Coding Interview University
I originally created this as a short to-do list of study topics for becoming a software engineer,
but it grew to the large list you see today. After going through this study plan, I got hired
as a Software Development Engineer at Amazon!
You probably won't have to study as much as I did. Anyway, everything you need is here.
The items listed here will prepare you well for in an interview at just about any software company,
including the giants: Amazon, Facebook, Google or Microsoft.
Best of luck to you!
- Tiếng Việt - Vietnamese
- Português Brasileiro
Translations in progress:
- Bahasa Indonesia
- Japanese (日本語)
What is it?
This is my multi-month study plan for going from web developer (self-taught, no CS degree) to software engineer for a large company.
This is meant for new software engineers or those switching from
software/web development to software engineering (where computer science knowledge is required). If you have
many years of experience and are claiming many years of software engineering experience, expect a harder interview.
If you have many years of software/web development experience, note that large software companies like Google, Amazon,
Facebook and Microsoft view software engineering as different from software/web development, and they require computer science knowledge.
If you want to be a reliability engineer or operations engineer, study more from the optional list (networking, security).
Table of Contents
---------------- Everything below this point is optional ----------------
Why use it?
When I started this project, I didn't know a stack from a heap, didn't know Big-O anything, anything about trees, or how to
traverse a graph. If I had to code a sorting algorithm, I can tell ya it wouldn't have been very good.
Every data structure I've ever used was built into the language, and I didn't know how they worked
under the hood at all. I've never had to manage memory unless a process I was running would give an "out of
memory" error, and then I'd have to find a workaround. I've used a few multidimensional arrays in my life and
thousands of associative arrays, but I've never created data structures from scratch.
It's a long plan. It may take you months. If you are familiar with a lot of this already it will take you a lot less time.
How to use it
Everything below is an outline, and you should tackle the items in order from top to bottom.
I'm using Github's special markdown flavor, including tasks lists to check progress.
Create a new branch so you can check items like this, just put an x in the brackets: [x]
Fork a branch and follow the commands below
git checkout -b progress
git remote add jwasham https://github.com/jwasham/coding-interview-university
git fetch --all
Mark all boxes with X after you completed your changes
git add .
git commit -m "Marked x"
git rebase jwasham/master
git push --force
More about Github-flavored markdown
Don't feel you aren't smart enough
About Video Resources
Some videos are available only by enrolling in a Coursera, EdX, or Lynda.com class. These are called MOOCs.
Sometimes the classes are not in session so you have to wait a couple of months, so you have no access. Lynda.com courses are not free.
I'd appreciate your help to add free and always-available public sources, such as YouTube videos to accompany the online course videos.
I like using university lectures.
Interview Process & General Interview Prep
Pick One Language for the Interview
You can use a language you are comfortable in to do the coding part of the interview, but for large companies, these are solid choices:
You could also use these, but read around first. There may be caveats:
You need to be very comfortable in the language and be knowledgeable.
Read more about choices:
See language resources here
You'll see some C, C++, and Python learning included below, because I'm learning. There are a few books involved, see the bottom.
This is a shorter list than what I used. This is abbreviated to save you time.
If you have tons of extra time:
If short on time:
- [ ] Write Great Code: Volume 1: Understanding the Machine
- The book was published in 2004, and is somewhat outdated, but it's a terrific resource for understanding a computer in brief.
- The author invented HLA, so take mentions and examples in HLA with a grain of salt. Not widely used, but decent examples of what assembly looks like.
- These chapters are worth the read to give you a nice foundation:
- Chapter 2 - Numeric Representation
- Chapter 3 - Binary Arithmetic and Bit Operations
- Chapter 4 - Floating-Point Representation
- Chapter 5 - Character Representation
- Chapter 6 - Memory Organization and Access
- Chapter 7 - Composite Data Types and Memory Objects
- Chapter 9 - CPU Architecture
- Chapter 10 - Instruction Set Architecture
- Chapter 11 - Memory Architecture and Organization
If you have more time (I want this book):
You need to choose a language for the interview (see above). Here are my recommendations by language. I don't have resources for all languages. I welcome additions.
If you read though one of these, you should have all the data structures and algorithms knowledge you'll need to start doing coding problems.
You can skip all the video lectures in this project, unless you'd like a review.
Additional language-specific resources here.
I haven't read these two, but they are highly rated and written by Sedgewick. He's awesome.
