Minimum average case time complexity for sorting algorithms

There are certainly many sorting algorithms in this modern world of Computers, most of which work in second-order time and some in linearithmic time, but none have achieved more than that. There is none. However, is it even possible to hit the bottom more than that? The minimal temporal complexity that an ordering modus operandi may achieve goes in the order of O(nlog2n)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(n\log _2n)$$\end{document}, without considering any modifications to the generalized computer architecture, according to a rigorous mathematical analysis presented in this paper. However, we have also taken into account the average time complexities of the algorithms to disperse throughout the smallest potential time complexity that a sorting algorithm may achieve. Three different search algorithms, namely, Binary, Interpolation, and Jump search, have been used in this article. The interpolation search takes less time if the array’s items are arranged in arithmetic progression, and there are many more similar biased situations where a certain approach produces superior results. Sorting algorithms have been proposed herewith, with Searching Techniques as intermediate. The Computational Complexity of the Sorting Algorithm amalgamated with Interpolation Search as an Intermediate Step is compared with Sorting Algorithms amalgamated with Jump Search, Binary Search as an intermediate.