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The step-by-step process of replacing pairs of items during the shell sorting algorithm. Shellsort, also known as Shell sort or Shell's method, is an in-place. It can be seen as either a generalization of sorting by exchange or sorting by insertion. The method starts by sorting pairs of elements far apart from each other, then progressively reducing the gap between elements to be compared.
Starting with far apart elements, it can move some out-of-place elements into position faster than a simple nearest neighbor exchange. Published the first version of this sort in 1959.
The running time of Shellsort is heavily dependent on the gap sequence it uses. For many practical variants, determining their remains an. Contents. Description Shellsort is a generalization of that allows the exchange of items that are far apart. The idea is to arrange the list of elements so that, starting anywhere, considering every hth element gives a sorted list. Such a list is said to be h-sorted.
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Equivalently, it can be thought of as h interleaved lists, each individually sorted. Beginning with large values of h, this rearrangement allows elements to move long distances in the original list, reducing large amounts of disorder quickly, and leaving less work for smaller h-sort steps to do. If the list is then k-sorted for some smaller integer k, then the list remains h-sorted. Following this idea for a decreasing sequence of h values ending in 1 is guaranteed to leave a sorted list in the end. An example run of Shellsort with gaps 5, 3 and 1 is shown below. A 1 a 2 a 3 a 4 a 5 a 6 a 7 a 8 a 9 a 10 a 11 a 12 Input data 62 83 18 53 07 17 95 86 47 69 25 28 After 5-sorting 17 28 18 47 07 25 83 86 53 69 62 95 After 3-sorting 17 07 18 47 28 25 69 62 53 83 86 95 After 1-sorting 07 17 18 25 28 47 53 62 69 83 86 95 The first pass, 5-sorting, performs insertion sort on five separate subarrays ( a 1, a 6, a 11), ( a 2, a 7, a 12), ( a 3, a 8), ( a 4, a 9), ( a 5, a 10). For instance, it changes the subarray ( a 1, a 6, a 11) from (62, 17, 25) to (17, 25, 62).
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 but almost ordered. In both cases insertion sort works efficiently. Shellsort is not: it may change the relative order of elements with equal values.
It is an in that it executes faster when the input is partially sorted. Pseudocode Using Marcin Ciura's gap sequence, with an inner insertion sort.
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Sedgewick focuses on practical applications, giving readers all the information, diagrams, and real (not pseudo-) code they need to confidently implement, debug, and use the algorithms he presents. Together these books present nearly 2,000 new exercises, hundreds of new figures, and dozens of new programs.