If you have a better recommendation for C++, please let me know. Looking for a comprehensive resource.
- [ ] Data Structures and Algorithms in Java
- by Goodrich, Tamassia, Goldwasser
- used as optional text for CS intro course at UC Berkeley
- see my book report on the Python version below. This book covers the same topics.
- [ ] Data Structures and Algorithms in Python
- by Goodrich, Tamassia, Goldwasser
- I loved this book. It covered everything and more.
- Pythonic code
- my glowing book report: https://startupnextdoor.com/book-report-data-structures-and-algorithms-in-python/
Some people recommend these, but I think it's going overboard, unless you have many years of software engineering experience and expect a much harder interview:
[ ] Algorithm Design Manual (Skiena)
- As a review and problem recognition
- The algorithm catalog portion is well beyond the scope of difficulty you'll get in an interview.
- This book has 2 parts:
- class textbook on data structures and algorithms
- is a good review as any algorithms textbook would be
- nice stories from his experiences solving problems in industry and academia
- code examples in C
- can be as dense or impenetrable as CLRS, and in some cases, CLRS may be a better alternative for some subjects
- chapters 7, 8, 9 can be painful to try to follow, as some items are not explained well or require more brain than I have
- don't get me wrong: I like Skiena, his teaching style, and mannerisms, but I may not be Stony Brook material.
- algorithm catalog:
- this is the real reason you buy this book.
- about to get to this part. Will update here once I've made my way through it.
- Can rent it on kindle
[ ] Introduction to Algorithms
Important: Reading this book will only have limited value. This book is a great review of algorithms and data structures, but won't teach you how to write good code. You have to be able to code a decent solution efficiently.
- aka CLR, sometimes CLRS, because Stein was late to the game
[ ] Programming Pearls
- The first couple of chapters present clever solutions to programming problems (some very old using data tape) but
that is just an intro. This a guidebook on program design and architecture, much like Code Complete, but much shorter.
~~"Algorithms and Programming: Problems and Solutions" by Shen~~
- A fine book, but after working through problems on several pages I got frustrated with the Pascal, do while loops, 1-indexed arrays, and unclear post-condition satisfaction results.
- Would rather spend time on coding problems from another book or online coding problems.
Before you Get Started
This list grew over many months, and yes, it kind of got out of hand.
Here are some mistakes I made so you'll have a better experience.
1. You Won't Remember it All
I watched hours of videos and took copious notes, and months later there was much I didn't remember. I spent 3 days going
through my notes and making flashcards so I could review.
Read please so you won't make my mistakes:
Retaining Computer Science Knowledge
2. Use Flashcards
To solve the problem, I made a little flashcards site where I could add flashcards of 2 types: general and code.
Each card has different formatting.
I made a mobile-first website so I could review on my phone and tablet, wherever I am.
Make your own for free:
Keep in mind I went overboard and have cards covering everything from assembly language and Python trivia to machine learning and statistics. It's way too much for what's required.
Note on flashcards: The first time you recognize you know the answer, don't mark it as known. You have to see the
same card and answer it several times correctly before you really know it. Repetition will put that knowledge deeper in
An alternative to using my flashcard site is Anki, which has been recommended to me numerous times. It uses a repetition system to help you remember.
It's user-friendly, available on all platforms and has a cloud sync system. It costs $25 on iOS but is free on other platforms.
My flashcard database in Anki format: https://ankiweb.net/shared/info/25173560 (thanks @xiewenya)
3. Review, review, review
I keep a set of cheat sheets on ASCII, OSI stack, Big-O notations, and more. I study them when I have some spare time.
Take a break from programming problems for a half hour and go through your flashcards.
There are a lot of distractions that can take up valuable time. Focus and concentration are hard.
What you won't see covered
These are prevalent technologies but not part of this study plan:
- HTML, CSS, and other front-end technologies
The Daily Plan
Some subjects take one day, and some will take multiple days. Some are just learning with nothing to implement.
Each day I take one subject from the list below, watch videos about that subject, and write an implementation in:
- C - using structs and functions that take a struct * and something else as args.
- C++ - without using built-in types
- C++ - using built-in types, like STL's std::list for a linked list
- Python - using built-in types (to keep practicing Python)
- and write tests to ensure I'm doing it right, sometimes just using simple assert() statements
- You may do Java or something else, this is just my thing.
