Time complexity I want to tell you guys one story. It
happened like this , I was bored in my house. I was so bored that I needed some
entertainment. This guy has amazing games like Pubg and GTA5. So he has a collection of
games. He likes playing games a lot. And you can get every type of game from him. But
there is one problem , I also use jio. He also uses jio and we get just 1 Gb for one day. And
with more internet , we ca n't sell files and all. So for me , what is the fastest way to take the
game from this friend. So what will I do ? I will take my bike As the size of this input will get
increased, the runtime of the algorithms will increase. This means that as the input size is
increasing like that The time required to send the file , That is also increasing. There is a
hard disk then there is your motorcycle. You will go on that bike. And you will take it and in
hard disk whether you bring 250kb or Tb. As the input size of algo2 increased like that what
happened ? For that , there was no change in the runtime. Runtime remained the same. So
we say as the size of the input keeps on increasing , Similarly, what is the effect of the
algorithm on runtime. We are to trying to remove the time complexity of them.
Big O notation
We are not studying algorithms, we are listening to a story. We are doing a real-world
analysis of things. Big O is called a constant runtime algorithm. Because it was constant we
remove n to power 0 and make it 1. So this is Big O of n to the power 0. If I do T algo1 then
what will happen here ? What do I have to do ? When I am sending data then I must upload
and send. My main time is required in that ok. Now, considering I turn on my computer In
that , I will need time L1 After that what happened ? Consider all preparation I required L1
which will be a constant 5 secs,2 secs , 10 secs. If there is an SSD in your computer then it
will open in 4 secs If you are using a supercomputer then it can even open in 1 sec. L1+
consider your speed is L2. Ok, so it takes a constant speed of your This is not equal to.
Writing equal to is wrong here. So here I will say that The most difference that will be visible
It will be because of this term. Because n to power 1 , if I increase input and make it 10 lakh.
So this was of 2 lines but this will become 10 lakhs. So the higher degree term in the
polynomial In any equation The most impactful term It is taken ok. So I picked this because
in comparison with n to the power 0 it is big. And I want to see things in a simple way.
Big O of n square. Big O is a log that scales according to the time required to run your
algorithm. Linearly if your time scales with the input size. If it runs in linear time Big O. If your
time runs in constant time, Big O is 1 ok. O in the industry means the order of And its
mathematical definition that I will tell you. Industry definition is a minimum of this. But when
you are answering in industry Then industry definition is used. When I use its mathematical
definition then I say Big O But when I give industry definition Or I am answering any
interview. Then I will say an order of because big O has a different definition. But they are
used interchangeably. The graph of Big O of 1 is plotted like this. It does not mean it is 1 's
graph. Do n't confuse it with the x=1 graph. This is the graph of x=k. Constant , whatever
constant was there in constant time it was running. And this y=mx+c It can be somewhat
distorted.
Time complexity is the study of the efficiency of algorithms. How time taken to execute an
algorithm Grows with the size of the input. Time will increase and time will increase or
decrease. Here I am giving a real-world example because the examples we took were very
naive. They were very simple. Shubham 's algorithm took 180ms. And over there Rohan's
algorithm was around 120-130ms. It took 121 ms. After that when I gave 1000 elements for
happened like this , I was bored in my house. I was so bored that I needed some
entertainment. This guy has amazing games like Pubg and GTA5. So he has a collection of
games. He likes playing games a lot. And you can get every type of game from him. But
there is one problem , I also use jio. He also uses jio and we get just 1 Gb for one day. And
with more internet , we ca n't sell files and all. So for me , what is the fastest way to take the
game from this friend. So what will I do ? I will take my bike As the size of this input will get
increased, the runtime of the algorithms will increase. This means that as the input size is
increasing like that The time required to send the file , That is also increasing. There is a
hard disk then there is your motorcycle. You will go on that bike. And you will take it and in
hard disk whether you bring 250kb or Tb. As the input size of algo2 increased like that what
happened ? For that , there was no change in the runtime. Runtime remained the same. So
we say as the size of the input keeps on increasing , Similarly, what is the effect of the
algorithm on runtime. We are to trying to remove the time complexity of them.
Big O notation
We are not studying algorithms, we are listening to a story. We are doing a real-world
analysis of things. Big O is called a constant runtime algorithm. Because it was constant we
remove n to power 0 and make it 1. So this is Big O of n to the power 0. If I do T algo1 then
what will happen here ? What do I have to do ? When I am sending data then I must upload
and send. My main time is required in that ok. Now, considering I turn on my computer In
that , I will need time L1 After that what happened ? Consider all preparation I required L1
which will be a constant 5 secs,2 secs , 10 secs. If there is an SSD in your computer then it
will open in 4 secs If you are using a supercomputer then it can even open in 1 sec. L1+
consider your speed is L2. Ok, so it takes a constant speed of your This is not equal to.
Writing equal to is wrong here. So here I will say that The most difference that will be visible
It will be because of this term. Because n to power 1 , if I increase input and make it 10 lakh.
So this was of 2 lines but this will become 10 lakhs. So the higher degree term in the
polynomial In any equation The most impactful term It is taken ok. So I picked this because
in comparison with n to the power 0 it is big. And I want to see things in a simple way.
Big O of n square. Big O is a log that scales according to the time required to run your
algorithm. Linearly if your time scales with the input size. If it runs in linear time Big O. If your
time runs in constant time, Big O is 1 ok. O in the industry means the order of And its
mathematical definition that I will tell you. Industry definition is a minimum of this. But when
you are answering in industry Then industry definition is used. When I use its mathematical
definition then I say Big O But when I give industry definition Or I am answering any
interview. Then I will say an order of because big O has a different definition. But they are
used interchangeably. The graph of Big O of 1 is plotted like this. It does not mean it is 1 's
graph. Do n't confuse it with the x=1 graph. This is the graph of x=k. Constant , whatever
constant was there in constant time it was running. And this y=mx+c It can be somewhat
distorted.
Time complexity is the study of the efficiency of algorithms. How time taken to execute an
algorithm Grows with the size of the input. Time will increase and time will increase or
decrease. Here I am giving a real-world example because the examples we took were very
naive. They were very simple. Shubham 's algorithm took 180ms. And over there Rohan's
algorithm was around 120-130ms. It took 121 ms. After that when I gave 1000 elements for
