Given an array with n elements, we want to rearrange them in ascending order. In this paper, we introduce Quick Sort, a divide-and-conquer algorithm to sort an N element array. We evaluate the O(NlogN) time complexity in best case and O(N) in worst case theoretically. We also introduce a way to approach the best case.

Given a sequence of N elements a1, a2, a3, ..., aN. The desired output will be a’1, a’2, a’3,..., a’N such that a’1≤, a’2≤, a’3≤...≤a’N using merge sort. In this paper, we propose a modification to the existing merge sort algorithm to sort the given elements when the input sequence (or a part of it) is in ascending or descending order in a more efficient way by reducing the number of comparison...

Sorting in plain TEX is implemented via heap sort. The heap sort algorithm is explained and the encoding given.

[3] D. J. Bryden. A didactic introduction to arithmetic, sir charles cotterell's 'instrument for arithmeticke' of 1667. " Note, this book contains a flawed conclusion as to the priority of the invention of the sliderule. See [9]. [9] Florian Cajori. On the history of gunter's scale and the slide rule during the seventeenth century.

This paper proposes a new sieving algorithm that employs a bucket sort as a part of a factoring algorithm such as the number field sieve. The sieving step requires an enormous number of memory updates; however, these updates usually cause cache hit misses. The proposed algorithm dramatically reduces the number of cache hit misses when the size of the sieving region is roughly less than the squa...