Summer 2008 CMSC 351: Homework 4 Clyde Kruskal
Due at the start of class Wednesday, June 18, 2008.
Problem 1. Consider the following recurrence, defined for na power of 5:
T(n) = (19 if n= 1
3T(n/5) + n−4 otherwise
(a) Solve the recurrence exactly using the iteration method. Simplify as much as
possible.
(b) Use mathematical induction to verify your solution.
Problem 2. Use the formulas derived in class to obtain exact solutions to the following
two recurrences.
(a) Let nbe a power of 2.
T(n) = (4 if n= 1
5T(n/2) + 3n2otherwise
(b) Let nbe a power of 4.
T(n) = (3 if n= 1
2T(n/4) + 4n+ 1 otherwise
Problem 3. Consider the following recurrence.
T(n) = (0 if n= 0
T(⌊n/2⌋) + T(⌊n/4⌋) + 3notherwise
Use constructive induction to find a constant csuch that T(n)≤cn.
Problem 4. Do Problem 4-2 on page 85 of CLRS.