Mastering Data Structures and Algorithms: Comprehensive Notes and Practice Guide
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DSA
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DSA
Unlock the power of Data Structures and Algorithms with our comprehensive and expertly crafted DSA Notes. Designed to accelerate your learning and enhance your problem-solving skills, our meticulously organized and easy-to-understand notes offer a treasure trove of knowledge.
Inside, you'll find...
Course Introduction
This course is designed for placement preparation and will mainly cover
data structures and algorithms using C and C++. Even if you do not know
C++, you will still be able to follow along easily. The notes will be made
available as a PDF in the description below.
Data Structures and Algorithms
Data structures are used to arrange data in main memory for efficient
usage while algorithms are a sequence of steps to solve a given problem.
In this course, we will cover arrays, linked lists, and graphs as examples of
data structures and dive into solving problems using different algorithms.
Programming Languages
C and C++ will be the primary languages used in this course but Java can
also be used to implement the algorithms. I do not recommend Python or
JavaScript for beginners but rather suggest learning C to get a solid
foundation in programming.
Time Complexity and Big O Notation
I have a story to share with you all. One day, I was feeling extremely
bored at home, and nothing seemed to interest me. I decided to call
up my friend who lives 10km away from me. Let's refer to my friend
as X.
Manoj, okay. And this friend lives 10km away. Listen carefully. Now,
what happened was, I was feeling really bored and needed some
entertainment. This guy has amazing games like PUBG and GTA5. He
has a collection of games and enjoys playing them a lot. You can get
every type of game from him, but there is one problem:
He lives 10km away
I also use Jio. He also uses Jio. What does he use? He also uses Jio.
We get 1Gb. We get just 1 Gb for one day. And we are not much into
broadband internet. And with more internet, we can't sell files and
all. So if I have to take the game from him, So for me
Fastest Way to Obtain a Game
,If you are looking to obtain a game quickly, perhaps from a friend, there
are a few options to consider:
Ask your friend to share the game with you digitally
Borrow the physical copy of the game from your friend
Purchase the game online for immediate download
Ultimately, the choice will depend on your friend's willingness to share or
lend the game, as well as your own preference for digital or physical
copies.
Copy the hard disk and transport it. To accomplish this, I will use my bike.
I am currently going through my bike. I plan to retrieve a game and indulge
in it to satisfy my soul. However, you may be wondering why I am telling
you this story. I simply want to inquire whether it is worth it for me to
retrieve a game that is only 250kb in size. Do I really need to go to the
owner's house and bring it back on a hard disk?
Asymptotic Notations: Big O, Big Omega and Big Theta Explained
When comparing two sorting algorithms for an array, it can be difficult to
determine which is better and by how much. In this video, we will discuss
asymptotic notation and how it can help us evaluate the efficiency of
different algorithms.
If you have not already accessed the Data Structures Algorithms playlist, be
sure to check it out in the description for all the necessary materials,
including PDF notes for this video and previous and future videos.
Asymptotic Notations
If you want to compare algorithms, you need to use asymptotic notations.
There are three primary types of asymptotic notation:
Big O
Big Theta (Θ)
Big Omega (Ω)
Let's take a closer look at the differences between these three types.
,Understanding notations like big O, omega, and theta becomes crucial
when it comes to exams or interviews. However, I'll simplify these
concepts for you in easy language. By the end of this video, you'll have a
clear understanding of these three notations.
Let's start with big O. It's represented by the capital letter O and refers to
the upper bound of an algorithm's time complexity. In other words, big O
notation tells us the maximum amount of time an algorithm will take to
complete.
In English, we have the concept of Big O notation. Essentially, Big O
describes the relationship between two functions: f(n) and g(n). We say
that f(n) is O(g(n)) if there exists a constant c and a constant n such that 0 ≤
f(n) ≤ cg(n).
To better understand this definition, let's try visualizing it. Imagine a graph
with function f(n) on the y-axis and n on the x-axis. The graph of f(n) should
be below or equal to the graph of cg(n). This is what we mean when we say
f(n) is O(g(n)).
When discussing a function, it is important to understand the concept of
big O notation. A function f(n) is said to be O(g(n)) if there exist a pair of
constants (c) and (n0) where the following condition applies:
n ≥ n0
0 ≤ f(n) ≤ cg(n)
Essentially, this means that the growth rate of f(n) is no greater than the
growth rate of g(n). It is important to understand this concept when
analyzing algorithms and their efficiency.
A constant n-node is defined as follows:
0 ≤ f(n) ≤ cg(n)
This definition can be found in the notes and should not cause any issues.
Best Case, Worst Case and Average Case Analysis of an Algorithm
, Have you ever experienced a moment in your daily life where something
really good happens to you? It could be anything from getting a promotion
at work to finding money on the street.
Study Hack:
One way to make the most out of these moments is to harness the
positive energy and use it to fuel your studies.
Take a few minutes to reflect on the good thing that happened
and allow yourself to fully appreciate it.
Then, channel that positive energy into your studies by setting
goals, tackling difficult tasks, and staying focused.
Remember, success breeds success, and the more you can harness positive
energy and use it to fuel your studies, the more successful you will be.
Have you ever found yourself in a situation where you haven't prepared for
an exam, only for it to get cancelled? Or, even worse, you haven't prepared
and then get surprised with a test on the same day? These scenarios can
be stressful and leave you feeling unprepared.
In the world of algorithms, a common occurrence is encountering inputs
that elicit a response of amusement or satisfaction. These moments can be
seen as small victories for the algorithm, as it is able to process and
analyze the input effectively.
"I was able to solve this problem in constant time (Big-O(1)). However,
there are inputs that can cause the program to struggle. It may be
overwhelmed by the amount of work it needs to do for certain inputs."
Algorithm Definition and Life Events
Algorithm Definition: An algorithm is a set of instructions
designed to solve a particular problem or accomplish a specific
task.
Algorithm Life Events: The life of an algorithm can be broken
down into several key events, including:
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