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A more recent variant uses a bucket index with smaller sub-buckets to reduce memory usage. Most implementations delegate to multikey quicksort, an extension of three-way radix quicksort, to sort the contents of the buckets. By dividing the input into buckets with common prefixes, the sorting can be done in a cache-efficient manner.
Timsort is a stable sorting algorithm (order of elements with same key is kept) and strives to perform balanced merges (a merge thus merges runs of similar sizes). In order to achieve sorting stability, only consecutive runs are merged. Between two non-consecutive runs, there can be an element with the same key inside the runs.
For example, bubble sort and timsort are both algorithms to sort a list of items from smallest to largest. Bubble sort organizes the list in time proportional to the number of elements squared ((), see Big O notation), but only requires a small amount of extra memory which is constant with respect to the length of the list (()).
A kind of opposite of a sorting algorithm is a shuffling algorithm. These are fundamentally different because they require a source of random numbers. Shuffling can also be implemented by a sorting algorithm, namely by a random sort: assigning a random number to each element of the list and then sorting based on the random numbers.
Like most variants of bubble sort, cocktail shaker sort is used primarily as an educational tool. More efficient algorithms such as quicksort , merge sort , or timsort are used by the sorting libraries built into popular programming languages such as Python and Java.
Flashsort is an efficient in-place implementation of histogram sort, itself a type of bucket sort. It assigns each of the n input elements to one of m buckets, efficiently rearranges the input to place the buckets in the correct order, then sorts each bucket. The original algorithm sorts an input array A as follows:
In computer science, smoothsort is a comparison-based sorting algorithm.A variant of heapsort, it was invented and published by Edsger Dijkstra in 1981. [1] Like heapsort, smoothsort is an in-place algorithm with an upper bound of O(n log n) operations (see big O notation), [2] but it is not a stable sort.
Proportion extend sort was published by Jing-Chao Chen in 2001 [2] as an improvement on his earlier proportion split sort design. [3] Its average-case performance, which was only experimentally measured in the original paper, was analyzed by Richard Cole and David C. Kandathil in 2004 [4] and by Chen in 2006, [5] and shown to require log 2 n + O(n) comparisons on average.