Complexity A Quicksort starts by partitioning the input into two chunks: it chooses a “pivot” value, and partitions the input into those less than the pivot value and those larger than the pivot value (and, of course, any equal to the pivot value have go into one or the other, of course, but for a … Read more
For LINQ to Objects, it’s a stable quicksort that is used. For any other kind of LINQ, it’s left to the underlying implementation.
I find this in the Java doc. The sorting algorithm is a Dual-Pivot Quicksort by Vladimir Yaroslavskiy, Jon Bentley, and Joshua Bloch. This algorithm offers O(n log(n)) performance on many data sets that cause other quicksorts to degrade to quadratic performance, and is typically faster than traditional (one-pivot) Quicksort implementations. Then I find this in … Read more
TimSort is a highly optimized mergesort, it is stable and faster than old mergesort. when comparing with quicksort, it has two advantages: It is unbelievably fast for nearly sorted data sequence (including reverse sorted data); The worst case is still O(N*LOG(N)). To be honest, I don’t think #1 is a advantage, but it did impress … Read more
Make the graph bigger and you’ll see that O(n logn) isn’t quite a straight line. But yes, it is pretty near to linear behaviour. To see why, just take the logarithm of a few very large numbers. For example (base 10): log(1000000) = 6 log(1000000000) = 9 … So, to sort 1,000,000 numbers, an O(n … Read more
def sort(array): “””Sort the array by using quicksort.””” less = [] equal = [] greater = [] if len(array) > 1: pivot = array[0] for x in array: if x < pivot: less.append(x) elif x == pivot: equal.append(x) elif x > pivot: greater.append(x) # Don’t forget to return something! return sort(less)+equal+sort(greater) # Just use the … Read more
The true quicksort has two beautiful aspects: Divide and conquer: break the problem into two smaller problems. Partition the elements in-place. The short Haskell example demonstrates (1), but not (2). How (2) is done may not be obvious if you don’t already know the technique!
Choosing a random pivot minimizes the chance that you will encounter worst-case O(n2) performance (always choosing first or last would cause worst-case performance for nearly-sorted or nearly-reverse-sorted data). Choosing the middle element would also be acceptable in the majority of cases. Also, if you are implementing this yourself, there are versions of the algorithm that … Read more
The most likely reason: quicksort is not stable, i.e. equal entries can change their relative position during the sort; among other things, this means that if you sort an already sorted array, it may not stay unchanged. Since primitive types have no identity (there is no way to distinguish two ints with the same value), … Read more
Quicksort has O(n2) worst-case runtime and O(nlogn) average case runtime. However, it’s superior to merge sort in many scenarios because many factors influence an algorithm’s runtime, and, when taking them all together, quicksort wins out. In particular, the often-quoted runtime of sorting algorithms refers to the number of comparisons or the number of swaps necessary … Read more