I’m trying to understand how the time complexity of various sorting algorithms, like Bubble Sort, Merge Sort, and Quick Sort, affects their performance in real-world applications. I’m particularly interested in a detailed breakdown of how these complexities translate into practical performance differences under various conditions.

I have reviewed the theoretical time complexities of these algorithms, but I’m struggling to grasp how these complexities impact performance in practice. For example, I expected Quick Sort to always outperform Bubble Sort, but I’ve read that in some cases, Bubble Sort might be more efficient. I haven’t run benchmarks yet, but I’m curious if others have experience or data that could clarify this.

I’m looking for insights into when one sorting algorithm might be more effective than another, even if its theoretical time complexity is worse. Should I run benchmarks with my specific data to get a more accurate understanding, or are there general rules of thumb that apply?