Abstract
Among comparison sorts, no algorithm excels a current set lower bound of O(nlogn) in operation. Quicksort, the fastest of its kind, has a complexity of O(nlogn) at its best and on average and at worst. This paper thus presents two methods: first is an O(n+k) simple counting sort which operates much more speedily than an O(n+k), (k=maximum value) counting sort, and second is an O(ln) radix counting sort which counts the frequency of numbers in the digit l of a data and saves it in a corresponding virtual bucket in an array, only to virtually divide the array into radix digit numbers. For the 6 experimental data, the proposed algorithm makes O(nlogn) or of Quicksort simple into O(n+k) or O(ln). After all, the proposed sorting algorithm has proved to be much faster than the counting sort and Quicksort.
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