Luke Dunn wrote:
yes power towers are allowed
right, okay, without coding it here's my thought.
factorise the numbers you have but only allowing primes that exist in
your digit set.
then take that factorisation and turn any repeated runs of digits
multiplied by themselves into power-towers
any remainder can then be created in other ways, starting with a way
other than exponentiation that is able to create the largest number,
i.e. multiplication, then addition...
I've not got time to put it into code right now but it shouldn't be too
hard...
e.g.
digits : 3, 2, 1
n : 10
10 = 2*5 - but we don't have 5...
10 = 3*3 + 1
10 = 3^2+1
3 digits
n : 27
27 = 3*3*3
27 = 3^3
2 digits
n : 33
33 = 3*3*3 + 6
33 = 3*3*3 + 3*2
33 = 3^3+3*2
4 digits
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
<mailto: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
<mailto: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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