Re: [algogeeks] Re: Number Theory (Power of 3 )

2011-12-10 Thread tech coder
u people absolutely correct that log operation take much time , i just
given an approach

On Sat, Dec 10, 2011 at 7:25 AM, Dave dave_and_da...@juno.com wrote:

 @Gaurav: Even though this is O(log n), it is bound to be slow, since
 it would use division and modulus are among the slowest operations on
 modern computers, some of which don't even have an integer division
 instruction. Here is a revision to my earlier code, for 32-bit
 integers. It should be faster since it contains no loops.

 bool PowerOfThree(unsigned int n)
 {
int powsof3[32] =
 {1,3,0,9,27,0,81,243,0,729,0,2187,6561,0,19683,59049,0,
  177147,0,531441,1594­
 323,0,4782969,14348907,0,43046721,

 129140163,0,387420489,0,1162261467,3486784401};
int i = if( n  16 ) ? 16 : 0;
if( n  (i+8) ) i += 8;
if( n  (i+4) ) i += 4;
if( n  (i+2) ) i += 2;
if( n = (i+1) ) i += 1;
return powsof3[i] == n;
 }

 As in the previous algorithm, the first few statements use a binary
 search to find the bit number of the highest order bit set. There can
 be at most one power of three corresponding to each high-order-bit
 number, so we then check to see if the input number is the only
 possible power of three in the table of powers of 3 that is indexed by
 the high-order-bit number.  The zeros in powsof3[] correspond to high-
 order-bit numbers that have no power of three.

 Dave

 On Dec 9, 2:35 am, Gaurav Kumar gkuma...@gmail.com wrote:
  What if we create a base 3 number from the given number N and then check
 if there is only 1 bit with value 1 and all values should be 0. For
 example, if lets say the number is 27. Its base 3 number will be 1 0 0 0,
 now since there is only 1 single 1 present in this representation, it is a
 power of 3.
 
  Gaurav
 
  On Dec 7, 2011, at 6:03 PM, saurabh singh wrote:
 
 
 
   Originaly problem rules out the use of log.Moreover log (or any
 floating point operations) take lot of hardware time as they are emulated
 on the floating point environment on most machines.Thirdly precision
 problem for higher values of n may cause your solution to give wron g
 answers,,,
 
   On Wed, Dec 7, 2011 at 11:54 PM, tech coder techcoderonw...@gmail.com
 wrote:
   what about this   log(base 3 n)  is of  integral type then n is a
 power of 3
 
   On Mon, Dec 5, 2011 at 11:36 PM, Dave dave_and_da...@juno.com wrote:
   @Carl: You can generate the constants the first time the procedure is
   called. There is no need to do them every time. So the first call
   would be O(wordsize) but subsequent calls are O(1).
 
   Dave
 
   On Dec 5, 10:28 am, Carl Barton odysseus.ulys...@gmail.com wrote:
Sorry, I was being a bit vague. I meant what would the time
 complexity be
then?
As I understand your Constant time is Dependant on the constant pre
computation you do, which is no longer the case when you generalise
 
On 5 December 2011 16:14, Dave dave_and_da...@juno.com wrote:
 
 @Carl: Of course. For any given word size, extend the tables of
 powers
 of 2 and of 3 and change the for loop limit.
 
 Dave
 
 On Dec 5, 9:36 am, Carl Barton odysseus.ulys...@gmail.com wrote:
  Ah I see, in which case could you not generalise your solution
 for all
  integers?
  By taking into account the size of words on the computer for
 example?
 
  On 5 December 2011 15:09, Dave dave_and_da...@juno.com wrote:
 
   @Carl: Yes, as coded, my algorithm is for 32-bit integers. But
 the
   original poster asked for a solution using bit manipulation,
 and
   modulus and division are arithmetic operations, not bit
 operations.
 
   Dave
 
   On Dec 5, 8:56 am, Carl Barton odysseus.ulys...@gmail.com
 wrote:
@Dave Yours only works for a certain subset of all possible
 powers
 or 3
doesn't it? So WgpShashank's would be more general?
 
On 5 December 2011 14:30, Dave dave_and_da...@juno.com
 wrote:
 
 @WgpShashank: Yours is an O(log n) solution. Mine is O(1).
 
