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John VanSickle wrote:
> Tim Attwood wrote:
>> I'm mostly stalled at 43%, I've seen several
>> problems that are easy enough to express
>> solutions to that are none-the-less difficult
>> to compute in any reasonable amount of time.
>
> Some of the questions state an iterative problem for which there is a
> direct solution.
>
> For instance, the second problem looks iterative, but there is a direct
> formula for any member of the Fibonacci series, there is a direct
> formula for the sum of a power series, and the even-valued members of
> the Fibonacci series occur at every third position starting with 0. When
> you put that together, the sum is
>
> (1/sqrt(5) * ( (phi^(n+3)-1)/(phi-1) - ((1-phi)^(n+3)-1)/(1-phi-1) )
It turns out that this formula is wrong. The correct formula is:
1/sqrt(5) *
( (phi^(n+3)-1)/(phi^3-1) - ((1-phi)^(n+3)-1)/((1-phi)^3-1) )
Regards,
John
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nemesis wrote:
> "Tim Attwood" <tim### [at] comcast net> wrote:
>> According to the statistics page on Project Euler there's about
>> three times as many people using C/C++ as Haskell, and about
>> twice as many using Python as Haskell.
>
> OTOH, most C++ solutions I've seen in the forum are the trivial, straightforward
> loopy and slow performant solutions, using pretty much the same obvious
> algorithm. Many Haskell solutions came up with amazingly concise and creative
> algorithms.
I admit that for the C++ solutions I've been resorting to brute force,
but for these problems I'm not aware of any solution that avoids the
brute force approach. For instance, in the problem for summing the
prime numbers less than one million, I'm not aware of any theorem which
calculates such a sum for any range without testing each odd number for
primality and then adding the primes.
It could be that the C++ coders either aren't aware of the
computationally less-expensive solutions, or they simply assume that the
relative efficiency of C++ (save counter-arguments for another thread,
please) enables them to not worry about computational efficiency.
Regards,
John
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John VanSickle <evi### [at] hotmailcom> wrote:
> For instance, in the problem for summing the
> prime numbers less than one million, I'm not aware of any theorem which
> calculates such a sum for any range without testing each odd number for
> primality and then adding the primes.
http://en.wikipedia.org/wiki/Prime-counting_function
--
- Warp
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Warp wrote:
> John VanSickle <evi### [at] hotmailcom> wrote:
>> For instance, in the problem for summing the
>> prime numbers less than one million, I'm not aware of any theorem which
>> calculates such a sum for any range without testing each odd number for
>> primality and then adding the primes.
>
> http://en.wikipedia.org/wiki/Prime-counting_function
I didn't read all of it, but it's not obvious how helpful that would
be...other than getting an idea of the number of primes under a million.
When you get that many then you can stop (assuming the estimate is good
enough).
I'm not aware of any better way to do this than to simply get all the
primes under a million and add them up. The only variation is how one
obtains all the primes. You could use a Sieve method, or do what many
people did: Test each odd number by dividing it by all possible primes
less than sqrt(number). For all the prime problems, I was using a sieve,
but apparently for a lot of problems (all so far?), simply testing by
dividing appears to be faster. I think the sieve wins out once you the
numbers get large enough, though.
--
Diplomacy - the art of letting someone have your way.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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Orchid XP v7 wrote:
> (E.g., problem 1, I wrote something that loops over the numbers 1 to 100
> finding those that fit the divisibility requirements and summing them.
> Somebody else managed to produce a closed-form *formula* for the answer.
> Beat that!)
Not particularly hard. You have a formula for the sum of all integers
from 1 to 100. And one for the sum of all multiples of 3 till 100. Ditto
for multiples of 5. Now just subtract the sum of all multiples of 15.
> The few Haskell solutions I've seen look unecessarily wordy - like they
> were written by somebody just learning Haskell. But then, the Haskell
> Wiki has a section devoted to Project Euler, and most solutions there
> look rather childish and unperformant too, so...
I do stuff in Python. Even though some manage to solve whole problems
with one line solutions, it is generally frowned upon in the Python
community if it gets challenging to read: They generally perform about
the same as more readable code.
So perhaps those Haskell users were converts from Python...
