> 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/13.9-summary.md).

# 13.9 Summary

To summarize this chapter:

* Given a piece of code, we can express its runtime as a function $$R(N)$$
  * $$N$$ is a **property** of the input of the function often representing the **size** of the input
* Rather than finding the exact value of $$R(N)$$, we only worry about finding the **order of growth** of $$R(N)$$.
* One approach (not universal):
  * Choose a representative operation
  * Let $$C(N)$$ be the count of how many times that operation occurs as a function of $$N$$.
  * Determine order of growth $$f(N)$$ for $$C(N)$$, i.e. $$C(N)\in \Theta(f(N))$$
  * Often (but not always) we consider the worst case count.
  * If operation takes constant time, then $$R(N)\in \Theta(f(N))$$.


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