Core: Introduction to Asymptotic Analysis, Part 2

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Del curso dictado por University of California San Diego

Data Structures and Performance

1346 calificaciones

University of California San Diego

Data Structures and Performance

1346 calificaciones

Curso 4 de 4 en SpecializationObject Oriented Programming in Java

How do Java programs deal with vast quantities of data? Many of the data structures and algorithms that work with introductory toy examples break when applications process real, large data sets. Efficiency is critical, but how do we achieve it, and how do we even measure it? This is an intermediate Java course. We recommend this course to learners who have previous experience in software development or a background in computer science, and in particular, we recommend that you have taken the first course in this specialization (which also requires some previous experience with Java). In this course, you will use and analyze data structures that are used in industry-level applications, such as linked lists, trees, and hashtables. You will explain how these data structures make programs more efficient and flexible. You will apply asymptotic Big-O analysis to describe the performance of algorithms and evaluate which strategy to use for efficient data retrieval, addition of new data, deletion of elements, and/or memory usage. The program you will build throughout this course allows its user to manage, manipulate and reason about large sets of textual data. This is an intermediate Java course, and we will build on your prior knowledge. This course is designed around the same video series as in our first course in this specialization, including explanations of core content, learner videos, student and engineer testimonials, and support videos -- to better allow you to choose your own path through the course!

De la lección

Efficiency Analysis and Benchmarking

Welcome to week 3! The text-editor application you worked with last week does something, but it doesn't do it particularly fast. This week we'll start talking about efficiency. We'll introduce the concept of "Big-O" notation, which sounds a little silly, but is really a powerful (and extremely common) way of analyzing a program's efficiency, independent of the system that it's running on and the exact details of how it's implemented. Then we'll go the other direction and dive into the details, talking about how to measure the actual running time of a piece of code to get an idea of how it really performs in practice.

Core: Our Motivation for Asymptotic Analysis8:28

Core: Counting Operations9:57

Core: Introduction to Asymptotic Analysis, Part 19:11

Core: Introduction to Asymptotic Analysis, Part 23:48

Core: Computing Big O with Consecutive Operations5:19

Core: Computing Big O with Nested Operations5:22

Concept Challenge: Classifying Functions using Big O7:52

Support: Analyzing Selection Sort8:41

Concept Challenge: Estimating Big O from Code6:08

Core: Worst, Best, and Average Cases8:16

In the Real World: Worst Case Analysis1:30

Core: Analyzing Search Algorithms6:25

Core: Analyzing Sorting Algorithms9:25

When I struggled: Algorithm performance1:31

Core: Merge Sort11:07

Core: A Summary of Sorting4:00

Core: Common Pitfalls in Asymptotic Analysis5:51

Conoce a los instructores

Christine Alvarado
Associate Teaching Professor
Computer Science and Engineering
Mia Minnes
Assistant Teaching Professor
Computer Science and Engineering
Leo Porter
Assistant Teaching Professor
Computer Science and Engineering

[MUSIC]

Okay, so let's see how that is going to translate and

basically we're going to start with seeing how to compute big O and

then afterwards give the formal definition.

So our big O class is supposed to capture eventual rates of growth.

And so we don't care about constants.

And so in big O world,

in asymptotic world, whether we have a million or one, same difference.

The big O is exactly the same.

And so we say that a million is big O(1).

So, notice that the way that I'm reading the sentence, the equals and

then the capital O and then the bracket's another function.

The way that we read it is,

the left hand side is big O of what's ever inside those brackets.

And so here we have that a million is big O(1).

And the idea here is those constants might just be that initialization cost when we

start off a new program.

Then we might have to do a whole lot of busy work at the very beginning, but

that busy work is the same, no matter what our input is.

And so even if it's a million steps or one step that's not going to tell us how that

program behaves as our input gets bigger and bigger and

bigger and so we don't need to worry about it.

We just lump it all into a single constant and say that's big O(1).

It's not changing as n changes.

Okay, so that's one of our principles.

Our second principles with asymptotic analysis is that we only care

about the dominant term.

So we only care about the piece of the calculation

that's going to make the biggest impact to our outcome.

And so we only want to keep the part of the function that is the fastest growing.

So for example, when we think back about our linear function before,

we had 3n+3 in that calculation of the number of operations.

But notice that we've got two terms here.

We've got the 3n term and we've got the 3.

Now, 3n grows as n grows.

3 does not.

And so the dominant term of those 2 pieces of the sum is the 3n, and

in our big O analysis we're just going to keep that.

So 3n+3 is big O(3n).

But now think back to our previous observation, we're going to drop constants

and so 3n is exactly the same as n in this big O sense.

Okay, so you've got these two principles.

How do we know they're okay?

Where are they coming from?

Well, before we get there, let's do some examples,

make sure that we're comfortable.

And so in the next couple of in-video quizzes,

we're going to encourage you to think about some calculations with big O.

So, hopefully those quizzes were helpful for getting a flavor for

how you deal with big O classes and

how you compare two different functions based on these asymptotics.

But you might be wondering, how can we make these choices and

what's a principled way for understanding asymptotic analysis?

So here's the formal definition of what it means when we say that f(n) is

big O (g(n)).

And what we mean, really, is that there are these two constants, n and c.

So that eventually, so for inputs of sizes bigger than this capital N, we

can upper bound our function f(n) by some constant multiple of our function g(n).

Okay, and so you can spend many pleasant hours playing with this definition and

figuring out exactly why it means that we can drop constants and

just keep the dominant term.

But really for practice and for what we're gonna be doing in this class,

I encourage you to not worry too much about this formal definition.

And really make sure that you are comfortable with looking at code and

getting at the asymptotics based on that code.

Looking through the execution and really picking out the big O class for

the runtime of that code.

And so that's what we'll be practicing next.

We'll be looking at a few different code snippets and for

each one of them computing the big O classes of its runtime.

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