yes power towers are allowed exponentiation, multiplication, division, addition and subtraction. Brackets when necessary but length is sorted on number of digits not number of operators plus digits.
I always try my homework myself first. in 38 years of life I've learned only to do what i want, if I wanted everyone else to do my work for me I'd be a management consultant ! On Fri, Feb 20, 2009 at 3:52 PM, Luke Dunn <luke.d...@gmail.com> wrote: > I am teaching myself coding. No university or school, so i guess its > homework if you like. i am interested in algorithms generally, after doing > some of Project Euler. Of course my own learning process is best served by > just getting on with it but sometimes you will do that while other times you > might just choose to ask for help. if no one suggests then i will probably > shelve it and come back to it myself when I'm fresh. > > no it's not a real world problem but my grounding is in math so i like pure > stuff anyway. don't see how that is a problem, as a math person i accept the > validity of pure research conducted just for curiosity and aesthetic > satisfaction. it often finds an application later anyway > > Thanks for your helpful suggestion of trying other methods and i will do > that in time. my motive was to share an interesting problem because a human > of moderate math education can sit down with this and find minimal solutions > easily but the intuition they use is quite subtle, hence the idea of > converting the human heuristic into an algorithm became of interest, and > particularly a recursive one. i find that the development of a piece of > recursion usually comes as an 'aha', and since i hadn't had such a moment, i > thought i'd turn the problem loose on the public. also i found no online > reference to this problem so it seemed ripe for sharing. > > On Fri, Feb 20, 2009 at 3:39 PM, Nigel Rantor <wig...@wiggly.org> wrote: > >> Trip Technician wrote: >> >>> anyone interested in looking at the following problem. >>> >> >> if you can give me a good reason why this is not homework I'd love to hear >> it...I just don't see how this is a real problem. >> >> we are trying to express numbers as minimal expressions using only the >>> digits one two and three, with conventional arithmetic. so for >>> instance >>> >>> 33 = 2^(3+2)+1 = 3^3+(3*2) >>> >>> are both minimal, using 4 digits but >>> >>> 33 = ((3+2)*2+1)*3 >>> >>> using 5 is not. >>> >>> I have tried coding a function to return the minimal representation >>> for any integer, but haven't cracked it so far. The naive first >>> attempt is to generate lots of random strings, eval() them and sort by >>> size and value. this is inelegant and slow. >>> >> >> Wow. Okay, what other ways have you tried so far? Or are you beating your >> head against the "search the entire problem space" solution still? >> >> This problem smells a lot like factorisation, so I would think of it in >> terms of wanting to reduce the target number using as few operations as >> possible. >> >> If you allow exponentiation that's going to be your biggest hitter so you >> know that the best you can do using 2 digits is n^n where n is the largest >> digit you allow yourself. >> >> Are you going to allow things like n^n^n or not? >> >> n >> >> >> >
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