This two-part course introduces the basic mathematical and programming principles that underlie much of Computer Science. Understanding these principles is crucial to the process of creating efficient and well-structured solutions for computational problems. To get hands-on experience working with these concepts, we will use the Python programming language. The main focus of the class will be weekly mini-projects that build upon the mathematical and programming principles that are taught in the class. To keep the class fun and engaging, many of the projects will involve working with strategy-based games. In part 2 of this course, the programming portion of the class will focus on concepts such as recursion, assertions, and invariants. The mathematical portion of the class will focus on searching, sorting, and recursive data structures. Upon completing this course, you will have a solid foundation in the principles of computation and programming. This will prepare you for the next course in the specialization, which will begin to introduce a structured approach to developing and analyzing algorithms. Developing such algorithmic thinking skills will be critical to writing large scale software and solving real world computational problems.
What is Algorithmic Thinking?
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來自 Rice University 的課程
Principles of Computing (Part 2)
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Modeling, Assertions, and Invariants
This week, we will explain the importance of modeling. We will also explore how to use assertions and invariants to ensure that our models are always consistent and correct.
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Scott RixnerProfessor
Computer Science
Joe WarrenProfessor
Computer Science
Luay NakhlehAssociate Professor
Computer Science; Biochemistry and Cell Biology
So what does algorithmic thinking, and how does it differ from, for example,
a traditional algorithm score?
So in my opinion, traditional algorithm scores have the following structure, okay.
Here's the problem, write an algorithm for it and
analyze the algorithm, its correctness, its complexity and so on.
But the question is, the broader question is, for us, in computer science,
where do we come up with these problems, okay?
So, when someone gives me a problem, say, write an algorithm for
it, that problem is mathematically formulated,
all I need to do is just come up with an algorithm for it.
But who formulated that problem?
Where did that problem come from, okay?
And why am I solving that problem, okay?
So algorithmic thinking is that the way we designed this course is to try to
tie all these things together and put it in the broader
theme which is what is our computer science used for in many domains?
So the way I look at algorithmic thinking is basically a five step process.
The first process or the first step, sorry.
The first step is about getting a problem from a domain expert and
trying to understand what that problem is.
Just to give you an example, suppose I'm talking to a social scientist and
that social scientist tells me that they want to understand if friendship is
transitive or in some sense, if it's always the case or
how often is it the case that the friend of my friend is also my friend, okay?
So if I'm friends with person B, and B is friend with person C,
is C my friend as well?
Okay, it's a question of interest to social scientists and
even beyond that, not necessarily in terms of friendship but
this kind of transitivity is of interest in biology for example and other domains.
So my first question going back to the social scientist in this case
is that what is it that you are going to give me and
what is it that you want back from me, right?
So input output, this is crucial when we develop an algorithm and
when we write a program.
What is it that the social scientist is going to give me?
What is it that the social scientist going to need back from me?
And the other thing is I need to start understanding if there are multiple
possible solutions which one does the social scientist prefer?
So, I go back to the social scientist say, Okay,
what is the data that you are going to give me.
Today, in today’s age, the social scientist might say,
I have created some data, some Facebook data on thousands of individuals, okay?
So they're going to give me some Facebook data, you know, accounts for users and
also there's going to be some information about if user A and
user B are friends on Facebook.
And what they want to get back from me, after talking back to them,
they say I want you to quantify how often it is the case that if A is
a friend with B, and B is a friend with C, then is A also a friend with C?
Okay?
So the first part is that I went back and
forth with a social scientist, I understood what they want from me.
What is they're going to provide to me?
What am I going to provide to them?
Okay, the second step in algorithmic thinking
is going to be about formulating that problem, okay?
You know, saying Facebook network is basically,
this is not something that's well-defined for a computer.
If I'm going to write a computer program and enter analyzed data,
I cannot say the data is Facebook network.
I have to encode it somehow, right?
So the second step is going to be about formulating the problem in terms of input,
output.
So, in this case, its very important to use our mathematical skills and
use knowledge of representations to represent the data.
So, in the case of again, this friendship question,
it makes sense that once the social scientist give me the data
that I represent the data as follows, for every individual.
