Assignment two appears to be progressing nicely.
Question#1
The OMCOFS recursive definition ended up being easy to find....once I realised that for string length 5 there is 8, not 7 possibilities (11011 alluded me for a stressful 10min ). Completing the question after that was not exceedingly difficult.
Question#2
Showing the intuitive non-decreasing property was easy. Showing that T(n) is of order log(n) is slightly more difficult for me because I forget how to show Big Theta. Currently I am waiting for the prof to post his most recent lecture notes and I'm sure it will shed a bit more light on the situation or if worse comes to worse I'll have to revisit the the dark, dark abyss; my notes from 165.
On an unrelated note I have noticed that where ever I walk there seem to be stray dogs, so I hypothesised that stray dogs must have at least 3 noses so they can better tell my position and walk near me. And believe it or not I was able to prove it:
Proof. No dog has 2 noses. Since one dog has one more nose than no dog, it must have three noses.
Carl
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