 Dave
 
 On Dec 5, 6:21 am, WgpShashank shashank7andr...@gmail.com
 wrote:
  @SAMMM  have a look
 
  * *solution is to keep dividing the number by 3, i.e, do
 n = n/3
  iteratively. In any iteration, if n%3 becomes non-zero
 and n is
 not 1
 then
  n is not a power of 3, otherwise n is a power of 3
 
  check it out ?http://codepad.org/863ptoBE
 
  Thanks
  Shashank
  Computer Science
  BIT Mesrahttp://
www.facebook.com/wgpshashankhttp://shashank7s.blogspot.com/
 
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Re: [algogeeks] Re: Number Theory (Power of 3 )

2011-12-07 Thread tech coder
what about this   log(base 3 n)  is of  integral type then n is a power of 3

On Mon, Dec 5, 2011 at 11:36 PM, Dave dave_and_da...@juno.com wrote:

 @Carl: You can generate the constants the first time the procedure is
 called. There is no need to do them every time. So the first call
 would be O(wordsize) but subsequent calls are O(1).

 Dave

 On Dec 5, 10:28 am, Carl Barton odysseus.ulys...@gmail.com wrote:
  Sorry, I was being a bit vague. I meant what would the time complexity be
  then?
  As I understand your Constant time is Dependant on the constant pre
  computation you do, which is no longer the case when you generalise
 
  On 5 December 2011 16:14, Dave dave_and_da...@juno.com wrote:
 
 
 
   @Carl: Of course. For any given word size, extend the tables of powers
   of 2 and of 3 and change the for loop limit.
 
   Dave
 
   On Dec 5, 9:36 am, Carl Barton odysseus.ulys...@gmail.com wrote:
Ah I see, in which case could you not generalise your solution for
 all
integers?
By taking into account the size of words on the computer for example?
 
On 5 December 2011 15:09, Dave dave_and_da...@juno.com wrote:
 
 @Carl: Yes, as coded, my algorithm is for 32-bit integers. But the
 original poster asked for a solution using bit manipulation, and
 modulus and division are arithmetic operations, not bit operations.
 
 Dave
 
 On Dec 5, 8:56 am, Carl Barton odysseus.ulys...@gmail.com wrote:
  @Dave Yours only works for a certain subset of all possible
 powers
   or 3
  doesn't it? So WgpShashank's would be more general?
 
  On 5 December 2011 14:30, Dave dave_and_da...@juno.com wrote:
 
   @WgpShashank: Yours is an O(log n) solution. Mine is O(1).
 
   Dave
 
   On Dec 5, 6:21 am, WgpShashank shashank7andr...@gmail.com
 wrote:
@SAMMM  have a look
 
* *solution is to keep dividing the number by 3, i.e, do n =
 n/3
iteratively. In any iteration, if n%3 becomes non-zero and n
 is
   not 1
   then
n is not a power of 3, otherwise n is a power of 3
 
check it out ?http://codepad.org/863ptoBE
 
Thanks
Shashank
Computer Science
BIT Mesrahttp://
  www.facebook.com/wgpshashankhttp://shashank7s.blogspot.com/
 
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*

 Regards*
*The Coder*

*Life is a Game. The more u play, the more u win, the more u win , the
more successfully u play*

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Re: [algogeeks] Re: Number Theory (Power of 3 )

2011-12-07 Thread saurabh singh
Originaly problem rules out the use of log.Moreover log (or any floating
point operations) take lot of hardware time as they are emulated on the
floating point environment on most machines.Thirdly precision problem for
higher values of n may cause your solution to give wron g answers,,,

On Wed, Dec 7, 2011 at 11:54 PM, tech coder techcoderonw...@gmail.comwrote:

 what about this   log(base 3 n)  is of  integral type then n is a power of
 3


 On Mon, Dec 5, 2011 at 11:36 PM, Dave dave_and_da...@juno.com wrote:

 @Carl: You can generate the constants the first time the procedure is
 called. There is no need to do them every time. So the first call
 would be O(wordsize) but subsequent calls are O(1).

 Dave

 On Dec 5, 10:28 am, Carl Barton odysseus.ulys...@gmail.com wrote:
  Sorry, I was being a bit vague. I meant what would the time complexity
 be
  then?
  As I understand your Constant time is Dependant on the constant pre
  computation you do, which is no longer the case when you generalise
 
  On 5 December 2011 16:14, Dave dave_and_da...@juno.com wrote:
 
 
 
   @Carl: Of course. For any given word size, extend the tables of powers
   of 2 and of 3 and change the for loop limit.
 
   Dave
 
   On Dec 5, 9:36 am, Carl Barton odysseus.ulys...@gmail.com wrote:
Ah I see, in which case could you not generalise your solution for
 all
integers?
By taking into account the size of words on the computer for
 example?
 
