dsa problem solving course

15 Best Courses for Data Structures and Algorithms (2024)

Introduction, best data structures and algorithms courses (2024), 1. scaler academy’s data structure and algorithm course, 2. algorithms & data structures-part 1 and 2 (coursera), 3. data structures-university of california san diego, 4. data structures-by nptel, 5. cs50’s introduction to computer science, 6. introduction to algorithms, 7. data structures and algorithms specialization program (coursera), 8. algorithms specialization by stanford university, 9. free algorithms course by iit bombay (edx), 10. data science foundations: data structures and algorithms specialization, 11. advanced-data structures-mit open courseware, 12. programming foundations: algorithms, 13. python data structures, 14. master the coding interview: data structures + algorithms, 15. accelerated computer science fundamentals specialization by the university of illinois, frequently asked questions, q.1: why are data structures and algorithms important, q.2: can i learn data structures and algorithms in python, q.3: where data structures and algorithms are used, useful resources, other courses.

The world of computer science revolves around data structures and algorithms. They serve as the bedrock for all other parts of computer science and development. This is why firms like Google, Microsoft, and Facebook are on the lookout for programmers who are knowledgeable about data structures and algorithms. Learning DSA could be beneficial whether you are seeking a new job or attempting to improve your skills. To learn how to code, you don’t need to spend loads of money on a college education. This is when online courses come in handy. They are a great source of learning and act as proof of skill during interviews.

You’ve come to the right place if you want to learn about data structures and algorithms. We made an effort for you. We searched through the highest-rated courses on the web and hand-picked 15 of the best to help you become an expert on the most-wanted skill right now.

Scaler Academy by InterviewBit offers a thoughtfully designed curriculum to make you understand the toughest of DSA concepts easily. Courses are available for all levels-beginners, intermediate, and expert. The curriculum can be optimized to your pace of learning. Projects and assignments at the end of topics help you cement the concepts you have learned. This course will teach you how to become an expert in data structures and algorithms, as well as how to ace product interviews so you can advance in your computer career.

Confused about your next job?

The course covers

• The basics of programming
• Time Complexity
• Binary Search
• 2 Pointers, Recursion
• Bit manipulation
• Linked Lists
• Greedy Algorithms
• DP (Dynamic Programming)
• Database concepts
• OS, and 
• Computer Networks

Duration: 44 weeks Eligibility: Anyone who graduated in 2022 can apply Price: 3.59 lakhs, but your monthly payment might be as low as Rs 8,370 per month with scholarship and EMI choices

Check Out: Scaler Academy’s Data Structure and Algorithm Course

This course covers the principles of algorithms and data structures that every serious programmer should know, with a focus on Java implementations and scientific performance analysis. Basic data structures, sorting, and searching strategies are covered in the first section of the course. The second section of the course is dedicated to graph and string processing techniques. This course includes all the features for free. It comes with a certificate when you finish it, but you have to pay for the certificate. 

Topics covered in part 1:  

• Analysis of algorithms
• Stacks and queues
• Elementary sorts
• Priority queues
• Elementary symbol tables
• Balanced search trees
• Geometric applications of BSTs
• Hash Tables
• Symbol table application

Duration: 53 hours approx. You can set deadlines according to your schedule. Level: Intermediate level Price: Free to enrol

The common data structures that are utilized in many computational problems are discussed in this online course. You will learn how to implement these data structures in various programming languages and will experience doing so in our programming assignments. This will assist you in understanding what is happening inside a specific built-in implementation of a data structure and what to expect from it. The prerequisite of the course is any object-oriented programming language. You’ll also learn about common applications for these data structures.

Topic covered:

• Basic Data structures (arrays, linked list, stacks, queues)
• Dynamic arrays and amortized analysis
• Priority queues and disjoint sets
• Hash tables
• Binary search trees 

Duration: 25 hours approx. You can set deadlines according to your schedule. Level: Intermediate level Price: Free to enroll

This data structure course by NPTEL will teach you-efficient storage mechanisms of data for easy access, to design and implementation of various basic and advanced data structures to introduce various techniques for the representation of the data in the real world, to develop applications using data structures, to teach the concept of protection and management of data, to improve the efficiency of any algorithm by using the suitable data structure.

Topics covered:

• Introduction to List 
• Array and Linked List  
• Stack Implementation using array and linked list – Applications of Stack
• Queue Implementation – Application of Queues
• Trees and Terminologies – Tree Traversals
• In order Traversal-Binary Search Tree – Implementation of Search Algorithm
• AVL Tree Insertion, Deletion
• Graph representation, Shortest Path Algorithm
• Sorting, Heap Techniques, Hashing
• Sorting Algorithms, Divide and Conquer algorithms
• Selection Sort, Brute force sort, Bubble Sort
• Insertion Sort, Quicksort applications
• Prim’s Algorithm, Kruskal’s Algorithm
• Bucket Sorting, Radix Sort, Merge Sort
• Directories and Contiguous allocation, File maintenance
• External Sorting, Cascade Merge Sort
• B + Tree maintenance and efficiency, Construction of B-tree, B+tree insertion and deletion

Duration: 12 weeks Level: Undergraduate/Postgraduate

CS50x is a Harvard University course that introduces majors and non-majors alike, with or without prior programming experience, to the academic pursuits of computer science and the art of programming. CS50x is an introductory computer science course given by David J. Malan that teaches students:

• How to think algorithmically and solve problems quickly
• Abstraction
• Data structures
• Encapsulation
• Resource management
• Software engineering, and
• Web development 

C, Python, SQL, and JavaScript, as well as CSS and HTML, are among the languages available. Real-world domains such as biology, encryption, economics, forensics, and gaming-inspired problem sets are present in this course. CS50, Harvard’s largest course, is the on-campus version of CS50x. A certificate is awarded to students who get an acceptable grade on nine problem sets (programming assignments) and a final project. CS50x is a self-paced course that you can do at your own speed.

