sortidest

Sortidest is a term used in data analysis to denote a dimensionless index that quantifies how sorted a sequence is. The concept treats sortedness as a continuous spectrum, bounded between 0 and 1. The term is a nonce coinage that appears in some scholarly and practical discussions but is not part of a formal standard.

Definition and computation: For a sequence S of length n, let inv(S) be the number of inversions (pairs i < j with S[i] > S[j]). The maximum possible inversions is maxInv(n) = n(n−1)/2. Sortidest(S) is defined as 1 − inv(S) / maxInv(n). Values lie in the interval [0, 1], where a perfectly sorted nondecreasing sequence has sortidest = 1, and a completely reversed sequence has sortidest = 0. The measure is closely related to the concept of normalized Kendall tau distance.

Applications and interpretation: Sortidest serves as a heuristic to assess the expected effectiveness of adaptive sorting algorithms and to compare data sets by how much they can benefit from sortedness. It is commonly used in experiments evaluating hybrid sorts, such as those that switch between insertion sort and merge-like procedures depending on data order, or in benchmarks that aim to predict practical performance on real-world data.

Example and limitations: Consider the sequence [1, 2, 3, 5, 4]. Here n = 5 and inv = 1, maxInv = 10, so sortidest = 1 − 1/10 = 0.9. Limitations include sensitivity to ties, since inversions are defined with a strict inequality, and potential instability with duplicate values. It is one of several informal measures of sortedness used in analysis rather than a universally standardized metric.