You don't need all these. You need only one language for the interview.
Why code in all of these?
- Practice, practice, practice, until I'm sick of it, and can do it with no problem (some have many edge cases and bookkeeping details to remember)
- Work within the raw constraints (allocating/freeing memory without help of garbage collection (except Python))
- Make use of built-in types so I have experience using the built-in tools for real-world use (not going to write my own linked list implementation in production)
I may not have time to do all of these for every subject, but I'll try.
You can see my code here:
You don't need to memorize the guts of every algorithm.
Write code on a whiteboard or paper, not a computer. Test with some sample inputs. Then test it out on a computer.
Algorithmic complexity / Big-O / Asymptotic analysis
- Implement an automatically resizing vector.
- [ ] Description:
- [ ] Implement a vector (mutable array with automatic resizing):
- [ ] Practice coding using arrays and pointers, and pointer math to jump to an index instead of using indexing.
- [ ] new raw data array with allocated memory
- can allocate int array under the hood, just not use its features
- start with 16, or if starting number is greater, use power of 2 - 16, 32, 64, 128
- [ ] size() - number of items
- [ ] capacity() - number of items it can hold
- [ ] is_empty()
- [ ] at(index) - returns item at given index, blows up if index out of bounds
- [ ] push(item)
- [ ] insert(index, item) - inserts item at index, shifts that index's value and trailing elements to the right
- [ ] prepend(item) - can use insert above at index 0
- [ ] pop() - remove from end, return value
- [ ] delete(index) - delete item at index, shifting all trailing elements left
- [ ] remove(item) - looks for value and removes index holding it (even if in multiple places)
- [ ] find(item) - looks for value and returns first index with that value, -1 if not found
- [ ] resize(new_capacity) // private function
- when you reach capacity, resize to double the size
- when popping an item, if size is 1/4 of capacity, resize to half
- [ ] Time
- O(1) to add/remove at end (amortized for allocations for more space), index, or update
- O(n) to insert/remove elsewhere
- [ ] Space
- contiguous in memory, so proximity helps performance
- space needed = (array capacity, which is >= n) * size of item, but even if 2n, still O(n)
- [ ] Description:
- [ ] C Code (video)
- not the whole video, just portions about Node struct and memory allocation.
- [ ] Linked List vs Arrays:
- [ ] why you should avoid linked lists (video)
- [ ] Gotcha: you need pointer to pointer knowledge:
(for when you pass a pointer to a function that may change the address where that pointer points)
This page is just to get a grasp on ptr to ptr. I don't recommend this list traversal style. Readability and maintainability suffer due to cleverness.
- [ ] implement (I did with tail pointer & without):
- [ ] size() - returns number of data elements in list
- [ ] empty() - bool returns true if empty
- [ ] value_at(index) - returns the value of the nth item (starting at 0 for first)
- [ ] push_front(value) - adds an item to the front of the list
- [ ] pop_front() - remove front item and return its value
- [ ] push_back(value) - adds an item at the end
- [ ] pop_back() - removes end item and returns its value
- [ ] front() - get value of front item
- [ ] back() - get value of end item
- [ ] insert(index, value) - insert value at index, so current item at that index is pointed to by new item at index
- [ ] erase(index) - removes node at given index
- [ ] valuenfrom_end(n) - returns the value of the node at nth position from the end of the list
- [ ] reverse() - reverses the list
- [ ] remove_value(value) - removes the first item in the list with this value
- [ ] Doubly-linked List
- [ ] Using Queues First-In First-Out(video)
- [ ] Queue (video)
- [ ] Circular buffer/FIFO
- [ ] Priority Queues (video)
- [ ] Implement using linked-list, with tail pointer:
- enqueue(value) - adds value at position at tail
- dequeue() - returns value and removes least recently added element (front)
- [ ] Implement using fixed-sized array:
- enqueue(value) - adds item at end of available storage
- dequeue() - returns value and removes least recently added element
- [ ] Cost:
- a bad implementation using linked list where you enqueue at head and dequeue at tail would be O(n)
because you'd need the next to last element, causing a full traversal each dequeue
- enqueue: O(1) (amortized, linked list and array [probing])
- dequeue: O(1) (linked list and array)
- empty: O(1) (linked list and array)
- [ ] Videos:
- [ ] Online Courses:
- [ ] implement with array using linear probing
