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Topic: HARD: Help with math problems involving algorithms
Replies: 2   Last Post: Feb 18, 1999 9:55 PM

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Albert Y.C. Lai

Posts: 28
Registered: 12/6/04
Re: HARD: Help with math problems involving algorithms
Posted: Feb 18, 1999 9:55 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply writes:

> 3) Use mathematical induction to show that the solution of the recurrence
> T(n) = {2 if n = 2
> {2(n/2) + n if n = 2^k, k>1
> is T(n) = n lg n (where I belive lg n is base 2) for all values of n
> that are exact powers of 2.

Exact powers of 2 have the form 2^k for some non-negative integer k.
So it suffices to show T(2^k) = (2^k) * lg (2^k) for all non-negative
integers k. Now you can apply induction on k.

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