solutions to big oh questions in exam papers

Hi here are some solutions for the 2004/2005 big oh questions

2004 question 1b)

algorithm A - O(n) as n increases by 10 the running time also increases by 10.

algorithm B - O(n2) (that's n squared) as n increases by 10 the running time increases by 10 squared (ie 100).

algorithm C - O(log n)(thats log to the base 10) the running time increases slowly. Running time T = 10 log n - 10.

When you see that the running time is increasing slowly it is most likely a log function.

2005 question 1a)

Algorithm A O(n) see A above

Algorithm B O(n log n) (thats log to the base 10) Running time T = 2n log n.

If you look at this algorithm you will notice that it is not quite O(n) nor is O(n squared). It is someting in between hence it most likey O(n log n). From this you can determine that T=2n log n.

regards
Lazarus

I spent a good hour on the 2004 Big O questions and I wasnt quite sure of my answers. Turns out I had algorithm B completely wrong, thanks for helping out!

Hi,

I have recently moved and have not received any post from UNISA lately. Can anyone please send me exam papers to esckays@gmail.com

Did we receive any answer to the exam papers ? If not, does anyone have any suggested solutions.

Please help ....

Thanks,
Esckays

Hi there

Any one knows the solution to Algo C in the 2005 paper?

My answers for 2005

algorithm A
When n=100 2ms per n
When n=1000 2ms per n
When n=10000 2ms per n
so O=(n)

algorithm B
n=100 4ms per n
n=1000 6ms per n
n=10000 8ms per n
time grows more than n but less than n2 (square)
so O=(n*log2n)

algorithm C
always takes 54ms so O=(1) {it never changes regardless of the size of n}

b) i) O=(n2) (square)
b) ii) O=(n) {n+n}

Ok great! That makes sense!!

Thank you & good luck for 2morrow...

for algorithm B, O=2nlogn.
for n=1000 := 2*1000*3 = 6000
for n=10000:= 2*10000*4 = 80000

for algorithm B, O=2nlogn.
for n=1000 := 2*1000*3 = 6000
for n=10000:= 2*10000*4 = 80000

Yes, but Big-O will still be nlogn. Constants can be ignored, so O(n*logn) is my bet.