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1 . By definition, show that 1 k + 2 k + + nk is O ( nk + 1 ) , where k is
By definition,
show that k k nk is Onk where k is a positive integer. points
Order the following functions into a list such that if f n comes before gn in the list then
f n Ogn If any two or more of the same asymptotic order, indicate which. Start with these
basic functions points
nn n lg n n lg n n nn n lg n
Find the solution for each of the following recurrences, and then give tight bounds for Tn
points
with T
with T where c is some constant
with T
Use the master theorem to give tight asymptotic bounds for the following recurrences. points
a
n
b
c
dT
c
e
Bonus points
f
n Bonus points
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