Algorithm Design

Search engines often index their collections of documents so that they can easily return an ordered set of documents that contain a given query word, w. Such a data structure is known as an inverted file. In order to construct an inverted file, we might start with a set of n triples of the form, (w, d, r), where w is a word, d is an identifier for a document that contains the word w, and r is a rank score for the popularity of the document d. Often, the next step is to sort these triples, ordered first by w, then by r, and then by d. Assuming each of the values, w, d, and r, are represented as integers in the range from 1 to 4n, describe a linear-time algorithm for sorting a given set of n such triples.