Complexity and Guarantee of Permutation Assertion for Sorting

Abstract

Asseritons for sorting functions are widely used as an example in discussions of software specification needs two assertions: order and permutation. The order assertion checks whether the output array monotonically increases (or decreases). The permutation assertion checks whether the output order assertion is simple ans fast, whereas permutation assertion is considered to be time-consuming. This paper gives a ddetailed analysis of which is shown O(n log n). This complexity is no simpler than that of sorting. This correctness of a sorting procedure by replacing assignments with swap operations on any two array elements. The technique can bge aplied to sorting algorith ms that are in-place. This shows that complete checking for sorting can be achieved in linear time.