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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.
This popular sorting algorithm has an average-case performance of O(n log(n)), which contributes to making it a very fast algorithm in practice. But given a worst-case input, its performance degrades to O(n 2). Also, when implemented with the "shortest first" policy, the worst-case space complexity is instead bounded by O(log(n)).
The patience sorting algorithm can be applied to process control. Within a series of measurements, the existence of a long increasing subsequence can be used as a trend marker. A 2002 article in SQL Server magazine includes a SQL implementation, in this context, of the patience sorting algorithm for the length of the longest increasing subsequence.
For example, simple, comparison-based sorting algorithms are quadratic (e.g. insertion sort), but more advanced algorithms can be found that are subquadratic (e.g. shell sort). No general-purpose sorts run in linear time, but the change from quadratic to sub-quadratic is of great practical importance.
The next pass, 3-sorting, performs insertion sort on the three subarrays (a 1, a 4, a 7, a 10), (a 2, a 5, a 8, a 11), (a 3, a 6, a 9, a 12). The last pass, 1-sorting, is an ordinary insertion sort of the entire array (a 1,..., a 12). As the example illustrates, the subarrays that Shellsort operates on are initially short; later they are longer ...
Sorting a set of unlabelled weights by weight using only a balance scale requires a comparison sort algorithm. A comparison sort is a type of sorting algorithm that only reads the list elements through a single abstract comparison operation (often a "less than or equal to" operator or a three-way comparison) that determines which of two elements should occur first in the final sorted list.
Introsort or introspective sort is a hybrid sorting algorithm that provides both fast average performance and (asymptotically) optimal worst-case performance. It begins with quicksort, it switches to heapsort when the recursion depth exceeds a level based on (the logarithm of) the number of elements being sorted and it switches to insertion sort when the number of elements is below some threshold.
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.