Algorithms Explained for Beginners - How I Wish I Was Taught

Summary

This video script emphasizes the significance of algorithms in the field of computer science and coding interviews. It explains that algorithms are a set of instructions to achieve a goal, and their efficiency is crucial when dealing with massive datasets as encountered by tech giants like Google and Facebook. The script introduces two search algorithms: linear search, which is straightforward but slow (O(n)), and binary search, which is faster (O(log n)) by narrowing down the search space significantly with each step. The importance of algorithm design is highlighted, as it can lead to substantial performance gains, even surpassing a decade's worth of hardware improvements. The video also touches on sorting algorithms, mentioning the inefficiency of basic algorithms compared to optimized ones like merge sort. It concludes with recommendations for learning more about algorithms through courses like CS50, online platforms like Zero to Mastery, and books like 'Cracking the Coding Interview', as well as the practical advice of solving problems on platforms like LeetCode.

Takeaways

• 📘 Algorithms are a series of steps to perform an action or reach a goal, often involving data processing.
• 🚀 The importance of algorithms is highlighted by their central role in coding interviews and the tech industry's focus on them.
• 🧠 Designing efficient algorithms can allow us to solve much larger problems and achieve significant performance gains in technology.
• 📈 The speed and memory usage of an algorithm are crucial factors, especially when dealing with large datasets as seen in companies like Google and Facebook.
• 🔍 Linear search is a simple algorithm that checks each element in a list sequentially, but it's not efficient for large data sets.
• 🔑 Big O notation is used to express the worst-case scenario of an algorithm's running time, which is essential for analyzing scalability.
• ⏬ The binary search algorithm is more efficient than linear search as it reduces the problem size by half with each step, with a running time of O(log n).
• 📚 Reading books or summaries like 'Algorithms to Live By' can provide insights into applying algorithmic thinking to everyday life.
• 🎓 Taking courses like CS50, Zero to Mastery, Stanford's Algorithm Specialization, and Princeton's Algorithms Specializations can build a strong foundation in algorithms.
• 📝 'Cracking the Coding Interview' is a valuable resource for reviewing key topics and practicing problems before interviews.
• 💻 Regular practice on platforms like LeetCode is essential for mastering data structures and algorithms.

Q & A

What is the primary focus of the video?

The video focuses on explaining the importance of algorithms, why they are crucial in coding interviews, and how understanding them can help solve complex problems more efficiently.

Why do companies place a significant emphasis on algorithms during their recruitment process?

Companies emphasize algorithms because they are fundamental to solving large-scale problems that these companies face. The ability to design and understand efficient algorithms can lead to significant performance gains and is indicative of a candidate's problem-solving skills.

What is the basic definition of an algorithm?

An algorithm is a series of steps designed to perform a specific action or to reach a particular goal. It involves taking some input data and determining the logical steps a computer must take to produce the desired output.

Why is it important to study the speed of algorithms even when computers are very fast?

The speed of algorithms becomes critical when dealing with large datasets, as seen in companies like Google and Facebook. Even with fast computers, a poorly designed algorithm can lead to significantly longer processing times, which can affect the performance and efficiency of technology solutions.

What does the term 'Big O' refer to in the context of algorithms?

In computer science, 'Big O' refers to the worst-case scenario running time of an algorithm. It is a measure of how the runtime of an algorithm grows with the size of the input data, and it is used to predict the performance of an algorithm as the input size increases.

How does the linear search algorithm work?

The linear search algorithm works by sequentially checking each element in a list or book until the desired item is found. It is a straightforward but inefficient method, especially for large datasets, as it may require checking every single item in the worst-case scenario.

What is the main advantage of a binary search algorithm over a linear search?

The binary search algorithm has a significant advantage over linear search in terms of efficiency. It works by repeatedly dividing the search space in half, which reduces the problem size with each step. This approach results in a logarithmic running time (O(log n)), which is much faster than the linear time (O(n)) of a linear search for large datasets.