Duration: 12 weeks Level: Introductory Prerequisites: None

This open course from MIT provides an introduction to computational problems and mathematical modeling. It goes over the most prevalent algorithms, algorithmic paradigms, and data structures for solving these issues. The focus of the course is on the interaction between algorithms and programming, as well as basic performance measures and analysis approaches for these issues.

What you will learn:

• Introduction to mathematical modeling of computational problems
• Common algorithm
• Algorithm paradigms
• Relationship between algorithms and programming
• Basic performance measures and analysis techniques for these problems.

Duration: Not available Level: Undergraduate Prerequisites:  Basic understanding of Python as well as a solid background in discrete mathematics.

The University of California, San Diego, and the National Research Institute Higher School of Economics both offer this specialization in algorithms and data structures. Students learn the theory underlying algorithms, implement them in a programming language of their choice, and use them to solve actual problems in this curriculum, which offers a solid blend of theory and practice.

The program is divided into six courses, with the first two covering theory and basic algorithmic techniques before moving on to advanced algorithms and complexity. It includes the following topics:

• Using data structures to solve a variety of problems
• Graph data structure
• Graph-based algorithms
• Algorithms on strings
• Advanced algorithmic concepts like Network flows, linear programming, and NP-complete problems

Duration: 8 months Level: Intermediate-level course Prerequisites:  Basic knowledge of any one programming language like C, C++, Java, Python, JavaScript, or Kotlin Is required.

Stanford University offers this Coursera Algorithms speciality. Understanding the fundamentals of algorithms and related data structures is required for serious work in nearly every discipline of computer science. This course introduces learners to algorithms and emphasizes conceptual knowledge rather than diving right into mathematical specifics and low-level implementation. It aids in the development of the participants’ programming and thinking skills, preparing them to pursue serious software engineering, ace technical interviews, and study more sophisticated algorithms topics. 

• Asymptotic (“Big-oh”) notation
• Sorting and searching algorithms
• Master method for analyzing algorithms
• Quicksort algorithm and its analysis
• Data structures-heaps, balanced search trees, hash tables, bloom filters
• Dijkstra’s shortest-path algorithm
• Breadth-first and depth-first search and its applications
• Greedy algorithms (scheduling, minimum spanning trees, clustering, Huffman codes)
• Dynamic programming (knapsack, sequence alignment, optimal search trees)
• Shortest paths algorithms (Bellman-Ford, Floyd-Warshall, Johnson)
• NP-complete problems and exact and approximation algorithms for them
• Local search algorithms for NP-complete problems

Duration: 4 months Level: For intermediate-level learners Prerequisites: Not available

Expert academic members from the reputed IIT Bombay’s Department of Computer Science and Engineering designed this edX Algorithms course. It’s part of the Fundamentals of Computer Science XSeries Program at IIT Bombay, and it teaches students how to structure and use algorithms to solve real-world problems. Students learn how to think about algorithms and how to implement them using the best techniques in this computer science course. The course covers the following topics:

• Sorting algorithms such as quick sort and merge sort
• Searching algorithms
• Median finding
• Order statistics
• Geometric algorithms like Polynomial Multiplication
• String algorithms
• Numerical algorithms
• Matrix Operations, GCD, Pattern Matching, Subsequences, Sweep, and Convex Hull
• Graph algorithms like shortest path and spanning tree

Duration: 6 weeks Level: Intermediate-level course Prerequisites: Requires basic knowledge of data structures and their implementation.

Sriram Sankaranarayanan, the top instructor of Coursera, guides you through this advanced specialization. In this course, you will learn to organize, store and process data efficiently using advanced data structures, design algorithms and analyze their complexities in terms of running time and space usage, searching and sorting algorithms, and build applications that support highly efficient algorithms and data structures. This specialization is part of a Master of Science in data science degree from the University of Colorado Boulder. Learners are expected to have knowledge of calculus, Probability theory, and some programming experience in python. The duration of this course is approximately three months.

Skills that you’ll gain:

• Dynamic Programming
• Greedy algorithms
• Divide and Conquer algorithm
• Randomized algorithms
• Sorting algorithms
• Spanning tree
• NP-completeness

Duration: Approximately three months. Level: Intermediate Prerequisites:  Learners are expected to have knowledge of calculus, Probability theory, and some programming experience in python. Price: Free to enroll

This is a graduate-level course from MIT open courseware. Topics covered include

• Time travel
• Dynamic optimality
• Memory hierarchy
• Hashing 
• Dynamic graphs

Duration: Not available Level: Graduate level Prerequisites: The prerequisite to this course is an undergraduate-level understanding of the design and analysis of algorithms and basic knowledge of data structures.

Joe Marini, author, and developer, walks you through some of the most popular and effective algorithms for finding and sorting data, working with recursion, and understanding common data structures in this course. He also goes through the performance implications of various algorithms and how to evaluate an algorithm’s performance. The teachings are demonstrated in Python, but they can be applied to any programming language. Topics covered:

• Common data structures (Arrays, Linked List, Stacks, Queues, Hash Tables)
• Other Algorithms (Unique filtering with hash tables, Finding max value recursively)

The course costs 1150 rupees and LinkedIn also provides a certificate of completion. The course is self-paced, and any beginner can apply for this course.