- hash(k, m) - m is size of hash table
- add(key, value) - if key already exists, update value
- [ ] Bits cheat sheet - you should know many of the powers of 2 from (2^1 to 2^16 and 2^32)
- [ ] Get a really good understanding of manipulating bits with: &, |, ^, ~, >>, <<
- [ ] 2s and 1s complement
- [ ] count set bits
- [ ] round to next power of 2:
- [ ] swap values:
- [ ] absolute value:
Trees - Notes & Background
- [ ] Series: Core Trees (video)
- [ ] Series: Trees (video)
- basic tree construction
- manipulation algorithms
- BFS (breadth-first search)
- MIT (video)
- level order (BFS, using queue)
time complexity: O(n)
space complexity: best: O(1), worst: O(n/2)=O(n)
- DFS (depth-first search)
- MIT (video)
time complexity: O(n)
best: O(log n) - avg. height of tree
- inorder (DFS: left, self, right)
- postorder (DFS: left, right, self)
- preorder (DFS: self, left, right)
Binary search trees: BSTs
- [ ] Binary Search Tree Review (video)
- [ ] Series (video)
- starts with symbol table and goes through BST applications
- [ ] Introduction (video)
- [ ] MIT (video)
- [ ] Implement:
- [ ] insert // insert value into tree
- [ ] getnodecount // get count of values stored
- [ ] print_values // prints the values in the tree, from min to max
- [ ] delete_tree
- [ ] isintree // returns true if given value exists in the tree
- [ ] get_height // returns the height in nodes (single node's height is 1)
- [ ] get_min // returns the minimum value stored in the tree
- [ ] get_max // returns the maximum value stored in the tree
- [ ] isbinarysearch_tree
- [ ] delete_value
- [ ] get_successor // returns next-highest value in tree after given value, -1 if none
Heap / Priority Queue / Binary Heap
As a summary, here is a visual representation of 15 sorting algorithms.
If you need more detail on this subject, see "Sorting" section in Additional Detail on Some Subjects
Graphs can be used to represent many problems in computer science, so this section is long, like trees and sorting were.
You'll get more graph practice in Skiena's book (see Books section below) and the interview books
Even More Knowledge
System Design, Scalability, Data Handling
- You can expect system design questions if you have 4+ years of experience.
- Scalability and System Design are very large topics with many topics and resources, since
there is a lot to consider when designing a software/hardware system that can scale.
Expect to spend quite a bit of time on this.
- Distill large data sets to single values
- Transform one data set to another
- Handling obscenely large amounts of data
- system design
- features sets
- class hierarchies
- designing a system under certain constraints
- simplicity and robustness
- performance analysis and optimization
- [ ] START HERE: The System Design Primer
- [ ] System Design from HiredInTech
- [ ] How Do I Prepare To Answer Design Questions In A Technical Inverview?
- [ ] 8 Things You Need to Know Before a System Design Interview
- [ ] Algorithm design
- [ ] Database Normalization - 1NF, 2NF, 3NF and 4NF (video)
- [ ] System Design Interview - There are a lot of resources in this one. Look through the articles and examples. I put some of them below.
- [ ] How to ace a systems design interview
- [ ] Numbers Everyone Should Know
- [ ] How long does it take to make a context switch?
- [ ] Transactions Across Datacenters (video)
- [ ] A plain English introduction to CAP Theorem
- [ ] Paxos Consensus algorithm:
- [ ] Consistent Hashing
- [ ] NoSQL Patterns
- [ ] Scalability:
- [ ] Great overview (video)
- [ ] Short series:
- [ ] Scalable Web Architecture and Distributed Systems
- [ ] Fallacies of Distributed Computing Explained
- [ ] Pragmatic Programming Techniques
- [ ] Jeff Dean - Building Software Systems At Google and Lessons Learned (video)
- [ ] Introduction to Architecting Systems for Scale
- [ ] Scaling mobile games to a global audience using App Engine and Cloud Datastore (video)
- [ ] How Google Does Planet-Scale Engineering for Planet-Scale Infra (video)
- [ ] The Importance of Algorithms
- [ ] Sharding
- [ ] Scale at Facebook (2009)
- [ ] Scale at Facebook (2012), "Building for a Billion Users" (video)
- [ ] Engineering for the Long Game - Astrid Atkinson Keynote(video)
- [ ] 7 Years Of YouTube Scalability Lessons In 30 Minutes
- [ ] How PayPal Scaled To Billions Of Transactions Daily Using Just 8VMs
- [ ] How to Remove Duplicates in Large Datasets
- [ ] A look inside Etsy's scale and engineering culture with Jon Cowie (video)
- [ ] What Led Amazon to its Own Microservices Architecture
- [ ] To Compress Or Not To Compress, That Was Uber's Question
- [ ] Asyncio Tarantool Queue, Get In The Queue
- [ ] When Should Approximate Query Processing Be Used?
