CS 1050 B: Construction Proofs February 21, 2008
Homework 4
Lecturer: Sasha Boldyreva Due: February 28, 2008
Assignment 3.01 Do the assigned reading.
Assignment 3.02 Indicate how much time did you spend on this homework.
In all problems do not just give an answer, but explain your reasoning.
Problem 4.1, 5 points. Problem 16 from Section 3.2 of Rosen’s textbook.
Problem 4.2, 5 points. Problem 18 from Section 3.2 of Rosen’s textbook.
Problem 4.3, 15 points. Problem 24 from Section 3.2 of Rosen’s textbook.
Problem 4.4, 6 points. Problem 32 from Section 3.2 of Rosen’s textbook.
Problem 4.5, 10 points. Prove that if f(n) = O(g(n)) and h(n) = O(g(n)), then
f(n) + h(n) = O(g(n)).
Problem 4.6, 5 points. Problem 24 from Section 3.3 of Rosen’s textbook.
Problem 4.7, 5 points. Give an example of a function f(n) which is O(1). Write any
algorithm that takes input of size nand has O(1) running time. Describe in words what
does you algorithm do, and what do you consider to be a basic operation.