What are some resources recommended in the video for mastering algorithms and data structures?

The video recommends several resources, including CS50's third lecture, 'Zero to Mastery' coding courses, Stanford's Algorithm Specialization, Princeton's Algorithms I and II specializations, and the book 'Cracking the Coding Interview' for practice problems and interview preparation.

How does the video suggest one should approach learning algorithms and data structures?

The video suggests starting with a solid theoretical foundation through courses like CS50 or specialized algorithm courses. After gaining a theoretical understanding, one should then practice with resources like 'Cracking the Coding Interview' and engage in a lot of coding problems on platforms like LeetCode.

What is the role of Short Form in the video?

Short Form is mentioned as a sponsor of the video. They provide high-quality book summaries and study guides, which can be useful for quickly understanding the main ideas and concepts of a book before deciding to read it in full.

Why is it beneficial to understand the theory behind algorithms?

Understanding the theory behind algorithms is beneficial because it allows one to write efficient and effective code for solving complex problems. It also helps in performing well in coding interviews, which often focus on algorithmic thinking and problem-solving skills.

Outlines

00:00

📚 Introduction to Algorithms and Their Importance

The video begins by emphasizing the significance of algorithms in coding interviews and the tech industry. It mentions that understanding algorithms and data structures is crucial for anyone looking to succeed in these areas. The speaker aims to provide an intuitive understanding of algorithms, discussing why they are essential and how they are interconnected with data structures. The video also suggests a book titled 'Algorithms to Live By' for those interested in applying algorithmic thinking to everyday life, and highlights a sponsored service, Shortform, for book summaries.

05:02

🚀 The Relevance of Algorithm Efficiency

This paragraph delves into why algorithm efficiency matters, even with fast computers. It explains that for large-scale problems, such as those faced by companies like Google and Facebook, the design of an algorithm in terms of speed and memory consumption becomes critical. The video uses the analogy of searching for a page in a book to illustrate the concept of an algorithm and introduces the idea of Big O notation for expressing the worst-case scenario of an algorithm's running time.

10:03

🔍 Exploring Search Algorithms: Linear vs. Binary

The speaker explores two search algorithms: linear search and binary search. Linear search is described as a naive approach that checks each item sequentially, which is slow but guaranteed to find the target if it exists. On the other hand, binary search is introduced as a more efficient method that repeatedly divides the search space in half, significantly reducing the number of steps required to find the target. The video explains that binary search has a logarithmic running time, denoted as O(log n), which is much faster than linear search for large datasets.

15:03

📈 Sorting Algorithms and Their Performance

The video moves on to discuss sorting algorithms, noting that they are often the starting point for learning algorithms. It contrasts a slow sorting algorithm with O(N^2) complexity against a more efficient one like merge sort, which has a running time of O(N log n). The importance of using optimized algorithms is stressed, particularly for companies dealing with massive datasets. The video concludes with practical steps for mastering algorithms, including taking specific courses and practicing on platforms like LeetCode.

Keywords

💡Algorithms

Algorithms are a series of steps designed to perform a specific action or reach a particular goal. They are crucial in computer science for solving problems efficiently. In the video, the importance of algorithms is emphasized as they form a significant part of coding interviews and are essential for handling large data sets in companies like Google and Facebook.

💡Data Structures

Data structures are specialized formats for organizing, managing, and storing data. They are complementary to algorithms and often discussed together. The video mentions data structures as the first part of the equation in coding interviews, highlighting their interrelation with algorithms.

💡Big O Notation

Big O notation is a mathematical representation used to describe the performance or complexity of an algorithm. It expresses the upper bound of the time complexity in the worst-case scenario. In the video, Big O notation is used to illustrate the efficiency of different searching algorithms, such as linear search being O(n) and binary search being O(log n).

💡Linear Search

Linear search is a simple search algorithm that checks each element in a list sequentially until the desired item is found. It is characterized by its simplicity but inefficiency for large data sets. The video uses the example of finding a page in a book to explain how a linear search works.

