The way sorting algorithms work can be greatly affected by how much extra memory they need. This is especially true when we look at in-place and non-in-place sorting methods.

In-place Sorting Algorithms
In-place sorting algorithms, like Quick Sort and Heap Sort, try to use as little extra memory as possible. They are efficient because they usually need only a small amount of extra space. Their space usage is often $O(1)$ or $O(\log n)$. This means they don't require much more space than what is already used by the original list.

Non-In-place Sorting Algorithms
On the other hand, we have non-in-place sorting algorithms, like Merge Sort and Bubble Sort. These types of algorithms generally need more memory to work. For example, Merge Sort needs $O(n)$ extra space for the temporary lists it creates while sorting. This can be a big problem when sorting large groups of data since more memory usage can slow things down and create delays in the sorting process.

When to Choose Each Algorithm
The amount of extra space needed can also affect which sorting algorithm you pick depending on the situation:

• Limited Memory: If you are working on a computer with not much RAM, in-place algorithms are usually better choices since they use less extra space.

• Sorting Big Datasets: When you need to sort a lot of data, non-in-place algorithms might not work well because their higher memory needs can make them slower and less efficient.

Wrapping Up
In short, it's important to understand how much extra memory sorting algorithms require when choosing the right one for your needs. The space they use can greatly affect how fast and efficient they are, and this understanding can help developers pick the best algorithm for situations where memory is important.