- [ ] Google's Transition From Single Datacenter, To Failover, To A Native Multihomed Architecture
- [ ] Spanner
- [ ] Egnyte Architecture: Lessons Learned In Building And Scaling A Multi Petabyte Distributed System
- [ ] Machine Learning Driven Programming: A New Programming For A New World
- [ ] The Image Optimization Technology That Serves Millions Of Requests Per Day
- [ ] A Patreon Architecture Short
- [ ] Tinder: How Does One Of The Largest Recommendation Engines Decide Who You'll See Next?
- [ ] Design Of A Modern Cache
- [ ] Live Video Streaming At Facebook Scale
- [ ] A Beginner's Guide To Scaling To 11 Million+ Users On Amazon's AWS
- [ ] How Does The Use Of Docker Effect Latency?
- [ ] Does AMP Counter An Existential Threat To Google?
- [ ] A 360 Degree View Of The Entire Netflix Stack
- [ ] Latency Is Everywhere And It Costs You Sales - How To Crush It
- [ ] Serverless (very long, just need the gist)
- [ ] What Powers Instagram: Hundreds of Instances, Dozens of Technologies
- [ ] Cinchcast Architecture - Producing 1,500 Hours Of Audio Every Day
- [ ] Justin.Tv's Live Video Broadcasting Architecture
- [ ] Playfish's Social Gaming Architecture - 50 Million Monthly Users And Growing
- [ ] TripAdvisor Architecture - 40M Visitors, 200M Dynamic Page Views, 30TB Data
- [ ] PlentyOfFish Architecture
- [ ] Salesforce Architecture - How They Handle 1.3 Billion Transactions A Day
- [ ] ESPN's Architecture At Scale - Operating At 100,000 Duh Nuh Nuhs Per Second
- [ ] See "Messaging, Serialization, and Queueing Systems" way below for info on some of the technologies that can glue services together
- [ ] Twitter:
- For even more, see "Mining Massive Datasets" video series in the Video Series section.
- [ ] Practicing the system design process: Here are some ideas to try working through on paper, each with some documentation on how it was handled in the real world:
- review: The System Design Primer
- System Design from HiredInTech
- cheat sheet
- Understand the problem and scope:
- define the use cases, with interviewer's help
- suggest additional features
- remove items that interviewer deems out of scope
- assume high availability is required, add as a use case
- Think about constraints:
- ask how many requests per month
- ask how many requests per second (they may volunteer it or make you do the math)
- estimate reads vs. writes percentage
- keep 80/20 rule in mind when estimating
- how much data written per second
- total storage required over 5 years
- how much data read per second
- Abstract design:
- layers (service, data, caching)
- infrastructure: load balancing, messaging
- rough overview of any key algorithm that drives the service
- consider bottlenecks and determine solutions
This section will have shorter videos that you can watch pretty quickly to review most of the important concepts.
It's nice if you want a refresher often.
Coding Question Practice
Now that you know all the computer science topics above, it's time to practice answering coding problems.
Coding question practice is not about memorizing answers to programming problems.
Why you need to practice doing programming problems:
- problem recognition, and where the right data structures and algorithms fit in
- gathering requirements for the problem
- talking your way through the problem like you will in the interview
- coding on a whiteboard or paper, not a computer
- coming up with time and space complexity for your solutions
- testing your solutions
There is a great intro for methodical, communicative problem solving in an interview. You'll get this from the programming
interview books, too, but I found this outstanding:
Algorithm design canvas
No whiteboard at home? That makes sense. I'm a weirdo and have a big whiteboard. Instead of a whiteboard, pick up a
large drawing pad from an art store. You can sit on the couch and practice. This is my "sofa whiteboard".
I added the pen in the photo for scale. If you use a pen, you'll wish you could erase. Gets messy quick.
Read and Do Programming Problems (in this order):
See Book List above
Once you've learned your brains out, put those brains to work.
