The default Arrays.sort() implementation in Java 7 â¦ Uses: Insertion sort is used when number of elements is small. If you don't care about memory, a simple Mergesort would suffice. The answer, as is often the case for such questions, is "it depends". 4. Shell Sort is a variation of Insertion Sort. At the end of the day though, whatever the best sorting algorithm really is depends on the input (and who you ask). In Merge sort, we divide the array recursively in two halves, until each sub-array contains a single element, and then we merge the sub-array in a way that it results into a sorted array. Stable: Yes.It is stable sorting algorithm. The interval between the elements is gradually decreased based on the sequence used. So if we have a=2, b=2. Merge Sort is one of the best examples of Divide & Conquer algorithm. Similor to merge sort, Quicksort works on the divide and conquer algorithm. The performance of the shell sort depends on the type of sequence used for a given input array. This means the equation for Merge Sort would look as follows: $$ T(n) = 2T(\frac{n}{2})+cn $$ Mergesort is up there with the fastest standard sort algorithms. It sorts the elements of a container in the range pointed by the specified iterators using a comparator. With this algorithm, the array is sorted at a specific interval based on the chosen sequence. To sort an array in reverse/decreasing order, you can use std::sort algorithm provided by STL. ... a sorted array is returned. In the most general case, you'd go with an algorithm that happens to have the best average or best worst-case number of comparisons. The default comparator used is std::less> which sorts the container in ascending order using operator<. Average and Worst case sorting occurs when arrays are reverse sorted, Best case sorting occurs when arrays are already sorted. The merge step takes O(n) memory, so k=1. The general goal of a sorting algorithm is to minimize the number of comparisons. The default Collections.sort() implementation in Java 7 is a Mergesort algorithm adapted from 'TimSort.' If you want the best sorting algorithm that runs under assumption that âthe data is already sortedâ, then the best algorithm is âdo nothingâ which runs in no time. It can also be useful when input array is almost sorted, only few elements are misplaced in complete big array. If T(n) is runtime of the algorithm when sorting an array of the length n, Merge Sort would run twice for arrays that are half the length of the original array. ; Sorting In place: Yes.It does not uses extra space to sort the elements. Sorting algorithms have a lower bound and an upper bound on the number of comparisons( n log n worst-case for merge and heap sorts, n log n average case for quick sort). Sorting is a very classic problem of reordering items (that can be compared, e.g. Quicksort is one of the most efficient ways of sorting elements in computer systems. 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