1 / 10

CSE 321 Discrete Structures

CSE 321 Discrete Structures. Winter 2008 Lecture 12 Induction. Announcements. Readings Monday, Wednesday Induction and recursion 4.1-4.3 (5 th Edition: 3.3-3.4) Midterm: Friday, February 8 In class, closed book Estimated grading weight: MT 12.5%, HW 50%, Final 37.5%.

talmai
Télécharger la présentation

CSE 321 Discrete Structures

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CSE 321 Discrete Structures Winter 2008 Lecture 12 Induction

  2. Announcements • Readings • Monday, Wednesday • Induction and recursion • 4.1-4.3 (5th Edition: 3.3-3.4) • Midterm: • Friday, February 8 • In class, closed book • Estimated grading weight: • MT 12.5%, HW 50%, Final 37.5%

  3. Highlights from Lecture 11 • Public Key Cryptography ALICE BOB

  4. Induction Example • Prove 3 | 22n -1 for n  0 Examples to show its true P(0) P(k)  P(k+1)

  5. Induction as a rule of Inference P(0)  k (P(k)  P(k+1))  n P(n) Formal steps Show P(0) Assume P(k), Prove P(k+1), Conclude P(k) P(k+1) Conclude  k (P(k) P(k+1)) Conclude  n P(n)

  6. 1 + 2 + 4 + … + 2n = 2n+1 - 1

  7. Harmonic Numbers

  8. Cute Application: Checkerboard Tiling with Trinominos Prove that a 2k 2k checkerboard with one square removed can be tiled with:

  9. Strong Induction P(0)  k ((P(0)  P(1)  P(2)  …  P(k))  P(k+1))  n P(n)

  10. Player 1 wins n  2 Chomp! Winning strategy: chose the lower corner square Theorem: Player 2 loses when faced with an n  2 board missing the lower corner square

More Related