1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Constructive Induction

  1. Apr 22, 2008 #1
    Can someone explain this "constructive induction" needed to solve recursive equations?

    For example, use "constructive induction" to show that the following is [tex]\Theta (n)[/tex]

    [tex]T(n) = 1 \leftrightarrow n = 1,2[/tex]
    [tex]T(n) = T\lceil n/4\rceil + T \lceil 2n/3\rceil + \Theta (n) \leftrightarrow n > 2[/tex]
     
    Last edited: Apr 22, 2008
  2. jcsd
  3. Apr 22, 2008 #2
    Anyone? This is kinda urgent.
     
  4. Apr 23, 2008 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Since you haven't said what [itex]\Theta(n)[/itex] is, I don't see how any method can "prove" that is [itex]\Theta(n)[/itex].

    Whatever [itex]\Theta(n)[/itex] is, T(3) is definitely not equal to [itex]\Theta(3)[/itex], it is equal to [itex]\Theta(3)+ 2[/itex].
     
  5. Apr 23, 2008 #4
    [tex]\Theta (n)[/tex] in the recurrence is "some function" in the complexity class [tex]\Theta (n)[/tex].

    The complexity class [tex]\Theta (n)[/tex] is the intersection of [tex]O(n)[/tex] and [tex]\Omega (n)[/tex].
     
    Last edited: Apr 23, 2008
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Constructive Induction
  1. Constructing a triangle (Replies: 13)

  2. Constructing a function (Replies: 13)

  3. The construction of pi (Replies: 6)

Loading...