THE FASTEST WAY TO SORT N NUMBERS: sortN library 1.0

Have you ever thought about the fastest way to sort N numbers?Last week I wrote a post about the fastest way to sort 3 numbers, this week I show you a tricky way to optimize the sort of N numbers.The problem of sorting an array of numbers is probably the most studied in computer science. The efficiency of a sort algorithm depends essentially on the number of comparisons and swaps it needs to reach the solution. This post contains an optimized sort algorithm for small buckets (to my knowledge the fastest).Currently most of sorting algorithms uses quick sort for large buckets and insertion sort for smaller ones. Both these algorithms uses an optimized way to swaps and compare numbers. The sortN library is a further optimization of this operations. It does first all the needed comparisons and then, only in the end, it swaps values to reach the sorted solution only in the end. It is in practice an enhanced Insertion sort algorithm.The sortN libraryThe library is written in C++, but it can be written in any code, and supports arrays up to 7 elements. It can be applied , in theory, to array of any size but we will see this can not be realized in practice, only small arrays can be sorted.The sortN libary can be considered enhanced insertion sort algorithm.It contains a list of optimized function to sort 3,4,5,6,7 values. Each function is optimized to sort an N number of values.Here is the approach to the solution:N numbers can be disposed in Nc combinations where Nc is N!.We may think to write a recursive code that reach the sorted solution in the way algorithms for permutations does.The permutations represents all the possible solutions, depending on the value of each comparison (between 2 values of the array) a permutation is chosen or refused.This allows, depending on the results of the comparisons, to build a decisionary tree that unequivocally leads to the permutation that represents the solution. Once we know the solution we can optimize swaps to reach it.Notice that no swaps must be done done before we know the exact solution. This can be considered an enhanced insertion sort algorithm.The number of comparisons possible are great even for a relative small array, we can not think about writing by hand the code, we need some function to do job for us. Thatd-deOaos what the sort library does, it prints the enhanced insertion sort algorithm.There is a small disadvantage: the problem has size N!. It becomes huge for relative small buckets like 8 numbers. The sort8 function requires a 10MB file, I waited10 minutes for the compiler to build it, but no success, then I give up and decide to use the library till sort7 function.The sortN functionYou probably got confused, so here it is the code that I hope will clarify the concept.The sort N function is a MATLAB script that prints the enhanced insertionsort algorithm for N values.It recursively finds all the solutions and it prints optimized swaps.

Requirements:	No special requirements
Platforms:	Matlab
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