💡Binary Search

Binary search is an efficient algorithm used for finding an item from a sorted list of items. It works by repeatedly dividing the list in half and then determining if the desired item is in the left or right half, thereby reducing the search space. The video demonstrates that binary search has a time complexity of O(log n), making it much faster than linear search for large data sets.

💡Sorting Algorithms

Sorting algorithms are used to rearrange a list of items into a particular order, typically ascending or descending. The video discusses the importance of sorting algorithms in computer science and how different algorithms can have vastly different efficiencies, with some scaling as O(N^2) and others as O(N log n).

💡Merge Sort

Merge sort is an efficient, general-purpose, comparison-based sorting algorithm. It works by dividing the list into smaller parts, sorting them, and then merging the sorted parts back together. The video mentions merge sort as an example of a more optimized sorting algorithm with a time complexity of O(N log n), which is more efficient than O(N^2) algorithms.

💡Computer Resources

Computer resources refer to the hardware and software capabilities available to perform computational tasks. The video discusses how the study of computer algorithms is about applying these resources to solve mathematical operations or problems more efficiently than the human brain can, especially when dealing with large data sets.

💡Coding Interviews

Coding interviews are a part of the recruitment process for software engineering roles where candidates are assessed on their problem-solving skills using data structures and algorithms. The video emphasizes the importance of algorithms and data structures in these interviews, as they are often the focus of the questions asked.

💡Short Form Summaries

Short Form Summaries, as mentioned in the video, provide condensed versions of books, including key insights and interactive exercises. They are used as a way to quickly understand the main ideas of a book before deciding to invest time in reading the full text. The video suggests using Short Form Summaries to grasp the concepts of books like 'Algorithms to Live By'.

💡Cracking the Coding Interview

Cracking the Coding Interview is a book that provides a review and overview of topics necessary for technical interviews, along with practice problems. The video recommends this book as a resource for practice after gaining a theoretical understanding from other courses or materials.

Highlights

Introduction to the importance of algorithms and their critical role in coding interviews and computer science.

Discussion on the necessity of understanding algorithms for technical interviews at major tech companies.

Explanation of what an algorithm is: a series of steps to reach a goal with given input data.

The historical context of algorithms, dating back a thousand years, and their evolution with computing.

Introduction to the book 'Algorithms to Live By' and its application to everyday life.

Importance of understanding the speed and efficiency of algorithms due to the computational limitations despite fast hardware.

Explanation of linear search and its inefficiency through the analogy of finding a page in a book.

Introduction to Big O notation to describe worst-case scenario running times of algorithms.

Generalization of running time analysis in terms of input size for scalability and practicality.

Discussion of binary search algorithm as a more efficient alternative to linear search.

Analysis of the binary search algorithm's logarithmic running time and its efficiency.

Comparison of sorting algorithms, specifically focusing on the inefficiency of bubble sort vs. the efficiency of merge sort.

Importance of designing efficient algorithms to handle large-scale problems like those encountered by Google and Facebook.

Recommended practical steps for mastering algorithms, including courses and resources like CS50's third lecture.

Tips for preparing for coding interviews using resources like 'Cracking the Coding Interview' and practicing on LeetCode.

