![]() For example, in the card sorting example to the right, the cards are being sorted by their rank, and their suit is being ignored. Stable sort algorithms sort equal elements in the same order that they appear in the input. When they are sorted with a non-stable sort, the 5s may end up in the opposite order in the sorted output. When the cards are sorted by rank with a stable sort, the two 5s must remain in the same order in the sorted output that they were originally in. Stability An example of stable sort on playing cards. Online: An algorithm such as Insertion Sort that is online can sort a constant stream of input.Algorithms that take this into account are known to be adaptive. Adaptability: Whether or not the presortedness of the input affects the running time.The remainder of this discussion almost exclusively concentrates upon serial algorithms and assumes serial operation. Whether the algorithm is serial or parallel.Selection sorts include cycle sort and heapsort. Exchange sorts include bubble sort and quicksort. General method: insertion, exchange, selection, merging, etc.A comparison sort examines the data only by comparing two elements with a comparison operator. Whether or not they are a comparison sort.Stability: stable sorting algorithms maintain the relative order of records with equal keys (i.e., values).Recursion: Some algorithms are either recursive or non-recursive, while others may be both (e.g., merge sort). ![]() Strictly, an in-place sort needs only O(1) memory beyond the items being sorted sometimes O(log n) additional memory is considered "in-place". In particular, some sorting algorithms are " in-place". Memory usage (and use of other computer resources).Ideal behavior for a serial sort is O( n), but this is not possible in the average case. For typical serial sorting algorithms, good behavior is O( n log n), with parallel sort in O(log 2 n), and bad behavior is O( n 2). Best, worst and average case behavior in terms of the size of the list.Similarly optimal (by various definitions) sorting on a parallel machine is an open research topic. taking into account machine specific details) is still an open research problem, with solutions only known for very small arrays (<20 elements). Sorting small arrays optimally (in fewest comparisons and swaps) or fast (i.e. Sorting algorithms are prevalent in introductory computer science classes, where the abundance of algorithms for the problem provides a gentle introduction to a variety of core algorithm concepts, such as big O notation, divide-and-conquer algorithms, data structures such as heaps and binary trees, randomized algorithms, best, worst and average case analysis, time–space tradeoffs, and upper and lower bounds. ![]() Algorithms not based on comparisons, such as counting sort, can have better performance. Asymptotically optimal algorithms have been known since the mid-20th century – new algorithms are still being invented, with the widely used Timsort dating to 2002, and the library sort being first published in 2006.Ĭomparison sorting algorithms have a fundamental requirement of Ω( n log n) comparisons (some input sequences will require a multiple of n log n comparisons, where n is the number of elements in the array to be sorted). Bubble sort was analyzed as early as 1956. Among the authors of early sorting algorithms around 1951 was Betty Holberton, who worked on ENIAC and UNIVAC. The output is a permutation (a reordering, yet retaining all of the original elements) of the input.įor optimum efficiency, the input data should be stored in a data structure which allows random access rather than one that allows only sequential access.įrom the beginning of computing, the sorting problem has attracted a great deal of research, perhaps due to the complexity of solving it efficiently despite its simple, familiar statement.The output is in monotonic order (each element is no smaller/larger than the previous element, according to the required order).Sorting is also often useful for canonicalizing data and for producing human-readable output.įormally, the output of any sorting algorithm must satisfy two conditions: Efficient sorting is important for optimizing the efficiency of other algorithms (such as search and merge algorithms) that require input data to be in sorted lists. ![]() The most frequently used orders are numerical order and lexicographical order, and either ascending or descending. In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order.
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