following result:

Output