10736 - Series of PI

Observer · Post by **Observer** » Wed Oct 20, 2004 6:20 pm

I'm trying something with logarithms. I can get the sample i/o right, but still WA. Could anyone please tell me the correct output for the following test cases?

1
2
3
4
5
6
7
8
9
10
132641
245630
270863
284590
341722
346863
400320
416796
440342
468855
509756
563455
599997
599998
599999
600000
-2

Thanks in advance.

( Or is my idea totally wrong?

)

david · Post by **david** » Wed Oct 20, 2004 10:39 pm

My program outputs

2
3
4
5
7
8
10
11
13
14
220299
407969
449880
472680
567574
576113
664903
692269
731378
778737
846672
935864
996559
996561
996562
996564

(and yes, the key idea is to take logarithms)

Observer · Post by **Observer** » Thu Oct 21, 2004 2:22 am

Thanks a lot! AC now.

P.S. I've made a really silly mistake in my old code......

Sedefcho · Post by **Sedefcho** » Thu Aug 04, 2005 2:06 pm

The pictures are not visible on the main page of that problem.
I mean they are not visible on
http://acm.uva.es/p/v107/10736.html

Where can we find the pictures which are part of the
problem statement of problem 10736 ?

Cho · Post by **Cho** » Thu Aug 04, 2005 2:39 pm

or view the pdf file

Sedefcho · Post by **Sedefcho** » Thu Aug 04, 2005 3:34 pm

Tnanks, Cho!

I forgot there's always a PDF file

Stupid, I know. Anyway, I got ACC already.

It is really strange that the pictures are not
visible because they are present on the site
and also seems to me the links to them in the file in 10736.html
are also OK. Check these URLs:
http://acm.uva.es/p/v107/p10736a.gif
http://acm.uva.es/p/v107/p10736b.gif
http://acm.uva.es/p/v107/p10736c.gif
http://acm.uva.es/p/v107/p10736d.gif

One more important thing - my ACC program outputs
for N = 7 the answer 9 and not 10
as the ACC program from david ?!
All other answers of my program are same as his answers
( I mean if we use the input from Observer ).

That's just a notice to the future readers of david's sample output
for the input which Observer has posted.

And one last thing - here is another view to the series we
are dealing with. I think it makes it obvious what the formula for
the N-th term is. See below:

Good luck to everyone.

david · Post by **david** » Tue Sep 27, 2005 8:43 pm

Sedefcho wrote: One more important thing - my ACC program outputs
for N = 7 the answer 9 and not 10
as the ACC program from david ?!
All other answers of my program are same as his answers
( I mean if we use the input from Observer ).

The 10th term of the taylor expansion for arcsin(x) is 12155/1245184*x^19,
and the 11th one is 46189/5505024*x^21,
You can check that the 10th term of the final series is about 6435/557056*(1/2)^17 * 6 = 1.117e-7 > 1e-7, so the answer can't be 9.
The 11th term is the first one to become less than 1e-7, so I guess you're lucky your program passed the test data.