CS 2605 Homework 6 Summer I 2007
Last modified: 6/22/2007 11:06:52 AM 1
You will submit your solution to this assignment to the Curator System (as HW6). Your solution must be either a plain text file
or a MS Word document.
1. [20 points] Using the rules given in the course notes, perform an exact count complexity analysis of the body of the
following function. (Your answer should be a function of the parameter N.)
void Mystery(int M[N][N], const int N) {
for (int R = 0; R < N; R++) {
for (int C = 1; C < N; C++) {
if (M[R][C-1] < M[R][C])
M[R][C-1] = M[R][C];
else {
M[R][C] = M[R][C-1];
M[R][C-1] = 0;
}
}
}
}
Note: array index operations count 1 time unit each.
2. [10 points] For each of the following inequalities, what is the smallest value of N such that the inequality holds for all n
>= N?
(a) nn log101.0 ≥
(b) nnnn log20
2
12≤−
3. [25 points] Divide the following functions into non-overlapping categories (Θ equivalence classes), so that two
functions, say f(n) and g(n), are in the same category if and only if f(n) is Θ(g(n)). Arrange the categories from the
lowest order of magnitude to the highest. A function may be in a category by itself, or there may be several functions in
the same category.
5000 (log n)5 3
n
log n n + log n n3
n2 log n n2 – 100n 4n + n1/2
log log n2 n0.3 n
2
log n2 (n2 + 4)1/2 2
n
4. [10 points] Using any theorems from the course notes, give a formal proof that:
()
(
)
)( is log5 2
nnnnn Θ++−
