Mastering Algorithms and Data Structures for Beginners: A StepbyStep Guide and Complete Roadmap
Ouhadj ilyes
Software Engineer
Web Development
Category
Feb. 22, 2023
Updated on
This article is meant for absolute beginners that struggle to find the exact steps and resources to start learning Algorithms & Data Structures. Hopefully, at the end of this article, you'll be able to make a curriculum for yourself to get a really good understanding of Algorithms & Data Structures that will eventually make you a much better programmer.
The resources I provide in this article have helped me and many other software engineers to be better at problem solving, writing better software designs as well as thoroughly thinking of efficiency and performance when writing code.
I will just assume you know at least the definition of both Algorithms and Data Structures.
Without further intros, let's get started !
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 Algorithms & Data Structures
Why Bother With Algorithms & Data Structures ?
Algorithms and data structures are essential for all of the different roles and specialties in computer science and here's 3 reasons why you need to consider at least mastering the basics:

Improve Problem Solving Capabilities
An algorithm in its core definition is just the exact steps of solving a particular problem, and coding problems involve analyzing, storing and manipulating data, that's where comes the need for data structures which are nothing but “meaningful” arrangements of that data. However, sometimes there's different solutions for the same problem, algorithms will not only teach you how to solve problems but also how to find the best solutions for your problems.

Build Efficinet & Optimized Software
As I just mentioned, when there's different solutions for the same coding problem, the main goal of algorithms and data structures is to find the best solution that takes less time as well as less space in memory, and that's what efficient and performant software is all about.

Ace Job Interviews
Organizations such as Google and Facebook look for employees who have a good grasp of data structures and algorithms, and questions about such skills are frequently asked in job interviews.
CS50 : Start Here !
CS50 is an oncampus and online introductory course on computer science taught at Harvard University and Yale University. If you are an absolute beginner, the first thing to consider is an introduction to the world of algorithms and data structures, but while you find all the introductory resources online pretty boring and just making things more complicated, CS50 have got the best 2 introductory videos on this planet on algorithms and Data Structures.
Their way of explaining things is pretty simple and brilliant that anyone new to this field will feel comfortable learning these two skills. This has to be the best place to start from to get a really good grasp of the foundations.
You can watch the videos on their official website here. you can also find them on this Youtube Playlist on their channel.
Grokking Algorithms
Even though you can start from here as well, but I will highly recommend watching the CS50 videos on algorithms and data structures, they will give you a great understanding of the foundations of those two skills, and grasping the intermediate or advanced topics would be much easier.
After grasping the foundations, the next step would be reading a book about algorithms and data structures, not a detailed textbook or a 1000pages boring book, but Grokking Algorithms is the friendliest and easiest book to read ever written on algorithms and data structures, it's meant for absolute beginners so if you exposed yourself to the advanced topics so far then you are not going to learn much from this book.
Grokking Algorithms is a fully illustrated, friendly guide that teaches you how to apply algorithms and data structures to the practical problems you face every day as a programmer. it stands out with its really simple explanations and lots of real life examples and illustrations, it uses pythonbased code samples and over 400 pictures with detailed walkthroughs. But remember to practice, and make sure to complete all the exercises at the end of each chapter before looking at their solutions.
Once you finish reading this book, you'll be comfortable enough to study the advanced topics on your own (check out the Roadmap below), you may also consider reading a detailed textbook if you are into reading books. I will recommend reading Introduction to Algorithms by Thomas H. Cormen
Roadmap : Do It On Your Own
Once you consume the resources I provided in the previous sections or if you are not a beginner and already acquire the core concepts and foundations, here's a detailed roadmap for mastering algorithms and data structures, to help you find out where you are at your current stage and where to go next. I will also provide some links to resources that may be helpful to you to learn each topic on your own.

Prerequisites : Phase 0
The only prerequisite before learning algorithms and data structures is having some prior knowledge of at least one programming language, if you have no prior experience with any programming languages, I will recommend starting with Python as it is one of the most popular and easiest languages to learn and pick up quickly.
If you choose to go with python, you will only need to grasp the basics at least, here's a list of some of the python basics that you will most likely need before starting to learn algorithms and data structures:
 Variables
 Conditions
 Chained Conditionals
 Operators
 Control Flow (If/Else)
 Loops and Iterables
 Functions
 Mutable vs. Immutable
 Common Methods
 File IO
 ...
Resources for Python basics:
 Docs : Python Official Docs
 Book : Python Crash Course
 Online Course : A Beginners Guide to Python Programming
If you are not comfortable reading books or documentations, you can find great content on Youtube to learn the basics of Python.

