Sorting Lists with Equal Keys Using Mergesort in Linear Time

This article introduces a new optimization method to improve mergesort's runtime complexity, when sorting sequences that have equal keys to $O(n log_2 k)$, where $k$ is the number of distinct keys in the sequence. When $k$ is constant, it is evident that mergesort is capable of achieving linear time by utilizing linked lists as its underlying data structure. Mergesort linked list implementations can be optimized by introducing a new mechanism to group elements with equal keys together, thus allowing merge algorithm to achieve linear time.