Substitution method to prove recursion running time

Question

I am working on these three recursion funtion to prove a big-O. I tried to use substitution method. But, I have no clue to guess a proper upper bound.

(a) T(n) = T(n − 2q − 1) + T(3q/2) + T(q/2) + Θ(1) (b) T(n) = T(n − q − 1) + T(n/2 − q) + Θ(n) (c) T(n) = T(n − q − 1) + T(3q) + Θ(n)

where q is constant from 0 to n/4.

Can some one give me some suggestion?

How can a constant (`q`) be bound to `n`? – Leon Oct 14 '16 at 06:07 — Leon, Oct 14 '16 at 06:07

score 0 · Answer 1 · edited Jun 20 '20 at 09:12

0

T(n) = (a)+(b)-(c)

T(n) = T(n-2q-1) + T(3q/2) + T(q/2) + Θ(1) + T(n/2-q) - T(3q)

T(n) = T(n-2q-1) + T(n/2-q) + T(3q/2) + T(q/2) - T(3q) + Θ(1)

at this point i would try to build recursion tree and see how it behaves.

edited Jun 20 '20 at 09:12

Community

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answered Oct 14 '16 at 09:01

yd1

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actually there are three qurstions. They are not together. – Running.Pig Oct 14 '16 at 18:01
maybe you should build a recursion tree and see a pattern in the increasing levels. – yd1 Oct 15 '16 at 06:24

Substitution method to prove recursion running time

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