UMBC CMSC441, Design & Analysis of Algorithms, Fall 2014
Homework 2
Due Thursday, September 11, 2014
 For each pair of functions below, use O( ),
Ω( ), Θ( ), o( ) or ω( ) to describe the
relationship between the two functions. E.g., say "n^{2}
+ 3n is O(n^{2})". Make the most accurate
statement. E.g.,
"n^{2} is o(n^{3})"
is more accurate than
"n^{2} is O(n^{3})".
Briefly justify your answers.

n^{3}
versus
2n^{3} + 5n^{2}

2^{n}
versus
3^{n}

n^{2} log n
versus
n^{3}

n^{log n}
versus
( log n ) ^{n}
 Consider the recurrence relation:
T(n) = 6 T(n/3) + 3 n
Use the substitution method to show that:

T(n) ≤ n^{2}

T(n) ≥ n^{1.5}
Show all of your work.
 Use the recursion tree method to find an upper bound for
T(n) = 7 T(n/2) + n^{2}
Show all of your work.
Last Modified:
3 Sep 2014 13:16:09 EDT
by
Richard Chang
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