"cyclic artithmetic" is synonym for "modular arithmetic" (arithmetic over
Z/nZ fields, where n is a finite integer and the division is inversible,
unlike arithmetic on Z, Q, R or C with infinite bounds).
38 seconds on a Mac Pro is still lot of processing, and I'm sure you can
get a reply in a few milliseconds if you use the proper representation of
the problem: you'll end up decomposing integers into products of primes,
and this can dramatically reduce the number of tests to perform (on this
problem with 1027 data input, using basic brute force approache you end up
testing about 1 million possibilities and using lot of memory or two
embedded loops exploring the 1027*1027 possibilities to get a definite
response). This problem is very similar to breaking RSA with a 10-bit
public product key and looking for one of the two primes whose product
gives the 10 bit public key (note that RSA does not really uses primes
because they are too large to be tested, instead it uses two "most
probably" primes using a primarily test which is quite time intensive).
This problem exposes a part of the RSA difficulty (for breaking public
keys), based on the difficulty of decomposing very large integers into a
product of two integers. But within this problem the problem is more
limited because the product is still limited to 1027^2, so a brute force
attack still works (even if it's not efficient and can be made dramatically
faster by caching the decompositions in order to reduce the number of tests
to perform).
I've not programmed the way to do that, but some people may find an
efficient implemenhtation and new ideas to make this small problem much
faster, without requiring much memory (note that sorting in this problem is
not dramatically complex because you only sort rather small lists of about
one thousands item and we know we can do that quite efficiently in O(n log
n) time where n is about 1000, i.e. roughtly 10-bits only products; but for
actual modern use of RSA, working on 1024-bit products, this is not
possible in reasonnable time and with enough memory resources : this would
not even be possible if we could use use all existing computers on Earth,
because these huge numbers are many orders of magnitude above the total
number of atoms in our observable universe and could run them all at 10
Gigahertz.
This makes this problem very interesting in fact to explore in order to
find how we can optimie its resolution to get dramatically faster responses
(with less loops and modest memory usage to store and cache the
intermediate results).
The day 2 also explores such known computationally costly algorithms (here
it is a well known problem of regular expressions and the difficulty to
locate arbitrary long subtrings in a very large string (could be a entire
database), without having to reparse the whole with brute force exploring
M*N possibilities where M and N and the length of the substring and the
longer string to scan: as these problems will have their computation
difficulty growing each time, you won't be able to use basic tools like
Excel to sum a list, you'll need to program and think really about the
algorithms you use and the best data representation.
These problems are wellknown classes of algorithms where there's intensive
research, and most of them are based on arithmetic (and you need to know
many theorems on them): arithmetics on integers (or rationals) is one of
the most complex part of mathematics and whose results interest a lot the
whole computing industry, becaues these problems could reveal exploits that
could be harvested to break security or privacy, and can now have very
large impact on public freedoms and politics when all our economy now
depends so much on computers and automated decisions.
Okay, maybe I'm missing something. Since Lua is new to me and I started a
day late, I used C for the day one problem, to get the mechanics of the
website worked out. Like Philippe, I used Excel for the first star, but
then I saw the issue with that approach for the second star and switched to
C. I used a trivial list to store all "frequencies" as they occurred, and
the addFrequency() function returned an indication that the new value was
already there. My data stream was 959 items and the program required 38
seconds on a Macbook Pro. Since I don't even know what cyclic arithmetic
is, maybe I'm missing something really important, and bonus points to
anyone who'll enlighten me. For instance, are performance issues like
runtime and memory consumption counted?
Sadly, now I'm a) hooked and b) committed to the "different language every
day" idea. I'll try to do days 2 and 3 tomorrow.
interesting. The first star on day one is elementary to solve just with a
basic very Excel sheet, but the second star is much more difficult as it
involves cyclic aruthmetic (you can solve it by brute force but it rapidly
quite computing intensive as each test requires decomposing 1016 integers
into primes in order to test which position to look at (otherwise the
search loops are unbounded): you need some knowledge of cyclic arithmetic
to solve it with an efficient algorithm which is ensured to find a solution
in a bounded and in fact quite small time.
Your current test code in Haskell uses the brute force approach to repeat
searches in more and more repeated cycles, but even if you find a repeated
frequency with N cycles of the list, you could still find a lower frequency
located below in the input list. There's a more efficient solution by
sorting the frequencies produced by the first cycle. But then you need to
apply the algorithm to compute a lowest common multiplier and see if it's
divisible by a position in the sorted list. Finally you have to aplky a
second sort... Technically you can still do that within Excel by several
operations involding copying computed values from one column to another
(without their formula) and then apply a custom sort. over a group of
columns. All this could as well be done in Lua of course (instead of Excel,
you need Lua tables)
Post by PersonalThis is interesting. An interesting twist might be to use a different language each day.
--
Daryl Lee
Sent from my iPhone
Advent of Code [1] is a coding problem advent calendar: every day from
December 1 to December 25, they publish two code problems that can be
solved in any language.
Like last year, I am doing it in Lua (I may solve the problem in another
language as well some days, but I intend to do all of them in Lua at
least). I publish my solutions [2] on GitHub.
I am not interested in leaderboards (based on resolution time since
publication), first because for Europeans the only way to be competitive
would be to wake up very early or stay up very late, but also because I
only do this because it is somehow fun to me. Sometimes I may not have the
time to play at all on a given day and catch up later in the week.
Anyway, I thought it might interest some people on this list.
[1] https://adventofcode.com
[2] https://github.com/catwell/adventofcode/tree/master/2018
--
Pierre Chapuis
--
Daryl Lee
All our discontents about what we want appeared to
me to spring from the want of thankfulness for what we
have. -- Daniel Defoe