Am I doing this correctly? Recurrence Relations

Asked Sep 30 '14 at 23:03

Active Sep 30 '14 at 23:03

Viewed 31 times

The function is this:

function max-element
if n = 1
    return A[1]
else
    x = max-element(A[2...n])
    if A[1] > x
        return A[1]
    else
        return x

So to create to recurrence relation i've done this, which i'm unsure of...

T(1) = 2, because the function will only execute the first if and return if n=1

T(n) = T(n-1) + c, and c = 5 when n>1

T(n-1) = T(n-2) + c

T(n-2) = T(n-3) + c

generalized, T(n) = T(n-k) + 5k ... this is where I think i'm going off?

And in the worst-case, k=n-1..... T(n)=T(1)+5n-5=5n-3

Then T(n) = Theta(n).

Any help?

asked Sep 30 '14 at 23:03

Connal Sumlin

2

What is the question here? You should be able to tell yourself whether your own argument works or not. In this case, it does work. – Yuval Filmus Sep 30 '14 at 23:04
My question is if I am going about this correctly. I am trying to learn the concept through other examples, but I can't figure it out. At which point am I incorrect? – Connal Sumlin Sep 30 '14 at 23:24
I never said you're incorrect. – Yuval Filmus Sep 30 '14 at 23:26
Oh, I apologize, I misread your comment as "it does not work". – Connal Sumlin Sep 30 '14 at 23:28
See our reference questions, e.g., http://cs.stackexchange.com/q/2789/755 and http://cs.stackexchange.com/q/192/755 and http://cs.stackexchange.com/q/23593/755. – D.W. Oct 01 '14 at 01:08

0 Answers0