Homework #1 -- due Monday Wk 2

This homework involves topics that, for the most part, should have been covered in earlier courses (ICS 6A and ICS 23).

# required problems topic
1 CLR Exercise 3.1-1 on page 50 O-notation
2 CLR Problem 3-3(a) on pages 58-59 O-notation
3 CLR Exercise C.3-3 on page 1111 expected value
4 CLR Exercise A.2-1 on page 1067 bounding summations

# suggested problems topic
5 CLR Exercise 3.1-3 on page 50 O-notation
6 CLR Problem 3-4(d,e,f,g) on page 59 prove/disprove properties
7 Resolve the following questions, with proof:
  1. n log n = O(n2)?
  2. n/log n = O(n)?
  3. (log n)363 = O(n)?
  4. 2n = O(2n/2)?
  5. 3n = O(2n)?
O-notation
8 The following is known about functions f and g:
f(n) = θ(n) ; f(1) = 1 ;f(2) = 2
g(n) = θ(n3) ; g(1) = 1 ;g(2) = 8
Is f(3) < g(3)?     Explain why or why not. 		O-notation
9 Prove by induction that, for all n > 6, the unit square
can be partitioned into n squares (not necessarily of identical size). 		induction
10* CLR Exercise 3.2-4 on page 57 polynomially-bounded?
11* CLR Exercise C.2-9 on page 1106, explanation required probability

Dan Hirschberg
Computer Science Department
University of California, Irvine, CA 92697-3435
dan at ics.uci.edu
Last modified: Jun 18, 2008