This Python data structures course is part of the University of Michigan’s Python for Everyone Specialization on Coursera. It gives an overview of the Python programming language’s basic data structures. This is one of the most popular courses, with a 4.9 rating and almost half a million students who have already completed it. 12% of the learners who have completed the course got a tangible career. Topics covered:

• Installing Python
• Dictionaries

Financial aid is available for this course which takes 19 hours to complete. The good thing about the course is that it is beginner-friendly.

This course is designed for you if you want to work for a great tech business like Google, Microsoft, Facebook, Netflix, Amazon, or another company but are terrified by the interview process and code questions. This course covers subjects like non-technical interviews and compensation negotiations, in addition to algorithms. Topics covered are: 

• Big O notation
• Arrays Hash Tables Singly Linked Lists Doubly Linked Lists Queues Stacks Trees (BST, AVL Trees, Red-Black Trees, Binary Heaps) Tries Graphs
• Tree Traversal
• Breadth-First Search
• Depth First Search

Non-Technical

• How to get more interviews
• What to do during interviews
• What to do after the interview
• How to answer interview questions
• How to handle offers
• How to negotiate your salary
• How to get a raise

The price of the course is 3499 rupees. You need to have a basic understanding of any programming language for this course. The course consists of 261 20-hour lectures. 

The University of Illinois offers a Coursera Specialization in fundamental computer science algorithms and data structures. It’s a three-course curriculum created by computer science professor Wade Fagen-Ulmschneider to provide students with a route into computers and data science. Students must write C++ code snippets on a web-based interface in order to complete the program’s coding tasks. Each course also contains two projects in which students write C++ programs to do things like edit photographs, manipulate data structures efficiently, or solve a graph search problem. You will learn:

• Designing and implementing an object-oriented program in C++
• How to analyze time complexity and space required for an algorithm
• Selecting and implementing the best data structures that best use the resources to solve a computational problem.
• To implement and call sophisticated library functions after gaining a solid understanding of object data structures.

The course is flexible, and the learner should be able to write basic programs in any programming language. The duration of the course is 3 months.

Duration: 3 months with a flexible schedule Level: Intermediate level Prerequisites: None

There are so many courses available to learn data structures and algorithms, but few of them have the right balance between theory and practice. The courses that we covered in this article give a good mix of these two aspects of computing. They also contain every concept that you would need if someone asked you to code something real-world, out there. Anyway, I think this is enough information for you to make up your mind on which course you should take up next. Choose one of them and get started on your path to working for your dream company!

Ans: Data structure and algorithms are essential for developers since they show the problem-solving ability of the developer, the skill that recruiters value the most. Programmers with a strong understanding of data structures and algorithms can effortlessly handle data processing, reasoning, and calculations.

Ans: Yes, you can learn Data structures and algorithms in Python. 

Ans: DSA (Data Structure and Algorithm) is used in every aspect of computer science. Data structures are used to store information, while algorithms are used to solve problems with that data.

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DSA Tutorial

Linked lists, stacks & queues, hash tables, shortest path, minimum spanning tree, maximum flow, time complexity, dsa reference, dsa examples, learn data structures and algorithms.

Data Structures and Algorithms (DSA) is a fundamental part of Computer Science that teaches you how to think and solve complex problems systematically.

Using the right data structure and algorithm makes your program run faster, especially when working with lots of data.

Knowing DSA can help you perform better in job interviews and land great jobs in tech companies.

This Tutorial

This tutorial is made to help you learn Data Structures and Algorithms (DSA) fast and easy.

Animations, like the one below, are used to explain ideas along the way.

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First, you will learn the fundamentals of DSA: understanding different data structures, basic algorithm concepts, and how they are used in programming.

Then, you will learn more about complex data structures like trees and graphs, study advanced sorting and searching algorithms, explore concepts like time complexity, and more.

This tutorial will give you a solid foundation in Data Structures and Algorithms, an essential skill for any software developer.

Try it Yourself Examples in Every Chapter

In every chapter, you can edit the examples online, and click on a button to view the result.

The code examples in this tutorial are written in Python, C, and Java. You can see this by clicking the "Run Example" button.

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What You Should Already Know

Although Data Structures and Algorithms is actually not specific to any programming language, you should have a basic understanding of programming in one of these common programming languages:

DSA History

The word 'algorithm' comes from 'al-Khwarizmi', named after a Persian scholar who lived around year 800.

The concept of algorithmic problem-solving can be traced back to ancient times, long before the invention of computers.

The study of Data Structures and Algorithms really took off with the invention of computers in the 1940s, to efficiently manage and process data.

Today, DSA is a key part of Computer Science education and professional programming, helping us to create faster and more powerful software.

DSA Exercises

Test yourself with exercises.

What does DSA stand for?

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Advanced Data Structures, Algorithms, Problem Solving & System Design(HLD + LLD) (Duration: 7 months)

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What you’ll learn in the Course

Time complexity.

Learn fundamentals of programming and understand time complexity.

Array, String and Linked List

Master array, string and linked list and implement real time project on Git and GitHub.

Stack and Queue

Learn fundamentals of programming of stack and queue and its useage.

Hashing & Heap Sort

Learn fundamentals of programming the hashing/heap sort in very simpler way.

