Comparison between timsort and quicksort

More or less, it has to do with the fact that Timsort is a hybrid sorting algorithm. This means that while the two underlying sorts it uses (Mergesort and Insertion sort) are both worse than Quicksort for many kinds of data, Timsort only uses them when it is advantageous to do so.

On a slightly deeper level, as Patrick87 states, quicksort is a worst-case O(n²) algorithm. Choosing a good pivot isn't hard, but guaranteeing an O(n log n) quicksort comes at the cost of generally slower sorting on average.

For more detail on Timsort, see this answer, and the linked blog post. It basically assumes that most data is already partially sorted, and constructs "runs" of sorted data that allow for efficient merges using mergesort.

TimSort is a highly optimized mergesort, it is stable and faster than old mergesort.

when comparing with quicksort, it has two advantages:

1. It is unbelievably fast for nearly sorted data sequence (including reverse sorted data);
2. The worst case is still O(N*LOG(N)).

To be honest, I don't think #1 is a advantage, but it did impress me.

Here are QuickSort's advantages

1. QuickSort is very very simple, even a highly tuned implementation, we can write down its pseduo codes within 20 lines;
2. QuickSort is fastest in most cases;
3. The memory consumption is LOG(N).

Currently, Java 7 SDK implements timsort and a new quicksort variant: i.e. Dual Pivot QuickSort.

If you need stable sort, try timsort, otherwise start with quicksort.