Today:
- Announcements
- Sorry -- 2.4 homework isn't graded yet.
- Nonetheless, 2.5 is due (although as I said, you can get it to me
by next Tuesday -- but then you may not have it back in time for the test).
- Oh yeah, there's a test coming up! It will cover everything up to
2.5.
- Most recent notes are below.
- Last time we finished section
2.6: Analysis of Algorithms
- Fibonacci operations:
- Switching up a problem: converting it to something that
you can solve, and then converting the solution back.
- Using a method you've already solved on other problems
(e.g. using logs to transform the non-linear recurrence
relation with base cases $A(0)=1$, $A(1)=2$, and
\[
A(n)=A(n-1)*A(n-2)
\]
into a linear, constant coefficent, homogeneous, second-order
recurrence relation (Fibonacci-like). In fact, we can show that
$A(n)=2^{F(n)}$!
- Binary search (after a mergesort)
- Euclidean Algorithm (gcd)
- Deriving Euclid's method as a non-linear recurrence relation
- Using a linear recurrence relation to tell us about the
worst case behavior of a non-linear recurrence
relation.
- It turned out that consecutive Fibonacci numbers is the
worst case scenario for the Euclidean algorithm.
- Today we'll start section
3.1: Sets
- Links:
Website maintained by Andy Long.
Comments appreciated.