1) Suppose that you have an algorithm that required 10 seconds to run on a problem size of 1000. How long would you expect the algorithm to run on a problem size of 10,000?

2) Determine the theta notation for the following algorithm:

i := 1

while (i < n) do

for j := 1 to n do

some code that takes time

end for j

i := i * 2

end while

3) Determine the theta notation for the following algorithm:

i := n

while i > 0 do

j := 1

while j < i do

some code that takes time

j := j * 2

end while

i := i / 2

end while

4) Determine the theta notation for the following algorithm:

i := n

while (i >= 1) do

for j := 1 to i do

for k := 1 to n do

some code that takes time

end for k

end for j

i := i / 2

end while

5) Determine the theta notation for the following algorithm:

for i := 1 to n do

for j := 1 to i do

for k := j to (i + j) do

some code that takes time

end for k

end for j

end for i

6) Determine the theta notation for the following algorithm:

i := n

while i > 0 do

for k = 1 to n do

j := 1

while j < i do

some code that takes time

j := j * 2

end while

end for

i := i / 2

end while