Optimizing Complexity of Quick Sort

Md. Sabir Hossain, Snaholata Mondal, Rahma Simin Ali, Mohammad Hasan

Abstract: Quick Sort is considered as the fastest sorting algorithm among all the sorting algorithms. The idea of selecting a pivot was introduced in classical Quick Sort in 1962. This sorting algorithm takes favorably less time compared to other methods. It needs a complex time O(\( nlogn \)) for the best case and O(\( n^{2} \)) for worst-case which occurs when the input array is already sorted or reversely sorted. To reduce the worst-case complexity we provide a strong algorithm where it makes fewer comparisons and the time complexity after using this algorithm becomes a function of logarithm O(\( nlogn \)) for worst-case complexity. We experimentally evaluate our algorithms and compare them with classical algorithms and with other papers. The algorithm presented here has profound implications for future studies of handling worst-case complexity and may one day help to solve this occurrence of the fastest sorting method.