Dualpivot

Dualpivot is a sorting algorithm that is an improvement over the traditional quicksort algorithm. It was introduced by Vladimir Yaroslavskiy in 2009. The primary difference between dualpivot and quicksort lies in the partitioning process. While quicksort uses a single pivot, dualpivot uses two pivots, which can lead to better performance in certain scenarios.

The algorithm works by first selecting two pivots from the array. These pivots are typically chosen as the first and last elements of the array. The array is then partitioned into three sections: elements less than the first pivot, elements between the two pivots, and elements greater than the second pivot. This partitioning is done in a single pass through the array, which can be more efficient than the two passes required by quicksort.

After partitioning, the algorithm recursively sorts the three sections. The section between the two pivots is already sorted, so it does not need to be sorted again. This can lead to a reduction in the number of recursive calls, which can improve performance.

Dualpivot has been shown to perform well on a variety of data sets, including those with many duplicate elements. However, like quicksort, its performance can degrade to O(n^2) in the worst case, although this is rare with good pivot selection strategies. The average-case time complexity of dualpivot is O(n log n), the same as quicksort.

The algorithm is implemented in the Java standard library as the default sorting algorithm for primitive types and objects. It has also been adopted in other programming languages and libraries.