--
Diplomacy - the art of letting someone have your way.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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John VanSickle wrote:
> I admit that for the C++ solutions I've been resorting to brute force,
> but for these problems I'm not aware of any solution that avoids the
> brute force approach. For instance, in the problem for summing the
> prime numbers less than one million, I'm not aware of any theorem which
> calculates such a sum for any range without testing each odd number for
> primality and then adding the primes.
I've done brute force for a bunch, but at times I try to find
shortcuts. Sometimes the resulting program is even slower, but I suspect
it'll scale better.
Also, while a brute force solution in C/C++ may run in under a minute,
it occasionally will not in Python. So I'm forced to think of ways to
speed it up. I frequently find a "better" solution than mine in the
forums, though.
--
Diplomacy - the art of letting someone have your way.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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Mueen Nawaz <m.n### [at] ieeeorg> wrote:
> Warp wrote:
> > John VanSickle <evi### [at] hotmailcom> wrote:
> >> For instance, in the problem for summing the
> >> prime numbers less than one million, I'm not aware of any theorem which
> >> calculates such a sum for any range without testing each odd number for
> >> primality and then adding the primes.
> >
> > http://en.wikipedia.org/wiki/Prime-counting_function
> I didn't read all of it, but it's not obvious how helpful that would
> be...
I didn't mean for it to be an answer to the problem but as an interesting
thing to read about the subject.
--
- Warp
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Mueen Nawaz wrote:
> John VanSickle wrote:
>> I admit that for the C++ solutions I've been resorting to brute force,
>> but for these problems I'm not aware of any solution that avoids the
>> brute force approach. For instance, in the problem for summing the
>> prime numbers less than one million, I'm not aware of any theorem which
>> calculates such a sum for any range without testing each odd number for
>> primality and then adding the primes.
>
> I've done brute force for a bunch, but at times I try to find
> shortcuts. Sometimes the resulting program is even slower, but I suspect
> it'll scale better.
>
> Also, while a brute force solution in C/C++ may run in under a minute,
> it occasionally will not in Python. So I'm forced to think of ways to
> speed it up. I frequently find a "better" solution than mine in the
> forums, though.
It's interesting how many elaborate problems requiring multiple nested
loops and filtering take only about 10 instructions in assembly... (!)
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Currently for each problem, you either get the answer right or you get
it wrong. I think it would be nice if you could check intermediate parts
of the calculation. (E.g., is 103 a prime number? Is 187 an abundant
number? etc.)
On the other hand, I suppose they don't want to give too much data away,
otherwise you could just "solve" the problem by asking the Project Euler
website a sufficient number of questions. ;-)
Currently it seems the "ratings" are simply based on what fraction of
the problems you've solved. I think it would be nice if I get a bigger
score for solving problems that few other people have solved.
I'd kinda like to make my own website like Project Euler. However, I had
a look, and to get hosting that gives you server-side scripting and a
database is 5x the price of what I'm currently paying. :-S I can't
really afford that kind of money...
I suppose the alternative is to set up a Linux box in my house and host
a website from there [again]. But it's rather annoying when you're
playing a clan match and suddenly somebody hits your website and you
can't play properly any more. :-S
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Invisible wrote:
> Currently for each problem, you either get the answer right or you get
> it wrong. I think it would be nice if you could check intermediate parts
> of the calculation. (E.g., is 103 a prime number? Is 187 an abundant
> number? etc.)
Well, for all but one of the problems I've worked on, the definitions
in the problem statements are fairly unambiguous.
Besides, for things like those, you can use Google to get a list of
primes, abundant numbers, etc. But be "careful", sometimes a good Google
search will get you the very answer to the question being asked.
> On the other hand, I suppose they don't want to give too much data away,
> otherwise you could just "solve" the problem by asking the Project Euler
> website a sufficient number of questions. ;-)
True - almost. If you submit too many answers in a short period of
time, the Web site blocks you for a while.
> I'd kinda like to make my own website like Project Euler. However, I had
> a look, and to get hosting that gives you server-side scripting and a
> database is 5x the price of what I'm currently paying. :-S I can't
> really afford that kind of money...
The weakened Dollar may help you there.<G>
What price are you talking about. You definitely can get it for under
$10/mo, and if your needs aren't too stringent, probably $5/mo is not
hard to find.
The tricky part is making the problems interesting enough for people to
come. A number of problems on the Project Euler site *may* lead you into
some interesting number theory topics...
--
I considered atheism but there weren't enough holidays.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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