Take coding challenges every day, as many as you can.
Coding Interview Question Videos:
- IDeserve (88 videos)
- Tushar Roy (5 playlists)
- Project Euler (math-focused)
- Geeks for Geeks
- Sphere Online Judge (spoj)
- Interactive Coding Interview Challenges in Python
- Gainlo.co: Mock interviewers from big companies - I used this and it helped me relax for the phone screen and on-site interview.
- Pramp: Mock interviews from/with peers - peer-to-peer model of practice interviews
- Refdash: Mock interviews and expedited interviews - also help candidates fast track by skipping multiple interviews with tech companies.
Once you're closer to the interview
- [ ] Cracking The Coding Interview Set 2 (videos):
- See Resume prep items in Cracking The Coding Interview and back of Programming Interviews Exposed
Be thinking of for when the interview comes
Think of about 20 interview questions you'll get, along with the lines of the items below. Have 2-3 answers for each.
Have a story, not just data, about something you accomplished.
- Why do you want this job?
- What's a tough problem you've solved?
- Biggest challenges faced?
- Best/worst designs seen?
- Ideas for improving an existing product.
- How do you work best, as an individual and as part of a team?
- Which of your skills or experiences would be assets in the role and why?
- What did you most enjoy at [job x / project y]?
- What was the biggest challenge you faced at [job x / project y]?
- What was the hardest bug you faced at [job x / project y]?
- What did you learn at [job x / project y]?
- What would you have done better at [job x / project y]?
Have questions for the interviewer
Some of mine (I already may know answer to but want their opinion or team perspective):
- How large is your team?
- What does your dev cycle look like? Do you do waterfall/sprints/agile?
- Are rushes to deadlines common? Or is there flexibility?
- How are decisions made in your team?
- How many meetings do you have per week?
- Do you feel your work environment helps you concentrate?
- What are you working on?
- What do you like about it?
- What is the work life like?
Once You've Got The Job
You're never really done.
Everything below this point is optional.
By studying these, you'll get greater exposure to more CS concepts, and will be better prepared for
any software engineering job. You'll be a much more well-rounded software engineer.
These topics will likely not come up in an interview, but I added them to help you become a well-rounded
software engineer, and to be aware of certain technologies and algorithms, so you'll have a bigger toolbox.
Emacs and vi(m)
- Familiarize yourself with a unix-based code editor
Unix command line tools
- I filled in the list below from good tools.
- [ ] bash
- [ ] cat
- [ ] grep
- [ ] sed
- [ ] awk
- [ ] curl or wget
- [ ] sort
- [ ] tr
- [ ] uniq
- [ ] strace
- [ ] tcpdump
Information theory (videos)
- [ ] Khan Academy
- [ ] more about Markov processes:
- See more in MIT 6.050J Information and Entropy series below.
Parity & Hamming Code (videos)
Messaging, Serialization, and Queueing Systems
Fast Fourier Transform
- used to determine the similarity of documents
- the opposite of MD5 or SHA which are used to determine if 2 documents/strings are exactly the same.
- Simhashing (hopefully) made simple
van Emde Boas Trees
Augmented Data Structures
Balanced search trees
- Know least one type of balanced binary tree (and know how it's implemented):
- "Among balanced search trees, AVL and 2/3 trees are now passé, and red-black trees seem to be more popular.
A particularly interesting self-organizing data structure is the splay tree, which uses rotations
to move any accessed key to the root." - Skiena
- Of these, I chose to implement a splay tree. From what I've read, you won't implement a
balanced search tree in your interview. But I wanted exposure to coding one up
and let's face it, splay trees are the bee's knees. I did read a lot of red-black tree code.
- splay tree: insert, search, delete functions
If you end up implementing red/black tree try just these:
- search and insertion functions, skipping delete
- I want to learn more about B-Tree since it's used so widely with very large data sets.
- [ ] Self-balancing binary search tree
- [ ] AVL trees
- In practice:
From what I can tell, these aren't used much in practice, but I could see where they would be:
The AVL tree is another structure supporting O(log n) search, insertion, and removal. It is more rigidly
balanced than red–black trees, leading to slower insertion and removal but faster retrieval. This makes it
attractive for data structures that may be built once and loaded without reconstruction, such as language
dictionaries (or program dictionaries, such as the opcodes of an assembler or interpreter).