OOPS Concepts & Design

Learn fundamentals concepts of OOPs and use it real projects.

Competitive Programming

String based and mathematical competitive programming practise,Hackerank, Hackerearch Practise in Live classes

Binary Tree, N-ary Tree, Segment Tree etc

Learn fundamentals of binary tree and N-ary tree and use it project/assignements.

Greedy Algorithm

Learn all about building responsive websites using HTML5 and CSS3; discuss key HTML5 APIs and their use cases.

Backtracking & Recursion

Learn fundamentals of programming the world-wide web and its key stakeholders.

Graph Theory

Dynamic programming, advanced data structures.

Complete Advanced data structures like Trie, Suffix Tree, Suffix Tree, ternary search trees etc

Industry Projects

Learn real-time projects from industry experts, and use your learning expertise in the course by designing and coding projects from scratch. also, it enhanced your resume with good expertise in the design & implementation of real-time projects..

• Engage in collaborative real time projects with student-mentor interaction
• Learn faster in-person through guidance from expert mentors
• Personalized subjective feedback on your submissions to facilitate quick improvement

BookMyshow Design & Implement

This is a beginner-friendly real-time project using object-oriented principles and data structures and algorithms concepts. You will learn how to design & implement a ticket booking system that supports synchronization. ... Scalable user interaction and payment gateway integrated into the system. End to end complete flow implementation of the project Expand

E-commerce Websites (Amazon, Flipkart, etc)

Design and Implementation of a project of e-commerce product ( Like Amazon, Flipkart) where users can pick items to their cart, place orders, track orders, and conformation will be sent after delivery. The payment gateway should be supported in card/cash/UPI options. ... Your system accepts the concurrent request from millions of customers and process their order with minimum latency and high efficient system Expand

Design Social Media Network

Real time project to design the social media network having all functionality of connecting friends, communication and viewing news feed. Group, Post, Message, and Comment is primary features will implemented in the social media network project ... Complete end to end flow of object oriented design project of social media platform. Expand

Stock Brokerage System(e.g Zerodha, Upstocks etc)

Design Stock Brokerage System real time project from scratch. As the part of this project we will use all data structures and algorithms to write efficient code for selling and buying multiple types of stocks from our platform in a concurrent system. System mainly responsible for sending notifications for stock orders and periodically fetching stock quotes from the stock exchange ... It can register new account , place order, search stock inventory and deposit/withdraw money Expand

Food Ordering Website

This is a beginner-friendly full stack development project on HTML & CSS. You will use HTML and CSS to build a Blood Donation Website, appointment booking, motivational gal ... You will use HTML and CSS to build a Blood Donation Website that has a sign-up login page, appointment booking, motivational Expand

Restaurants Delivery Application

Online Pharmacy Website

Data Structure and Algorithm course curated by leading faculties and industry leaders to provide pratical learning experience with live interactive classes and projects.

Module 1: Complexity Analysis, Time & Space, Big O Calculation

Chapter 1: understanding complexity.

• • Order complexity analysis
• • What is Big 0 Notation, how to use it with various examples.

Chapter 2: Space & Time Complexity

What is space & time complexity, examples to find out space time complexity

Chapter 3: Worst, Average and Best Cases

• • Understanding Average, Best and Worst case of various programs.
• • Analysis of Loops, Time Complexity of Loop with Powers

Chapter 4: Analysis of Loops, Time Complexity of Loop with Powers

More complex examples which involves multiples exponential loops .

Module 2: Recursion Analysis, Recursion implementation & examples

Chapter 1: visualize call stack and recursion flow.

• What is recursion, how to analyse recursion in call stacks .

Chapter 2: Recursion Code and execution, Multiple recursive calls process

• • Understanding code flow of recursive call with examples

Chapter 3: Space complexity of a recursive algorithm

• • Difference between recursive and iterative approaches
• • Find space complexity of recursive calls.

Chapter 4: Double recursion, How to think recursively

• • More Complex examples involve recursion calls,

Module 3 - Array

Chapter 1: overview, applications & implementation.

• Understanding the Array computations with examples .
• Implementation of Array problems

Chapter 2: Advantages And Limitations

• Why do we need arrays ?
• Array Advantages And Limitation over other data structures

Chapter 3: How to use arrays to solve more complex problems

• Matrix related Problem(2-D array)
• Minimum Window Substring
• Two pointers approach etc

Chapter 4: Searching, sorting based problems

• Linting, formatting, understanding Python code,
• Array problems involves searching
• Array sorting efficient algorithms

Chapter 4: Problem & Solution, Interview Questions

• Discussion of Top product companies interview questions based on Array

Module 4: Strings

Chapter 1: how to solve string based problem.

• Most asked interview question are based on strings.
• How to efficiently solve strings problems

Chapter 2: Tips & tricks of string concepts

• Tricks of solving the strings problems techniques
• Two pointers tricks, window based problems etc

Chapter 3: Interview Questions on strings problems

• Discussion of Top product companies interview questions based on String

Module 5 - LinkedList, Doubly Linked List examples & problems

Chapter 1: linked list introduction & implementation.

• Linked List creation implementation
• Adding,deleting and finding specific nodes

Chapter 2: Circular linked list with examples

• Implementation of Doubly linked list
• Implementation of Circular linked list
• Problems based on DLL, Circular LinkedList.

