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Solve the recurrence: t(n) = t(n/2) + n + 2 (Solution included).

  1. Apr 25, 2012 #1

    s3a

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    1. The problem statement, all variables and given/known data
    The problem along with its solution is attached as Problem.jpg.

    2. Relevant equations
    Recurrence relation.

    3. The attempt at a solution
    I am confused as to what the solution is stating. I get up to and including (3) but I am stuck at (4). After (4), I get that k = log2(n) because n = 2^k = 2^(log2(n)) = n.

    I would greatly appreciate it if someone could help me get unstuck!
    Thanks in advance!
     

    Attached Files:

    Last edited: Apr 25, 2012
  2. jcsd
  3. Apr 25, 2012 #2
    You forgot to attach Problem.jpg.
     
  4. Apr 25, 2012 #3

    s3a

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    Lol. Thanks for telling me.
     
  5. Apr 26, 2012 #4

    NascentOxygen

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    Staff: Mentor

    Seems there is a "+" sign missing in (4). koZTB.gif

    It should be t(n/2k) + n + n/2 + ....

    Then in going from (5) to (6), make use of the fact that
    n/2k-1 ≡ n/(2k/2)
       ≡ 2n/2k, but k=log2n
       ≡ 2n/n
       ≡ 2 
     
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