> For the complete documentation index, see [llms.txt](https://cs61b-2.gitbook.io/cs61b-textbook/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://cs61b-2.gitbook.io/cs61b-textbook/13.-asymptotics-i/13.1-an-introduction-to-asymptotic-analysis.md). # 13.1 An Introduction to Asymptotic Analysis {% embed url="" %} Previously, we have focused on how to save time *writing* the program. Now, we will learn how to make the best use of our computer's time and memory. We can consider the process of writing efficient programs from two different perspectives: 1. Programming Cost *(everything in the course up to this date)* 1. How long does it take for you to develop your programs? 2. How easy is it to read or modify your code? 3. How maintainable is your code? (very important — much of the cost comes from maintenance and scalability, not development!) 2. Execution Cost *(everything in the course from this point on)* 1. **Time complexity**: How much time does it take for your program to execute? 2. **Space complexity**: How much memory does your program require? To give a sense of what is coming up, consider a **sorted** array. Our goal is to determine if there is a duplicate element in the list. ```java List example = [-3, -1, 2, 4, 4, 8, 10, 12]; ``` A **naïve algorithm** would be to compare every pair of elements. In the above example, we would compare -3 with every element in the list, then -1, then 2, etc. A **better algorithm** would be to take advantage of the sorted nature of the list! Instead of comparing every pair of elements, we can compare each element with just the element next to it. We can see that the **naïve algorithm** seems like it’s doing a lot more unnecessary, redundant work than the **better algorithm**. But how much more work is it doing? How do we quantify how efficient a program is? This chapter will provide you the formal techniques and tools to compare the efficiency of various algorithms! --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://cs61b-2.gitbook.io/cs61b-textbook/13.-asymptotics-i/13.1-an-introduction-to-asymptotic-analysis.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.