Chapter 3: Problems based on LinkedList

• Merge two sorted linked lists, merge sort of a linked list
• Reversing a linked list, k group Linked List etc

Chapter 4: Interview Questions on LinkedList, DLL

• Discussion of top product companies interview questions based on DLL, LinkedList

Module 6 - Binary Tree, BST

Chapter 1: introduction of binary tree.

• Introduction to Trees.
• Making a tree node class
• Tree traversals
• Destructor for tree node class

Chapter 2: Analysis, practical Applications of Binary tree

• Balanced Trees, How to maintain Tree Balance
• Self-balancing tree

Chapter 3: Binary Tree traversal

• In Order, Pre and Post-Order using recursion
• Problems based on Binary Tree traversal
• What Is a Binary Search Tree Used For?
• Left view, right view, bottom view of binary tree etc

Chapter 4: Interview Questions on Binary tree

• Discussion of Top product companies interview questions based on Binary tree

Chapter 5: Introduction of Binary Search Tree

• Introduction to Binary Search Trees
• Searching a node in BST
• Inserting and Deleting nodes in BST
• Types of balanced BSTs

Chapter 6: Interview Questions on Binary Search Tree(BST)

• Discussion of Top product companies interview questions based on BST

Chapter 7: Advanced Tree

• B Tree, B+ Tree & Threaded binary tree
• AVL Tree, Segment Tree
• N-ary Tree and Problems

Chapter 8: Interview Questions on Advanced Tree

• Discussion of Top product companies interview questions based on Advanced tree

Module 7: Stack Implementation & Problems

Chapter 1: stack: what is stack & how are stacks used.

• Operations on Stack LIFO operation.
• Applications & implementation of Stack Data Structure

Chapter 2: Stack Based Interview Question

• Valid parenthesis, find next greater element, prefix, postfix etc

Chapter 3: Advanced Problems based on Stack

• Complex problems of stack

Chapter 4: Interview Questions on Stack

• Discussion of Top product companies interview questions based on Stack LIFO operation

Module 8: Queue Implementation & Problems

Chapter 1: queue: what is the queue, how are they used.

• Operations on Queue FIFO operation.
• Applications & implementation of Queue Data Structure

Chapter 2: Queue Based Interview Question

• Discussion of Top product companies interview questions based on Queue

Chapter 3: Introduction & Implementation of Circular Queue

• Applications & implementation of Circular Queue Data Structure

Chapter 4: Interview Questions on Queue & Circular Queue

• Discussion of Top product companies interview questions based on Queue FIFO operation
• Medium to Advanced set of problems discussion

Module 9 - Heap & priority queue

Chapter 1: priority queue & heap overview.

• Implementation of Priority Queue using various data structures
• Insert, delete, peek operation in priority queue
• Binary Heap Time Complexity of building a heap
• Applications of Heap Data Structure

Chapter 2: What is heap, Min Heap & Max Heap introduction, approach

• Min heap, Max heap implementation
• Interview problems based on Min/Max Heap
• Basic heap operation, Heapify operation implementation

Chapter 3: Interview Questions on Heap & Priority Queue

• Discussion of Top product companies interview questions based on Heap & Priority Queue

Module 10: Hashing & Map

Chapter 1: hash table, functions & hashing techniques.

• Hashing DS, Hash table, hash function.
• Double hashing, probing
• Insert, delete & search in hash in O(1) time

Chapter 2: Hashing: Problem & Solution

• Top k elements, Smallest subarray, word count etc
• Product companies Hashing interview questions

Chapter 3: Design and implement LRU

• Implement LRU, various problems on LRU

Chapter 4: Interview Questions on Hashing and Map

• Discussion of Top product companies interview questions based on Hashing

Module 11: Graph (BFS, DFS, Topological sort etc)

Chapter 1: introduction, types & applications.

• Graph and its representations.
• Undirected Graph, Directed Graph, Connected Graph etc

Chapter 2: Graph Representation, Adjacency List & Traversals

• Graph implementation of Adjacency List
• Adjacency matrix representation of Graph

Chapter 3: Breadth First Search (BFS), Depth First Search (DFS)

• DFS implementation, Application
• BFS implementation , Application

Chapter 4: Problems based on BFS & DFS

• Medium to Advanced interview questions on BFS & DFS

Chapter 4: Shortest Path Algorithms

• All types & implementation of Shortest Path Algorithms
• Single-Source Shortest Paths in Directed & Undirected graph

Module 12: Advanced DSA Topics

Chapter 1: introduction, types & applications of trie.

• Trie Data Structure - Explained with Examples.
• Why use Trie Data Structure?

Chapter 2: Implementation of Trie

• Insert in Trie
• Search in Trie
• Trie Applications

Chapter 3: Interviews Questions Based on Trie

• Word search, Longest Common Prefix, Words in dictionary etc

Chapter 4: Suffix Array & Tree Implementation & Problems

• Suffix Tree Introduction
• Search a pattern using the built Suffix Array
• Longest common prefix of two substrings
• Finding the longest repeated substring
• Pattern searching

Chapter 4: Ternary search tree Introduction, Types & Applications

• Representation of ternary search trees
• Applications of ternary search trees

Chapter 5: Segment Tree

• Representation of Segment trees
• Construction of segment tree from array
• Interview questions of segment tree

Chapter 6: Interview Questions of Advanced DSA Topics

• Discussion of Top product companies interview questions based on Advanced DSA

Module 1: Complexity Analysis of Algorithms

Algorithms time complexity analysis.

