Construction, Évaluation et Amélioration Systématiques de Structures de Données

— A very simple formalism, viz. abstract data types, using équations and preconditions, is proposedfor describing the proper tie s oj the object s and the opérations ofa data structure. Two cases studies are detailed: sets, and dictionaries (viz. binary search trees). A small number of rules and heuristics are then developed in order to systematically construct the classical algorithms of search and insertion in a dictionary. The more original contribution of the paper is to extend this construction by additional phases: the complexity ofthe algorithms is evalued and then their efficiency is improved. We are thus led to transform the trivial insertion algorithm so that the height ofthe trees is kept constant as much as possible. Some opérations for rebalancing trees (viz. simple and double rotations) and a property of quasi-balanced (AVL) trees are thereby reinvented almost automatically. Oj course, a number of « eurekas » remain necessary; each of them is carefully pinpointed during construction. The algorithm obtainedfinally is not new; butit is sujficiently intricated so as tojustify the validity of this type of research, which is at the cross-roads of two concerns: the abstract spécifications of data structures, and the complexity analysis of algorithms. (*) Reçu en juillet 1978, révisé en janvier 1979. O Attaché de Recherche au Centre de Recherche en Informatique de Nancy, Nancy. R.A.I.R.O. Informatique théorique/Theoretical Informaties, 0399-0540/1980/ 83 $ 5.00 © AFCET-Bordas-Dunod