happy story to start the year … would be robber no longer in business. buys the farm instead.
on 01/01/2014 at 10:27 AM
The Welsh for microwave is popty-ping.
Their introduction must have been by a popcorn salesman.Posted by harleycowboy58
01/01/2014 at 11:38 AM
I think the pancake thing is a recursive computational problem similar to the classic Towers of Hanoi: to solve the problem for 3 pancakes, solve it for 2 pancakes and then add 1 flip.
Point is, the “Big Omega” - the maximum number of iterations - for both these problems can be calculated, and the Little Omega “best case” can be visualized as well. So while there are a nearly INFINITE number of ways N=20 pancakes can be stacked on a plate (Ok, 20! to be exact), which PRECLUDES any exact numeric universal answer, a fairly accurate ranging estimate can be derived (less than X maximum number of flips, more than Y minimum number of flips [which will ALWAYS be 0, for the one permutation where the stack of N pancakes is already size sorted. But you need that minimum value, just to say that the task can’t be done with a negative number of flips. Because math is like that.])
Also the method of flipping sounds a lot like a sorting algorithm. For the largest pancake in the stack, 1 flip to bring it to the top of the stack, then another flip of the entire stack to bring it to the bottom. So for N=20 pancakes you’d have 2N flips, or 40. But this is only the rough cut at a Big O maximum. As you flip the big pancakes to the bottom, the tiny ones are going to work their way up the stack, so that by the time you get near the end, the odds of the remaining pancakes already being size sorted increases ... for the last 1 pancake it’s a guarantee, but probably this holds for the last 2,3, 4 pancakes. So a better tuned Big O answer is going to be Number of flips = 2n-2 (+0/-2), which means 20 pancakes can be flip sorted in no more than 38 flips, but perhaps no more than 36 flips, no matter how they’re piled up. This may not be the “best tuned” answer, but I’m confident I’ll be within 1 or 2 flips no matter how many pancakes you’ve got, and I’m confident you’ll NEVER need more flips than what I’ve deduced.
Yes, I did in fact go to college to learn shit like this. It was called Computer Science, and is now nearly worthless given the nearly infinite storage and nearly infinite computing power at anyone’s disposal for almost no money.
Well of course it is. We all knew that. But the problem of the gahatess which is unlike anything known to man but many women understand, remains unsolv-ed.
"gahatess”?? Goddess? Lost me there my friend.