• • Optimizing algorithms & find time complexity of algorithms.
• • Complexity Analysis of exponential & factorial runtime

Algorithms space complexity analysis

• • Space time complexity of algorithms.
• • Techniques to find time & space complexity

Module 2: Searching Algorithms

Searching algorithms implementation & problems.

• Searching Algorithms Implementation & Problems

Binary search algorithm

• Binary search algorithm, implementation with examples

• Searching max value in ordering array & rotational array using binary search

Linear Search & Comparing basic search Algorithm

• Array overview & introduction

• Rotational array , Binary search advanced problem

Interview Question of Searching Algorithms

• Discussion of Top product companies interview questions based on Searching Algorithms

Module 3: Sorting Algorithms Implementation & Problems

What is sorting & why is it needed.

• Stable & unstable sorting

Basic sorting (Bubble, Selection, Insertion)

• Implementation & complexity of all sorting algorithms

Advance sorting (Radix, Merge, Quick, Heap, Counting)

• Advanced efficient sorting discussion

• Implementation of Advance sorting

Problems based on merge sorting algorithms

• Medium & Advanced problem based on merge sort

Problems based on Courting sorting algorithms

Problems based on quick sorting algorithms, interview problems on sorting algorithms, module 4: greedy algorithms implementation & problems, greedy algorithms introduction & examples.

• Steps for achieving a Greedy Algorithm

• How to identify greedy algorithms

• Does a greedy algorithm always work?

Standard problems of greedy algorithms

• Activity Selection Problem, Job sequencing and selection Problem

• Algorithm of Huffman Code

Interview problems of Greedy Algorithms

• Discussion of Top product companies interview questions based on Greedy algo

Module 5: Pattern Searching Algorithms

Naive pattern searching.

• Searching a string for a specific pattern or sub-string based problems

KMP Algorithm

• The Prefix Function, the KMP Matcher & running time

Rabin-Karp Algorithm

• Searching/matching patterns in the text using a hash function

Boyer Moore Algorithm

• Suffix search approach

Kadane Algorithms

• Maximum Subarray Problem, Subarray problems etc

Manacher’s Algorithm

• Intuition behind Manacher’s algorithm, Implementation

• Finding the Longest Palindromic Substring

Interview problems of Pattern Searching Algorithms

• Discussion of Top product companies interview questions based on Pattern Searching

Module 6: Backtracking Algorithms Implementation & Problems

How to apply backtracking using recursion.

• Understanding backtracking approach, how to Solve Problems

N Queen Problem, Rat Maze, Permutations of a given String etc

• Medium to Hard problems in Backtracking

Interview questions of Backtracking

• Discussion of Top product companies interview questions based on Backtracking

Module 7: Divide and Concur Algorithms

How to apply divide and concur algorithms, types of divide and concur algorithms, divide and concur examples & problems, interview questions on divide and concur, module 8 : bitwise algorithms, how to identify a dynamic programming, dynamic programming approach & examples of dp understanding, problems on dynamic programming, longest increasing subsequence(lis), longest common subsequence(lcs), longest palindromic substring(lps) etc, longest valid parentheses, decode ways(factorial based problems) etc, buy and sell stock k transaction, work break, continuous subarray sum etc, interview problems of dynamic programming, module 1 : basics of oops.

Introduction to OOPS, Creating objects, Getters and setters, Constructors and related concepts, Inbuilt constructor and destructor, Example classes

Module 2: Advanced Concepts of oops

Oops chapter 2.

Static members, Function overloading and related concepts, Abstraction, Encapsulation, Inheritance, Polymorphism, Virtual functions, Abstract classes, Exception handling

Module 3: How To Solve Competitive Programming

• • What is Competitive Programming and How to Prepare for It?
• • How to use mathematical algorithms to solve CP
• • String based competitive programming practise
• • Hackerank, Hackerearch , Codeforce Practise in Live classes

Code Management

Git-hub code tools.

• • Feature Branch Workflow
• • Git Commands & Examples
• • Branching and Merging
• • Centralized, Distributed, Localized version control systems

Version Control

Tracking and managing changes to software code.

• • Change Management in Software Development
• • Release management
• • Designing Software building process with sprints

Agile Mythology

Agile mythology concepts.

• • What is Agile Methodology, Process & Life Cycle
• • Scrum Testing, Process, Artifacts, Sprint
• • Agile Vs Waterfall, Agile Vs Scrum
• • Scrum Master Tutorial
• • Agile approach for the project

Use Cases,Implementation & testing

Oops test chapter 4.

Initial player aces are aces that are contained in the initial player hand (the first two cards dealt to the player) prior to the Ace Rule being satisfied; and are an important piece of the ‘Ace Rule.’

SDLC (Software Development Life Cycle)

Understanding of tools & library for sdlc.

• • Introduction to SDLC with Git
• • Reviewing and gathering tools for project
• • Build project, Identify and log bugs, Clear bugs
• • Designing Software building process

BookMyshow design & Implement

This is a beginner-friendly real-time project using object-oriented principles and data structures and algorithms concepts. You will learn how to design & implement a ticket booking system that supports synchronization.

Design and Implementation of a project of e-commerce product ( Like Amazon, Flipkart) where users can pick items to their cart, place orders, track orders, and conformation will be sent after delivery. The payment gateway should be supported in card/cash/UPI options. Your system acce

Real time project to design the social media network having all functionality of connecting friends, communication and viewing news feed. Group, Post, Message, and Comment is primary features will implemented in the social media network project Complete end to end flow of object oriented design project of social media platform.