Transcripts

hello and welcome back today's video is

a particularly important one because

today's video is about algorithms maybe

I don't need to convince you of the

importance of algorithms if you are

aware of how companies coding interviews

are generally formatted you are probably

aware that the sort of problems they ask

in or the interviews are related to data

structures and algorithms in my previous

video in the series we went through the

first part of this equation which is

data structures and today by popular

demand we will be covering the second

part which is algorithms as in my

previous video the goal of this video is

to give you an intuitive understanding

of what algorithms are why we need to

study them why companies care so much

about algorithms that literally their

entire recruiting process is structured

around testing these topics and of

course as you know on this channel we

always leave things off with practical

steps that you can take and the things

that you need to do Beyond this video to

master these topics I think this could

be one of the most important videos that

you watch our algorithms because as I

always say the most important aspect

about learning anything to me is being

excited about it and algorithms and data

structures are the kind of thing that

most people don't quite understand why

they are so important and that is

probably actually the thing that is

holding you back the most in fact I

think algorithms and data structures are

some of the most beautiful things about

coding and computer science and I hope

that with this video I can give you a

glimpse of this beauty and why I

appreciate them so much so that you can

actually start enjoying the process of

learning them and therefore wanting to

learn them more so what is an algorithm

an algorithm is a series of steps to

perform some action to reach some goal

we have some input so some data that we

want to do something to and we need to

figure out what are the logical steps

that we need to tell the computer to do

to reach the output that we desire you

can think of Designing a series of steps

to complete really anything you think

about a series of steps to get from your

house to the gym for example I was

reading about this the idea of

algorithms is like a thousand years old

so where do computers then come in well

the study of computer algorithms is just

about applying Computer Resources to

solve mathematical operations or

problems we want to solve instead of

using the human brain to solve them and

the advantage that computers have is a

computer scan perform these operations

blindly fast so that is really where

computers come in but before we go

deeper into specifically computer

algorithms there's a great book about

this idea of sort of applying

algorithmic thinking to your everyday

life it's called algorithms to live by

at least I recommend reading a summary

of it and an excellent way to get a

really good summary is actually today's

video sponsor short show form is the

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the thing about short form their

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they're more like study guides with like

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if you just want to get the main ideas

plus chapter by chapter summaries

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when you look at a book it can be

difficult to tell whether that book is

actually worth reading and so what I

often do first before reading a book I

will go read this short form guide of

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decide whether the ideas of the book are

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self-improvement business

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luck because you can go to the link in

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subscription and give a short form for

