This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is $n\lg n-1.4427n+O(\log n)$. For many efficient algorithms, the first $n\lg n$ term is easy to achieve and our focus is on the (negative) constant factor of the linear term. The current best value is −1.3999 for the MergeInsertion sort. Our new value is −1.4106, narrowing the gap by some 25%. An important building block of our algorithm is “two-element insertion,” which inserts two elements A and B, $A<B$, into a sorted sequence T. This insertion algorithm is still sufficiently simple for rigorous mathematical analysis and works well for a certain range of the length of T for which the simple binary insertion does not, thus allowing us to take a complementary approach together with the binary insertion.

本文研究了排序算法的比较次数的平均复杂度。它的信息理论下限是$ñ\lg ñ-1.4427ñ+Ø（\mathrm{日志}ñ）$。对于许多有效的算法，第一个$ñ\lg ñ$项很容易实现，我们的重点是线性项的（负）常数。对于MergeInsertion排序，当前的最佳值为-1.3999。我们的新值为-1.4106，使差距缩小了25％。我们算法的一个重要组成部分是“两元素插入”，它插入了两个元素A和B，$\mathrm{一种}<乙$成已排序的序列Ť。对于严格的数学分析，该插入算法仍然足够简单，并且对于T长度的特定范围（对于简单的二进制插入而言并非如此）也可以很好地工作，因此使我们能够采取与二进制插入一起的补充方法。