Design Stock Brokerage System real time project from scratch. As the part of this project we will use all data structures and algorithms to write efficient code for selling and buying multiple types of stocks from our platform in a concurrent system. System mainly responsible for sending notifications for stock orders and periodically fetching stock quotes from the stock exchange It can register new account , place order, search stock inventory and deposit/withdraw money.

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We offer fully online classes via live sessions due to the outbreak. That means you can talk to your instructor in real-time, just like a traditional face-to-face session. Additionally, at this time, all practical sessions of our data structures, algorithms & problem solving course will be conducted using cloud-based services.

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Firstly, we offer live online classes for our Data Structures, Algorithms & Problem solving course. Also, all of our students have access to recorded versions of those classes. In addition, we also give you unlimited access to these recorded sessions, so you can go back to them whenever you need theoretical help for your interview preparation. As a result, you need not be disappointed if you miss any of the live classes under our online training. However, we strongly advise you to participate in all live classes.

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EnjoyMathematics

Problem-Solving Approaches in Data Structures and Algorithms

This blog highlights some popular problem-solving strategies for solving problems in DSA. Learning to apply these strategies could be one of the best milestones for the learners in mastering data structure and algorithms.

An Incremental approach using Single and Nested loops

One of the simple ideas of our daily problem-solving activities is that we build the partial solution step by step using a loop. There is a different variation to it:

• Input-centric strategy: At each iteration step, we process one input and build the partial solution.
• Output-centric strategy: At each iteration step, we add one output to the solution and build the partial solution.
• Iterative improvement strategy: Here, we start with some easily available approximations of a solution and continuously improve upon it to reach the final solution.

Here are some approaches based on loop: Using a single loop and variables, Using nested loops and variables, Incrementing the loop by a constant (more than 1), Using the loop twice (Double traversal), Using a single loop and prefix array (or extra memory), etc.

Example problems:   Insertion Sort ,  Finding max and min in an array ,  Valid mountain array ,  Find equilibrium index of an array ,  Dutch national flag problem ,  Sort an array in a waveform .

Decrease and Conquer Approach

This strategy is based on finding the solution to a given problem via its one sub-problem solution. Such an approach leads naturally to a recursive algorithm, which reduces the problem to a sequence of smaller input sizes. Until it becomes small enough to be solved, i.e., it reaches the recursion’s base case.

Example problems:   Euclid algorithm of finding GCD ,  Binary Search ,  Josephus problem

Problem-solving using Binary Search

When an array has some order property similar to the sorted array, we can use the binary search idea to solve several searching problems efficiently in O(logn) time complexity. For doing this, we need to modify the standard binary search algorithm based on the conditions given in the problem. The core idea is simple: calculate the mid-index and iterate over the left or right half of the array.

Example problems: Find Peak Element , Search a sorted 2D matrix , Find the square root of an integer , Search in Rotated Sorted Array

Divide and Conquer Approach

This strategy is about dividing a problem into  more than one subproblems,  solving each of them, and then, if necessary, combining their solutions to get a solution to the original problem. We solve many fundamental problems efficiently in computer science by using this strategy.

Example problems:   Merge Sort ,  Quick Sort ,  Median of two sorted arrays

Two Pointers Approach

The two-pointer approach helps us optimize time and space complexity in the case of many searching problems on arrays and linked lists. Here pointers can be pairs of array indices or pointer references to an object. This approach aims to simultaneously iterate over two different input parts to perform fewer operations. There are three variations of this approach:

Pointers are moving in the same direction with the same pace:   Merging two sorted arrays or linked lists, Finding the intersection of two arrays or linked lists , Checking an array is a subset of another array , etc.

Pointers are moving in the same direction at a different pace (Fast and slow pointers):   Partition process in the quick sort , Remove duplicates from the sorted array , Find the middle node in a linked list , Detect loop in a linked list , Move all zeroes to the end , Remove nth node from list end , etc.

Pointers are moving in the opposite direction:  Reversing an array, Check pair sum in an array , Finding triplet with zero-sum , Rainwater trapping problem , Container with most water , etc.

Sliding Window Approach

A sliding window concept is commonly used in solving array/string problems. Here, the window is a contiguous sequence of elements defined by the start and ends indices. We perform some operations on elements within the window and “slide” it in a forward direction by incrementing the left or right end.

This approach can be effective whenever the problem consists of tasks that must be performed on a contiguous block of a fixed or variable size. This could help us improve time complexity in so many problems by converting the nested loop solution into a single loop solution.

Example problems: Longest substring without repeating characters , Count distinct elements in every window , Max continuous series of 1s , Find max consecutive 1's in an array , etc.

Transform and Conquer Approach

This approach is based on transforming a coding problem into another coding problem with some particular property that makes the problem easier to solve. In other words, here we solve the problem is solved in two stages:

• Transformation stage: We transform the original problem into another easier problem to solve.
• Conquering stage: Now, we solve the transformed problem.

Example problems: Pre-sorting based algorithms (Finding the closest pair of points, checking whether all the elements in a given array are distinct, etc.)

Problem-solving using BFS and DFS Traversal

Most tree and graph problems can be solved using DFS and BFS traversal. If the problem is to search for something closer to the root (or source node), we can prefer BFS, and if we need to search for something in-depth, we can choose DFS.

