CS 561: Fall 2004, Homework Assignment #1
Due Thursday, September 9, 2004
Problem 1.
Solve the following recurrences by unrolling the recurrence (or listing
the first few values), guessing the solution, and proving it correct.
f(n) = 3f(n-1) + 1, f(0) = 0
f(n) = 2f(n/4) + 1, f(0) = 0
Problem 2.
Solve the following recurrences in asymptotic terms (initial conditions
are not given, as they do not influence asymptotic behavior for algorithms).
Show your work.
f(n) = 5f(n-1) - 6f(n-2)
f(n) = 2f(n-1) - f(n-2)
f(n) = 3f(n-1) - 3f(n-2) + f(n-3)
Problem 3.
Show how to transform the following recurrences into finite-order
recurrences and solve them in asymptotic terms.
f(n) = 3f(n/3) + n2
f(n) = 2f(n/2) - f(n/4) + (logn)2
These recurrences have both a homogeneous and a inhomogeneous part,
so solve them separately, then decide which dominates the behavior.