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k-way merges are used in external sorting procedures. [4] External sorting algorithms are a class of sorting algorithms that can handle massive amounts of data. External sorting is required when the data being sorted do not fit into the main memory of a computing device (usually RAM) and instead they must reside in the slower external memory ...
For example, say that student records consisting of name and class section are sorted dynamically, first by name, then by class section. If a stable sorting algorithm is used in both cases, the sort-by-class-section operation will not change the name order; with an unstable sort, it could be that sorting by section shuffles the name order ...
Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases (e.g. Facebook or LinkedIn). 1-planarity [1] 3-dimensional matching [2] [3]: SP1 Bandwidth problem [3]: GT40 Bipartite dimension [3]: GT18 Capacitated minimum spanning tree [3]: ND5
Stable sorting algorithms maintain the relative order of records with equal keys (i.e. values). That is, a sorting algorithm is stable if whenever there are two records R and S with the same key and with R appearing before S in the original list, R will appear before S in the sorted list.
Batcher's odd–even mergesort [1] is a generic construction devised by Ken Batcher for sorting networks of size O(n (log n) 2) and depth O((log n) 2), where n is the number of items to be sorted. Although it is not asymptotically optimal, Knuth concluded in 1998, with respect to the AKS network that "Batcher's method is much better, unless n ...
def cycle_sort (array)-> int: """Sort an array in place and return the number of writes.""" writes = 0 # Loop through the array to find cycles to rotate. # Note that the last item will already be sorted after the first n-1 cycles. for cycle_start in range (0, len (array)-1): item = array [cycle_start] # Find where to put the item. pos = cycle_start for i in range (cycle_start + 1, len (array ...
The first phase of patience sort, the card game simulation, can be implemented to take O(n log n) comparisons in the worst case for an n-element input array: there will be at most n piles, and by construction, the top cards of the piles form an increasing sequence from left to right, so the desired pile can be found by binary search. [1]
As a baseline algorithm, selection of the th smallest value in a collection of values can be performed by the following two steps: . Sort the collection; If the output of the sorting algorithm is an array, retrieve its th element; otherwise, scan the sorted sequence to find the th element.