Sometimes, we can use both BFS and DFS traversals when node order is not required. But in some cases, such things are not possible. We need to identify the use case of both traversals to solve the problems efficiently. For example, in binary tree problems:

• We use preorder traversal in a situation when we need to explore all the tree nodes before inspecting any leaves.
• Inorder traversal of BST generates the node's data in increasing order. So we can use inorder to solve several BST problems.
• We can use postorder traversal when we need to explore all the leaf nodes before inspecting any internal nodes.
• Sometimes, we need some specific information about some level. In this situation, BFS traversal helps us to find the output easily.

To solve tree and graph problems, sometimes we pass extra variables or pointers to the function parameters, use helper functions, use parent pointers, store some additional data inside the node, and use data structures like the stack, queue, and priority queue, etc.

Example problems: Find min depth of a binary tree , Merge two binary trees , Find the height of a binary tree , Find the absolute minimum difference in a BST , The kth largest element in a BST , Course scheduling problem , bipartite graph , Find the left view of a binary tree , etc.

Problem-solving using the Data Structures

The data structure is one of the powerful tools of problem-solving in algorithms. It helps us perform some of the critical operations efficiently and improves the time complexity of the solution. Here are some of the key insights:

• Many coding problems require an effcient way to perform the search, insert and delete operations. We can perform all these operations using the hash table in O(1) time average. It's a kind of time-memory tradeoff, where we use extra space to store elements in the hash table to improve performance.
• Sometimes we need to store data in the stack (LIFO order) or queue (FIFO order) to solve several coding problems. 
• Suppose there is a requirement to continuously insert or remove maximum or minimum element (Or element with min or max priority). In that case, we can use a heap (or priority queue) to solve the problem efficiently.
• Sometimes, we store data in Trie, AVL Tree, Segment Tree, etc., to perform some critical operations efficiently. 

Example problems: Next greater element , Valid Parentheses , Largest rectangle in a histogram , Sliding window maximum , kth smallest element in an array , Top k frequent elements , Longest common prefix , Range sum query , Longest consecutive sequence , Check equal array , LFU cache , LRU cache , Counting sort

Dynamic Programming

Dynamic programming is one of the most popular techniques for solving problems with overlapping or repeated subproblems. Here rather than solving overlapping subproblems repeatedly, we solve each smaller subproblems only once and store the results in memory. We can solve a lot of optimization and counting problems using the idea of dynamic programming.

Example problems: Finding nth Fibonacci,  Longest Common Subsequence ,  Climbing Stairs Problem ,  Maximum Subarray Sum ,  Minimum number of Jumps to reach End ,  Minimum Coin Change

Greedy Approach

This solves an optimization problem by expanding a partially constructed solution until a complete solution is reached. We take a greedy choice at each step and add it to the partially constructed solution. This idea produces the optimal global solution without violating the problem’s constraints.

• The greedy choice is the best alternative available at each step is made in the hope that a sequence of locally optimal choices will yield a (globally) optimal solution to the entire problem.
• This approach works in some cases but fails in others. Usually, it is not difficult to design a greedy algorithm itself, but a more difficult task is to prove that it produces an optimal solution.

Example problems: Fractional Knapsack, Dijkstra algorithm, The activity selection problem

Exhaustive Search

This strategy explores all possibilities of solutions until a solution to the problem is found. Therefore, problems are rarely offered to a person to solve the problem using this strategy.

The most important limitation of exhaustive search is its inefficiency. As a rule, the number of solution candidates that need to be processed grows at least exponentially with the problem size, making the approach inappropriate not only for a human but often for a computer as well.

But in some situations, there is a need to explore all possible solution spaces in a coding problem. For example: Find all permutations of a string , Print all subsets , etc.

Backtracking

Backtracking is an improvement over the approach of exhaustive search. It is a method for generating a solution by avoiding unnecessary possibilities of the solutions! The main idea is to build a solution one piece at a time and evaluate each partial solution as follows:

• If a partial solution can be developed further without violating the problem’s constraints, it is done by taking the first remaining valid option at the next stage. ( Think! )
• Suppose there is no valid option at the next stage, i.e., If there is a violation of the problem constraint, the algorithm backtracks to replace the partial solution’s previous stage with the following option for that stage. ( Think! )

In simple words, backtracking involves undoing several wrong choices — the smaller this number, the faster the algorithm finds a solution. In the worst-case scenario, a backtracking algorithm may end up generating all the solutions as an exhaustive search, but this rarely happens!

Example problems: N-queen problem , Find all k combinations , Combination sum , Sudoku solver , etc.

Problem-solving using Bit manipulation and Numbers theory

Some of the coding problems are, by default, mathematical, but sometimes we need to identify the hidden mathematical properties inside the problem. So the idea of number theory and bit manipulation is helpful in so many cases.

Sometimes understanding the bit pattern of the input and processing data at the bit level help us design an efficient solution. The best part is that the computer performs each bit-wise operation in constant time. Even sometimes, bit manipulation can reduce the requirement of extra loops and improve the performance by a considerable margin.

Example problems: Reverse bits , Add binary string , Check the power of two , Find the missing number , etc.

Hope you enjoyed the blog. Later we will write a separate blog on each problem-solving approach. Enjoy learning, Enjoy algorithms!

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Scaler Topics free online course is designed to help you prepare for data structure and algorithm (DSA) interview questions using Java. It is suitable for beginners who want to learn DSA problem solving and its applications in job interviews.

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🕵️‍♂️ Elevate your problem-solving skills and gain a deeper understanding of Arrays and Array Manipulation.  Prepare to conquer your next interview with confidence and finesse by practicing our DSA Problems.