Core Algorithm Concepts : Phase 1

BigO Analysis
 Onotation. Ωnotation. θnotation
 Asymptotic Notation
 Standard Notations
 Common Functions
 Onotation. Ωnotation. θnotation

Algorithm Design
 Reasoning About Correctness
 Modeling The Problem
 Proof By Contradiction
 Estimation

Sorting
 Elementary Sorts
 Mergesort
 Quicksort
 Priority Queues

Searching
 Symbol Tables
 Binary Search
 Balanced Search
 Hash Tables

Recursion
 Base Case & Recursive Case
 The Stack
 TopDown Recursion
 The Staircase Problem

Divide & Conquer
 Multiplying Square Matrices
 Strassen's algorithm
 Solving Recurrences
 Proof of the continuous master theorem


Intermediate Topics : Phase 2

Two Pointers
 Two Pointer Technique
 Analysis
 Implementation

Binary Trees
 Binary Search Trees
 Analyzing Performance of Binary search Trees
 Using Binary Tree as (Key, Value) Symbol Table
 Using The Binary Tree as a Priority Queue

Backtracking
 Backtracking Technique
 Backtracking Algorithms

Dynamic Programming
 Rod Cutting
 Matrixchain multiplication
 Elements of dynamic programming
 Longest common subsequence
 Optimal binary search trees

Greedy Algorithms
 Activityselection problems
 Elements of the greedy strategy
 Huffman codes
 Offline caching

Amortized Analysis
 Aggregate analysis
 The accounting method
 The potential method
 Dynamic tables


Advanced Concepts : Phase 3

Graph Algorithms
 Elementary Graph Algorithms
 Minimum Spanning Trees
 SingleSource Shortest Paths
 AllPairs Shortest Paths
 Maximum Flow
 Matchings in Bipartite Graphs

Parallel Algorithms
 The basics of forkjoin parallelism
 Parallel matrix multiplication
 Parallel merge sort

Online Algorithms
 Waiting for an elevator
 Maintaining a search list
 Online caching

Matrix Operations
 Solving systems of linear equations
 Inverting matrices
 Symmetric positivedefinite matrices and leastsquares approximation

Linear Programming
 Linear programming formulations and algorithms
 Formulating problems as linear programs
 Duality

Polynomials and the FFT
 Representing polynomials
 The DFT and FFT
 FFT circuits

NumberTheoretic Algorithms
 Elementary numbertheoretic notions
 Greatest common divisor
 Modular arithmetic
 The RSA publickey cryptosystem
 Primality testing

String Matching
 The naive stringmatching algorithm
 The RabinKarp algorithm
 The KnuthMorrisPratt algorithm
 Suffix arrays

Approximation Algorithms
 The vertexcover problem
 The travelingsalesperson problem
 The setcovering problem
 Randomization and linear programming
 The subsetsum problem


Data Structures : Phase 4
Basic & Intermediate Data Structures:

Elementary Data Structures
 Arrays, matrices, stacks, queues
 Linked Lists
 Rooted Trees

Hash Tables
 Directaddress tables
 Hash tables
 Hash functions
 Open addressing

RedBlack Trees
 Properties of redblack trees
 Rotations
 Insertion
 Deletion
Advanced Data Structures:

Augmenting Data Structures
 Dynamic order statistics
 How to augment a data structure
 Interval trees

BTrees
 What is a BTree
 Operations on BTrees
 Deleting a key from a BTree

Data Structures for Disjoint Sets
 Disjointset operations
 Linkedlist representations of disjoint sets
 Disjointset forests
 Analysis of union by rank with path compression


Roadmap Learning Resources:

Books
Each one of these books covers from one to many topics listed on the Roadmap, by reading all of them you'll have covered all of the topics of this Roadmap (Make sure to practice for as much as possible, you can finish all of them in 12 weeks but without practicing, you are just wasting your time):

Online Courses
Some people prefer watching and listening rather than reading, but a combination of those two will make learning and grasping the concepts deeper and much easier. Here's some online courses that can help:

Conclusion
Now we would like to hear your thoughts, if you need more help or have any questions, feel free to reach out to us using the Contact Form or by Email and we would be happy to help !