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ProxmapSort, or Proxmap sort, is a sorting algorithm that works by partitioning an array of data items, or keys, into a number of "subarrays" (termed buckets, in similar sorts). The name is short for computing a "proximity map," which indicates for each key K the beginning of a subarray where K will reside in the final sorted order.
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 ).
Bucket sort can be implemented with comparisons and therefore can also be considered a comparison sort algorithm. The computational complexity depends on the algorithm used to sort each bucket, the number of buckets to use, and whether the input is uniformly distributed. Bucket sort works as follows: Set up an array of initially empty "buckets".
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.
Sorted arrays are the most space-efficient data structure with the best locality of reference for sequentially stored data. [citation needed]Elements within a sorted array are found using a binary search, in O(log n); thus sorted arrays are suited for cases when one needs to be able to look up elements quickly, e.g. as a set or multiset data structure.
In computer science, radix sort is a non-comparative sorting algorithm.It avoids comparison by creating and distributing elements into buckets according to their radix.For elements with more than one significant digit, this bucketing process is repeated for each digit, while preserving the ordering of the prior step, until all digits have been considered.
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.
As another example, many sorting algorithms rearrange arrays into sorted order in-place, including: bubble sort, comb sort, selection sort, insertion sort, heapsort, and Shell sort. These algorithms require only a few pointers, so their space complexity is O(log n). [1] Quicksort operates in-place on the data to be sorted.