Rangsort

Rangsort is a conceptual sorting algorithm that operates on a list of comparable elements. Its fundamental principle involves determining the rank of each element within the list. The rank of an element is defined as the number of elements that are strictly smaller than it. Once the ranks are determined for all elements, they can be placed into their correct sorted positions.

The process typically begins with an initial pass through the input list to calculate the rank for each element. For every element, the algorithm iterates through the entire list again, counting how many other elements are smaller. This results in a list of ranks corresponding to the original elements. Following the rank calculation, a new list or array is created to store the sorted output. The algorithm then iterates through the original list and its corresponding ranks. For an element with rank 'r', it is placed at index 'r' in the sorted output list. If there are duplicate elements, a slight modification is needed to handle their relative ordering, often by considering the number of preceding equal elements.

Rangsort is known for its stability, meaning that elements with equal values maintain their original relative order in the sorted output. However, its time complexity is generally higher than more common sorting algorithms like quicksort or mergesort, primarily due to the nested loops required for rank calculation. The outer loop iterates through each element, and the inner loop iterates through the entire list to determine its rank. This leads to an O(n^2) time complexity in its most straightforward implementation, where 'n' is the number of elements. Despite its performance drawbacks for large datasets, Rangsort provides an interesting theoretical approach to sorting and can be illustrative of fundamental sorting concepts.