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One implementation can be described as arranging the data sequence in a two-dimensional array and then sorting the columns of the array using insertion sort. The worst-case time complexity of Shellsort is an open problem and depends on the gap sequence used, with known complexities ranging from O ( n 2 ) to O ( n 4/3 ) and Θ( n log 2 n ).
A comparison sort cannot use less than log 2 (n!) comparisons on average to sort n items (as explained in the article Comparison sort) and in case of large n, Stirling's approximation yields log 2 (n!) ≈ n(log 2 n − log 2 e), so quicksort is not much worse than an ideal comparison sort. This fast average runtime is another reason for ...
Bubble sort, sometimes referred to as sinking sort, is a simple sorting algorithm that repeatedly steps through the input list element by element, comparing the current element with the one after it, swapping their values if needed. These passes through the list are repeated until no swaps have to be performed during a pass, meaning that the ...
Among quadratic sorting algorithms (sorting algorithms with a simple average-case of Θ(n 2)), selection sort almost always outperforms bubble sort and gnome sort. Insertion sort is very similar in that after the k th iteration, the first k {\displaystyle k} elements in the array are in sorted order.
The difference between pigeonhole sort and counting sort is that in counting sort, the auxiliary array does not contain lists of input elements, only counts: 3: 1; 4: 0; 5: 2; 6: 0; 7: 0; 8: 1; For arrays where N is much larger than n, bucket sort is a generalization that is more efficient in space and time.
In computing, natural sort order (or natural sorting) is the ordering of strings in alphabetical order, except that multi-digit numbers are treated atomically, i.e., as if they were a single character. Natural sort order has been promoted as being more human-friendly ("natural") than machine-oriented, pure alphabetical sort order.
The heapsort algorithm can be divided into two phases: heap construction, and heap extraction. The heap is an implicit data structure which takes no space beyond the array of objects to be sorted; the array is interpreted as a complete binary tree where each array element is a node and each node's parent and child links are defined by simple arithmetic on the array indexes.
Repeat until array is sorted. Insertion sort: Scan successive elements for an out-of-order item, then insert the item in the proper place. Selection sort: Find the smallest (or biggest) element in the array, and put it in the proper place. Swap it with the value in the first position. Repeat until array is sorted. Quick sort: Partition the ...