sponsoring this video and now let's get

into the meat of algorithms the big

question I had in the beginning and I

just couldn't really understand is if

computers are so incredibly fast why

does it even matter what kind of

algorithms we design why do we care so

much about the speed of algorithms on

like studying the theory of like

optimizing algorithms a lot because our

computers are so fast right but when you

think about sorting algorithms for

example there's also a problem you might

think about like sorting 100 numbers or

something but when it comes to computer

science and programming those are

actually not the interesting problems

any interesting problem in the domain of

computer science and like in The Cutting

Edge something that the input size is

ridiculously big when you think about

companies like Google and Facebook the

data sizes that they run these

algorithms with are not like a hundred

or a thousand items they can be like

billions and billions and billions in

these scales even with the power of

computers without we have today how your

algorithm is designed as in how fast it

is and how much memory it consumes

really starts to matter a lot so

simplify designing a faster algorithm

weekend number one solve much bigger

problems and number two we can literally

like achieve the same performance gains

in our technology as like a decade worth

of computer process for Speed

Improvement so in general about

algorithms the things we care about or

the speed at which it runs as well as

the memory that it uses so the very very

very low level we can think of the speed

of an algorithm just ask how many

instructions does it have to complete if

we can design an algorithm to do the

same thing using 10 instructions or

doing 100 instructions the algorithm

that we have designed that can run it

using 10 instructions is going to be

faster at the very very low level that

is what we really mean but as you'll see

in a moment there's actually a kind of

in practical way of actually thinking

about it okay so let's just think about

a very basic algorithm let's say you

have a book

and you want to find a specific page in

above let's say you want to tell someone

to find page 100 in the book How might

you go about doing that well one very

naive approach might be to just start

opening page one of the other and The

Logical instructions will be open page

see if the page is Page 100 if it is you

found it and you've completed the other

if it's not you open the next page it is

Page 100 no more doesn't expect is this

page 100 no move on to the next page and

this might sound a bit ridiculous but

actually if you do this 100 times

eventually you will reach page 100 and

you can say yes this is Page 100 yes it

is Page 100 even though like intuitively

to you as a human it seems like a very

stupid idea it does actually work so

what is actually wrong with this

algorithm it's very slow right and

there's probably a much better way to do

this we can use our idea from before of

thinking about the amount of

instructions we need to complete to

reach our goal so you might say that in

this particular case the running time of

our algorithm was a hundred iterations

or 100 instructions but the thing here

is that saying that this algorithm has a

runtime of 100 instructions it's not

very helpful because that depends on

these very specific case of us wanting

to find page 100 what if I had told you

to find page two in that case you would

open in page one and be like is this

page two no more on the next page is

this page two yes we have found the

solution so in this case the running

time would only be two but you might

think of the worst case where I tell you

to find the very last page of the book

you have 696 pages in this cracking the

coding in the new book it's a great book

by the way but in this case we would

have to complete

696 iterations to find the number and so

how can we just generalize this idea of

the running time in this particular

algorithm for computer scientists are

actually quite pessimistic whenever we

analyze algorithms we are always first

of all thinking about the worst possible

case we assume that we are the

unluckiest people and we always get the

absolute worst case possible so that is

why in computer science when you analyze

algorithms we would say that the Big O

running time aka the worst case running

time is 696 but what if we had a

different book what if we had Instead

This Book is the Leonardo da Vinci

biography this one has 599 pages so in

the case of this book the same algorithm

would have a running time of Big O 597

but this is also not very helpful

because now even though we've sort of

generalized in terms of thinking about

the worst case our running time still

depends on the actual book so how can we

generalize the running time of this

particular search algorithm which is

called the linear search by the way into

any problem so any book

and the way we think about this in

computer science is in terms of the

input size so in this case we think

about the running time of the algorithm

in terms of how much it scales when we

increase the size of the book so let's

say we had a book that was a thousand

pages long how does the running time of

the algorithm scale relative to the size

of the problem and in this case it

actually scales to linearly for every

page we add the book the running time of

our algorithm increases by one because

remember we're always thinking about the

absolute worst case so in computer

science lingo our algorithm has a linear

running time or in other words a running

time of O of n where n is the size of

the problem and the reason again why we

care about the input size so much is

because Google's the Facebooks they have

billions and billions and billions of

data points so for this book page

finding algorithm how could we find an

algorithm that's perhaps much faster

than

just opening a page one at a time you

might already intuitively think about

surely it doesn't make sense to start

even looking at the first Pages because

you know that is not going to be on the

first page right so you might just sort

of estimate and open is somewhere over

here actually landed on 149 which is a

pretty good guess and then you know that

because page 100 it's less than 149 we

can just open it somewhere over here

slightly behind it and then eventually

we find page 100 and if I told you to do

this that's probably how you would do it

right and it turns out that we can

actually instruct a computer to do it

almost like this in general what we can

tell the computer to do let's say just

in the first iteration let's tell our

computer to always try the middle page

to open it from the very middle of the

book so in this case it's going to open

it on page 336. what can we then do

afterwards well we can always check very

