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There is no single algorithm that is ideally suited to every type of sort. If all the data will fit into working memory, then you have a choice of algorithms depending on the size of the set, whether the sort should remain stable or not and how much auxiliary memory you wish to utilise. But if data will not fit into working memory all at once, your choice of algorithm is more limited.

Stability relates to elements with equal status. When the sort is stable, equal elements remain in the same order they were originally input while an unstable sort cannot guarantee this. Stable sorts are ideally suited to data that may be sorted by different primary keys, such that the previous sort order is automatically maintained. That is, if data may be sorted by name or by date, sorting by name and then by date keeps the names in the same order (by date). With an unstable sort, even if you keep track of secondary keys there is no guarantee the secondary or tertiary keys will maintain order.

For small sets of data that will easily fit into memory, an insertion sort offers the best performance with minimal auxiliary storage. This is a stable sort that can be done in place.

For larger sets, a quicksort offers the best performance but is unstable. However, stable versions exist at the cost of performance. Since the algorithm divides the set into smaller and smaller unsorted sets (where each set is in the correct order with respect to the other sets), switching to insertion sort to sort the smaller sets improves overall performance.

For disk-based sorting, merge sort is generally the most efficient. It utilises multiple disks and is stable.

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