Algorithms Explained for Beginners - How I Wish I Was Taught
Summary
TLDRThis 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
- đ Algorithms are a series of steps to perform an action or reach a goal, often involving data processing.
- đ The importance of algorithms is highlighted by their central role in coding interviews and the tech industry's focus on them.
- đ§ Designing efficient algorithms can allow us to solve much larger problems and achieve significant performance gains in technology.
- đ 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.
- đ Linear search is a simple algorithm that checks each element in a list sequentially, but it's not efficient for large data sets.
- đ 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).
- đ Reading books or summaries like 'Algorithms to Live By' can provide insights into applying algorithmic thinking to everyday life.
- đ Taking courses like CS50, Zero to Mastery, Stanford's Algorithm Specialization, and Princeton's Algorithms Specializations can build a strong foundation in algorithms.
- đ 'Cracking the Coding Interview' is a valuable resource for reviewing key topics and practicing problems before interviews.
- đ» 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
đ 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.
đ 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.
đ 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.
đ 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.
Mindmap
Keywords
đĄAlgorithms
đĄData Structures
đĄBig O Notation
đĄLinear Search
đĄBinary Search
đĄSorting Algorithms
đĄMerge Sort
đĄComputer Resources
đĄCoding Interviews
đĄShort Form Summaries
đĄCracking the Coding Interview
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
absolute best way I've found to get
really high quality book summaries and
the thing about short form their
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if you just want to get the main ideas
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when you look at a book it can be
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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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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
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