When we talk about algorithm complexity, there are some common misunderstandings that come up often. Let’s break them down:

1. Not all $O(n)$ algorithms are the same: Just because two algorithms are both labeled $O(n)$ doesn’t mean they work the same way. One might run faster than the other because of extra details that big-O notation doesn’t show.

2. Worst-case vs Average-case: A lot of students only think about worst-case scenarios. But looking at average-case complexity can give us a better idea of how an algorithm usually performs.

3. Space complexity is important too: People often focus only on time complexity, which is how fast an algorithm runs. But space complexity, which is about how much memory the algorithm needs, is also super important. This is especially true when dealing with large amounts of data.

4. Simple doesn’t always mean efficient: Just because an algorithm looks easy to understand doesn’t mean it will work well. Some simple algorithms can still be quite complicated in terms of how long they take to run.

Knowing about these important points helps us make smarter choices when we create and study algorithms!