- [ ] MIT AVL Trees / AVL Sort (video)
- [ ] AVL Trees (video)
- [ ] AVL Tree Implementation (video)
- [ ] Split And Merge
- [ ] Splay trees
- In practice:
Splay trees are typically used in the implementation of caches, memory allocators, routers, garbage collectors,
data compression, ropes (replacement of string used for long text strings), in Windows NT (in the virtual memory,
networking and file system code) etc.
- [ ] CS 61B: Splay Trees (video)
- [ ] MIT Lecture: Splay Trees:
- Gets very mathy, but watch the last 10 minutes for sure.
- [ ] Red/black trees
- these are a translation of a 2-3 tree (see below)
- In practice:
Red–black trees offer worst-case guarantees for insertion time, deletion time, and search time.
Not only does this make them valuable in time-sensitive applications such as real-time applications,
but it makes them valuable building blocks in other data structures which provide worst-case guarantees;
for example, many data structures used in computational geometry can be based on red–black trees, and
the Completely Fair Scheduler used in current Linux kernels uses red–black trees. In the version 8 of Java,
the Collection HashMap has been modified such that instead of using a LinkedList to store identical elements with poor
hashcodes, a Red-Black tree is used.
- [ ] Aduni - Algorithms - Lecture 4 (link jumps to starting point) (video)
- [ ] Aduni - Algorithms - Lecture 5 (video)
- [ ] Red-Black Tree
- [ ] An Introduction To Binary Search And Red Black Tree
- [ ] 2-3 search trees
- [ ] 2-3-4 Trees (aka 2-4 trees)
- In practice:
For every 2-4 tree, there are corresponding red–black trees with data elements in the same order. The insertion and deletion
operations on 2-4 trees are also equivalent to color-flipping and rotations in red–black trees. This makes 2-4 trees an
important tool for understanding the logic behind red–black trees, and this is why many introductory algorithm texts introduce
2-4 trees just before red–black trees, even though 2-4 trees are not often used in practice.
- [ ] CS 61B Lecture 26: Balanced Search Trees (video)
- [ ] Bottom Up 234-Trees (video)
- [ ] Top Down 234-Trees (video)
- [ ] N-ary (K-ary, M-ary) trees
- note: the N or K is the branching factor (max branches)
- binary trees are a 2-ary tree, with branching factor = 2
- 2-3 trees are 3-ary
- [ ] K-Ary Tree
- [ ] B-Trees
- fun fact: it's a mystery, but the B could stand for Boeing, Balanced, or Bayer (co-inventor)
- In Practice:
B-Trees are widely used in databases. Most modern filesystems use B-trees (or Variants). In addition to
its use in databases, the B-tree is also used in filesystems to allow quick random access to an arbitrary
block in a particular file. The basic problem is turning the file block i address into a disk block
(or perhaps to a cylinder-head-sector) address.
- [ ] B-Tree
- [ ] Introduction to B-Trees (video)
- [ ] B-Tree Definition and Insertion (video)
- [ ] B-Tree Deletion (video)
- [ ] MIT 6.851 - Memory Hierarchy Models (video)
- covers cache-oblivious B-Trees, very interesting data structures
- the first 37 minutes are very technical, may be skipped (B is block size, cache line size)
Disjoint Sets & Union Find
Math for Fast Processing
Linear Programming (videos)
Geometry, Convex hull (videos)
Additional Detail on Some Subjects
I added these to reinforce some ideas already presented above, but didn't want to include them
above because it's just too much. It's easy to overdo it on a subject.
You want to get hired in this century, right?
[ ] Union-Find
[ ] More Dynamic Programming (videos)
[ ] Advanced Graph Processing (videos)
[ ] MIT Probability (mathy, and go slowly, which is good for mathy things) (videos):
[ ] Simonson: Approximation Algorithms (video)
[ ] String Matching
- [ ] Rabin-Karp (videos):
- [ ] Knuth-Morris-Pratt (KMP):
- [ ] Boyer–Moore string search algorithm
- [ ] Coursera: Algorithms on Strings
- starts off great, but by the time it gets past KMP it gets more complicated than it needs to be
- nice explanation of tries
- can be skipped
[ ] Sorting
- [ ] Stanford lectures on sorting:
- [ ] Shai Simonson, Aduni.org:
- [ ] Steven Skiena lectures on sorting:
Sit back and enjoy. "Netflix and skill" :P
Computer Science Courses