Shell sort with expected complexity of O(nlog2n)

Theoretical analysis of the Shell sort algorithm has been a longstanding challenge, and there have been no reports of a Shell sort algorithm with a complexity of O(nlog2n). This study investigated the efficiency of the Shell sort algorithm using a specific increment sequence and conducted stability fitting. The fitting results strongly suggest that the number of key comparisons and movements follows the form cnln(n)+dn(lambda)ln(n), where lambda<1, implying an overall complexity of O (nlog(2)n).