Quick Sort is a popular sorting method. It usually does a great job, working at a speed of $O(n \log n)$ most of the time. This means it runs quickly, even with a decent number of items to sort.

But there's a catch! In the worst-case scenario, when things don't go well, it can slow down to $O(n^2)$. This happens when the pivot, the item we choose to help with sorting, is not a good choice.

Challenges:

• Picking a Pivot: If we pick a bad pivot, Quick Sort can take longer than we want.
• Not Stable: Quick Sort isn't stable. This means it doesn’t keep the same order for items that are equal, which can make sorting tricky sometimes.

Solutions:

• One way to make Quick Sort better is to use something called Median-of-three for picking the pivot. This helps improve the average speed of the sort.
• Another helpful idea is to use an adaptive sorting strategy. This means switching to a different, more stable method like Insertion Sort when sorting smaller groups of items.

These improvements can help Quick Sort perform much better in different situations!