A Unified Vista and Juxtaposed Study on k - ary Search Algorithms

With the surge in global development accompanied by adverse improvements in technology, data aspects have caught a great height these days. Now, there are a lot of actions that are to be taken on these chunks of data. Some of them are, searching, sorting, adding, deleting, merging, etc. In this research, we have worked out a unified inequality relating to the generic version of the class of Binary Search, i.e., k-ary Search Algorithms. A detailed comparative study is done on the average case computational complexity k-ary search for different parities of ‘k’. As per the studies conducted in the research, the summation of all computational complexities for even values of k is greater than the summation of all those for odd values of k. Further, a relation between the average case computational complexity and the partitional parameter k is derived with mathematical rigor; As per the results obtained in the research, they follow an inverse relationship, which have been established mathematically and graphically in the research.