This is individual one,
individual two, individual three, individual four, individual five.
For example, the social signs is giving me information about five individual.
In addition I'll tell the social scientist in your data,
I want to know which pairs of individuals has friendship relationship.
So they can tell me that these two are friends, these two are friends,
these two are friends and so on.
Okay, these two are friends.
Then what I have done now is that I have formulated the input
to my problem like this.
And this kind of structure where I have these nodes, circles that I call nodes,
and lines between them.
This is what we call graph.
So graph is a powerful representation,
in this case it consists of a set of nodes and a set of edges where
every edge links two nodes together to tell me if they are friends or not.
So this would be the input.
And then I have to say what is the output, okay?
Of course, when I say this is the input, in the course, in algorithmic thinking,
we will learn how to write this formally, right?
So this, I cannot input a drawing like this to the computer.
I have to encode it somehow.
And then what is the output?
Again, for example, they are telling me, quantify for me how many triplets
of nodes that have two edges and then also have a third edge?
Because this is what transitivity is.
If I1 and I 2 are friends, I2 and I4 are friends, are I1 and I4 friends as well?
So here, I need to basically say,
I need the quantity Q that corresponds or
quantifies transitivity in
the graph, in the input graph.
Okay?
Now, we have to write this formally.
Right I mean, what is that?
Because if I tell a computer scientist, quantity Q that corresponds to
transitivity in the input graph, I still haven't described it very well, right?
So we will be learning in this course how to write this formally so
that an algorithm's person can understand exactly what we want.
And we will learn how to do this specifically as well, okay?
So the second step of algorithmic thinking is being able to formulate the problem in
terms of input, output.
The third step will be now that we understand how the problem is formulated
and structured mathematically, I need to come up with an algorithm for
solving this problem in the sense that the algorithm will take this as input
will give us that as output, okay.
In this course we will be learning about different algorithmic scales or
different algorithmic techniques that will help us solve this kind of problem, okay?
And when we write that algorithm, we have to reason about its correctness.
We have to reason about its computational requirement.
How fast?
How slow?
Is it feasible to run on such a ground?
This is a graph with two, four, five nodes.
What if someone has curated the entire Facebook network?
Today Facebook is estimated to have over a billion nodes.
If I come up with an algorithm,
is it going to run on a graph with a billion nodes?
If not, I have to start thinking about this thing, okay.
So the third step is about developing the algorithm to solve the problem,
the fourth step after we have designed the algorithm,
made sure it is correct, it is efficient and so on, we have to implement it, right?
So in this course you will be implementing algorithms in Python.
And when we do the implementation it's interesting,
because going from the algorithm that we developed in the third step
to the implementation is not a simple translation.
Because you have to be very careful, the algorithm can be correct, you might make
mistake when you are writing the code, the algorithm can be efficient and you might
turn it into inefficient implementation when you write the code and so on.
But also, at the same, there is a positive side for
going from the theoretical description of the algorithm to the implementation.
Is that you can even use your programming scales to make the implementation
even much faster than the theoretical guarantees of the algorithm, okay?
So going from the algorithm to the implementation is not a simple
task of someone knowing the syntax of a programming language and
translating the algorithm into it.
No, you have to use some skills to make sure that you implement the algorithm
correctly but you also try to make it even more efficient.
So this is the fourth step of writing the program.
Then, the fifth step which is the final step,
is that I need to remember that when did this all started.
It started from a social scientist asking me a question.
So now that I have written the computer program I will take that program,
take the data set that the social scientist has,
analyze it using the program and then give back the scientist the answer.
So, in this case, for example, I might say, 78%.
Okay? What does that number mean?
I'm telling the social scientist that in 78% of the cases where A is friend with B,
B is a friend with C.
You also have A and C friends, okay?
So this is algorithmic thinking in my, the way I define it for
this course and the way we'll be using it in this course.
Again it's five steps.
Understanding the problem is the first formulating the problem is the second.
Developing an algorithm is the third.
Implementing the algorithm is the fourth.
And then the fifth one is running it on the data and
answering the original question.
