An Efficient Natural Merge Sort Incorporating Array Decomposition

Modifying an algorithm that has been established over many years and making it even faster has always been a fascinating and challenging area in the field of algorithms, which motivated us to take the challenge of improving the performance of Knuth’s NaturalMergeSort by reducing the runtime with considering both ascending and descending runs. The way we optimize it is by taking advantage of both ascending and descending runs, i.e., increasing the potential of the decomposition method compared to the existing algorithm. The proposed algorithm was implemented in C++, and the experiment was conducted with some random and manually prepared datasets that resulted in improving the worst case of NaturalMergeSort by an exceedingly large margin of 97.5%, demonstrating the efficiency and flexibility of our algorithm. Even for the average case, our proposed algorithm beats Knuth’s NaturalMergeSort by a slight margin, and it also outperforms traditional merge sort with 17.5% improvements. The performance and efficiency of our algorithm have been recorded and presented in graphical form by comparing time and space complexity with other competitor sorting algorithms.