Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

The number of operations executed by algorithms Aand B is 8nlogn and 2n 2 ,
respectively. Determine n 0 such that A is better than B for n ≥ n 0 .
R-4.7
The number of operations executed by algorithms A and B is 40n 2 and 2n 3 ,
respectively. Determine n 0 such that A is better than B for n ≥ n 0 .
R-4.8
Give an example of a function that is plotted the same on a log-log scale as it is
on a standard scale.
R-4.9
Explain why the plot of the function n c is a straight line with slope c on a loglog
scale.
R-4.10
What is the sum of all the even numbers from 0 to 2n, for any positive integer
n?
R-4.11
Show that the following two statements are equivalent:
(a)
The running time of algorithm A is O(f(n)).
(b)
R-4.12
In the worst case, the running time of algorithm A is O(f(n)).
Order the following functions by asymptotic growth rate.
R-4.13
4n log n + 2n 2 10 2 logn
3n+100 log n 4n 2 n
n 2 + 10n n 3 n log n
Show that if d(n) is O(f(n)), then ad(n) is O(f(n)), for any constant a>0.
249