Summer 2009 CMSC 351: Homework 7 Clyde Kruskal
Due at the start of class, Wednesday, July 1.
Problem 1. Assume you have a list of nelements where the first n/k elements are the
smallest (but not sorted), the next group of n/k elements are the next smallest (but
not sorted), ..., and the last n/k elements are the largest (but not sorted). You may
assume kdivides n.
(a) Give an algorithm that sorts this list with as few comparisons as possible (as a
function of nand k). Just get the high order term right. How many comparisons
does your algorithm use?
(b) Show that your algorithm is optimal using a decision tree argument on the entire
list. (I.e., do not argue that you must solve kindependent sorting problems.)
Problem 2. Do Exercise 8.2-4 on page 170 of CLRS.
Problem 3.
(a) Illustrate the operation of radix sort on the following list of English words:
RUTS, TOPS, SUNS, SPOT, TONS, OPTS, TORS, SOTS, ROOT, OUTS,
SUPS, PUTT
(b) Write an English sentence using both “tor” and “sot” (that indicates you under-
stand the meanings of both words).