LYCOS RETRIEVER 
Shell Sort: Array
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The trick in Shell Sort is to sort the subsequences of elements spaced k elements apart. There are k such sequences starting at positions 0 through k-1 in the array. In these sorts, elements k positions apart are exchanged, removing between 1 and 2(k-1)+1 inversions.
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Shell Sort subdivides the array of structures to be sorted into smaller pieces by selecting every nth record and then sorting that group of sturctures. By repeatedly reducing the value of n until it diminishes to 1 the array becomes sorted. The efficiency of Shell Sort comes from the fact that it is able to move structures which are greatly offset from their final location rapidly with few key comparisons.
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Shell sort improves insertion sort by comparing elements separated by a gap of several positions. This lets an element take "bigger steps" toward its expected position. Multiple passes over the data are taken with smaller and smaller gap sizes. The last step of Shell sort is a plain insertion sort, but by then, the array of data is guaranteed to be almost sorted.
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Shellsort is a simple extension of insertion sort which gains speed by allowing exchanges of elements that are far apart. The idea is to rearrange the array to give it the property that every hth element (starting anywhere) yields a sorted array. Such an array is said to be h-sorted.
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Various spacings may be used to implement a shell sort. Typically the array is sorted with a large spacing, the spacing reduced, and the array sorted again. On the final sort, spacing is one. Although the shell sort is easy to comprehend, formal analysis is difficult. In particular, optimal spacing values elude theoreticians. Knuth has experimented with several values and recommends that spacing h for an array of size N be based on the following formula:
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An ANSI-C implementation for shell sort is included. Typedef T and comparison operator compGT should be altered to reflect the data stored in the array. The central portion of the algorithm is an insertion sort with a spacing of h.
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