CSCI 2720			Data Structures			     Spring 2004


				Homework Set #1

Due at the start of class on Thursday, January 22.


All problems except for A, G and H (below) are from Chapter 1 of the text
by Lewis and Denenberg.  Each problem or part is 10 points.

15 (prove carefully)

17(a) (assume a, b > 0)

17(b) (assume a > b > 1)

22(a)

23(a)(c)(d)


For problems A, G and H assume that f is little-oh of h.  

A  If g(n) = ( f(n) + h(n) )/2 for all n, prove that g is in Theta of h.
   (Here g(n) is the arithmetic mean, or average, of f(n) and h(n).)

G  If g(n) = square_root( f(n)h(n) ) for all n, prove that g is in little-oh of
   h and that f is in little-oh of g.
   (Here g(n) is the geometic mean of f(n) and h(n).)

H  If g(n) = 2/( (1/f(n)) + (1/h(n)) ) for all n, prove that g is in Theta of f.
   (Here g(n) is the harmonic mean of f(n) and h(n).)