Generating Sorted Lists of Random Numbers

Abstract

The mpirical testing of a program often calls for generating a set of random numbers and then nnmedmtely sorting them. In this paper we consider the problem of accomplishing that process in a single step. generating a sorted list of random numbers (specifically, reals chosen uniformly from [0, 1]). The method we describe generates the randoms in linear worst-case time, is perfectly random (if it can call a perfectly random generator for a single uniform), and can be described in just a few lines of Algol or Pascal code. If the numbers are not requtred to be generated all at once {but are rather to be used one at a time), then the method can be implemented as a subroutine to produce the “next” number m constant tnne and requires only constant storage. © 1980, ACM. All rights reserved.