quickly using one instruction is is the

page we're looking for before the one we

opened or is it after the one we open

100 is less than 336 so in the next

iteration but if we tell the computer to

then open it on the middle of the left

section of the book and this time we're

opening on page 150 which is

approximating and again if we know that

is our page 100 less than 150 or more

than 150. we can again just forget about

the entirety rest of the book here and

just focus on the left side of 150

because we know that what we're looking

for is going to be in here and again

without the computer to open it again

now on the middle of this portion of the

book which will be on page 75 is 100

more than 75 or is it less than 75 but

it's more than 75 so at this point we

can just open it in the middle of 75 150

and just through this iterative process

we are going to get to our solution much

much much faster so essentially in every

instruction we are actually reducing the

problem size by half and sort of getting

closer and closer to the solution and it

turns out that the running time of this

algorithm is something called log n and

the log is something that can be a bit

confusing probably but essentially

although log N means as we double the

size of the book The amount of

instructions we have to do so the the

running time of the algorithm would only

go up by one instruction because if you

think about it we have two books when we

double the size of the input in our

binary search algorithm where we're

always opening the middle page it only

adds one more step because in this case

we would open it in the middle of these

two so in here and then we're going to

say well is it to the right or is it to

the left that says to the left so then

we can literally just forget about this

other half of the problem entirely and

now we're back in the same stage where

we started out before with just this one

or this half of the book and you can see

that even in this very small case using

this algorithm is much much faster you

would never use the first one because

it's so much slower and you can imagine

a similar problem like this where we

need to find a particular data point

from a list of like billions and

billions and billions of billions the

difference that this better algorithm

makes and literally shorten the running

time by like weeks or if months I think

I've seen so that is really why we care

so much about designing fast algorithms

and another very common problem that a

lot of algorithms courses start with at

first is sorting and I've actually coded

up a visualization that really shows the

difference between different kinds of

algorithms I'm not going to show the

implementation in this or anything but

you can call the description and find it

if you want in here we have a very slow

algorithm that scales at o of N squared

so as the input size doubles it's going

to go up by 2 squared so it's actually

even worse at the linear time thing that

we tried before

two thousand years later you can see

that it's taking quite a while whereas

if you use a more optimized algorithm

called merge saw where again you'll end

up studying the details of this later

and in whatever course designed to

follow this algorithm runs on N Times

log n which is actually much much faster

than N squared so I hope now you're sort

of starting to see why companies

actually put so much emphasis on hiring

people who understand algorithms who

understand how to write good algorithms

for their very very big problems that

they solve other companies in terms of

practical next steps for you to do it

you want to understand this topic if you

enjoyed this video first of all leave a

like because I actually find the

interaction algorithms quite exciting

and I really enjoy teaching them and

talking about them but I will only doing

if you guys really want me to do that so

if you want to see that go leave a like

down below and go leave a comment on the

specific topic about algorithms and data

structures that you would would like to

see next but first of all if you haven't

done cs50 yet specifically their third

lecture I'm going to leave the third

lecture of 650 in the description below

its YouTube video that lecture is

specifically on algorithms and it

essentially teaches what I've taught you

in this video except it's the two hour

version and probably a much much better

explained that that I ever explained but

obviously even that is not going to be

enough to pass interviews so what I

would do is just pick any popular course

on data structure and algorithms teaches

you the theory of the most important

algorithms and data structures that

you'll need

one that I did personally for myself was

zero to masteries master the coding

interview bootcamp zero to Mark 3 is a

coding course platform that's

essentially like a subscription model

where instead of paying for a Netflix

subscription you can pay for as an auto

Master research and characters so that

they're like 60 different coding courses

on a lot of different areas so I've done

a bunch of them those are really good uh

the teaching style is really engaging if

you are interested in sort of a more

academic and probably a more rigorous

approach there's two specific course

Sarah specializations that you can look

at I've actually done both of them the

first one is the Stanford algorithm

specialization that's really the most

theoretical approach that you'll

probably find online quite math heavy

but it's going to give you a very very

rigorous understanding the other one is

the Princeton algorithms one and albums

two specializations agents are also use

the textbook style one is Java based the

other specialization actually doesn't

basically on any specific programming

language because but they rather just go

through things either conceptual and a

mathematical level and of that something

like cracking the coding interview is

actually a very good book to get sort of

a review slash an overview of the topics

that you need for interviews plus a lot

of practice problems but I would not

choose this first I would choose one of

the three other courses to give you the

theory and the understanding and then

after that I have to go for something

like this because this is more like a

practice book something that you want to

use to prepare like right before your

interviews and obviously beyond that

lead code you don't need to pay for the

premium I've never paid for the premium

just keep doing a lot of lead code

problems so that is that this is

probably a very long video already if

you haven't seen my first part to this

series on data structures absolutely go

watch it now other than that I have this

other video where I talk about my

step-by-step plan of how I personally

learn all these topics so go watch one

of these videos next and I'll see you in

the next one

foreign