On 5 December 2011 15:09, Dave dave_and_da...@juno.com wrote:
 
 @Carl: Yes, as coded, my algorithm is for 32-bit integers. But the
 original poster asked for a solution using bit manipulation, and
 modulus and division are arithmetic operations, not bit
 operations.
 
 Dave
 
 On Dec 5, 8:56 am, Carl Barton odysseus.ulys...@gmail.com
 wrote:
  @Dave Yours only works for a certain subset of all possible
 powers
   or 3
  doesn't it? So WgpShashank's would be more general?
 
  On 5 December 2011 14:30, Dave dave_and_da...@juno.com wrote:
 
   @WgpShashank: Yours is an O(log n) solution. Mine is O(1).
 
   Dave
 
   On Dec 5, 6:21 am, WgpShashank shashank7andr...@gmail.com
 wrote:
@SAMMM  have a look
 
* *solution is to keep dividing the number by 3, i.e, do n
 = n/3
iteratively. In any iteration, if n%3 becomes non-zero and
 n is
   not 1
   then
n is not a power of 3, otherwise n is a power of 3
 
check it out ?http://codepad.org/863ptoBE
 
Thanks
Shashank
Computer Science
BIT Mesrahttp://
  www.facebook.com/wgpshashankhttp://shashank7s.blogspot.com/
 
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 *

  Regards*
 *The Coder*

 *Life is a Game. The more u play, the more u win, the more u win , the
 more successfully u play*

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-- 
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B.Tech (Computer Science)
MNNIT ALLAHABAD

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Re: [algogeeks] Re: Number Theory (Power of 3 )

2011-12-05 Thread Carl Barton
@Dave Yours only works for a certain subset of all possible powers or 3
doesn't it? So WgpShashank's would be more general?

On 5 December 2011 14:30, Dave dave_and_da...@juno.com wrote:

 @WgpShashank: Yours is an O(log n) solution. Mine is O(1).

 Dave

 On Dec 5, 6:21 am, WgpShashank shashank7andr...@gmail.com wrote:
  @SAMMM  have a look
 
  * *solution is to keep dividing the number by 3, i.e, do n = n/3
  iteratively. In any iteration, if n%3 becomes non-zero and n is not 1
 then
  n is not a power of 3, otherwise n is a power of 3
 
  check it out ?http://codepad.org/863ptoBE
 
  Thanks
  Shashank
  Computer Science
  BIT Mesrahttp://
 www.facebook.com/wgpshashankhttp://shashank7s.blogspot.com/

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Re: [algogeeks] Re: Number Theory (Power of 3 )

2011-12-05 Thread Carl Barton
Ah I see, in which case could you not generalise your solution for all
integers?
By taking into account the size of words on the computer for example?



On 5 December 2011 15:09, Dave dave_and_da...@juno.com wrote:

 @Carl: Yes, as coded, my algorithm is for 32-bit integers. But the
 original poster asked for a solution using bit manipulation, and
 modulus and division are arithmetic operations, not bit operations.

 Dave

 On Dec 5, 8:56 am, Carl Barton odysseus.ulys...@gmail.com wrote:
  @Dave Yours only works for a certain subset of all possible powers or 3
  doesn't it? So WgpShashank's would be more general?
 
  On 5 December 2011 14:30, Dave dave_and_da...@juno.com wrote:
 
 
 
   @WgpShashank: Yours is an O(log n) solution. Mine is O(1).
 
   Dave
 
   On Dec 5, 6:21 am, WgpShashank shashank7andr...@gmail.com wrote:
@SAMMM  have a look
 
* *solution is to keep dividing the number by 3, i.e, do n = n/3
iteratively. In any iteration, if n%3 becomes non-zero and n is not 1
   then
n is not a power of 3, otherwise n is a power of 3
 
check it out ?http://codepad.org/863ptoBE
 
Thanks
Shashank
Computer Science
BIT Mesrahttp://
  www.facebook.com/wgpshashankhttp://shashank7s.blogspot.com/
 
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Re: [algogeeks] Re: Number Theory (Power of 3 )

2011-12-05 Thread Carl Barton
Sorry, I was being a bit vague. I meant what would the time complexity be
then?
As I understand your Constant time is Dependant on the constant pre
computation you do, which is no longer the case when you generalise

On 5 December 2011 16:14, Dave dave_and_da...@juno.com wrote:

 @Carl: Of course. For any given word size, extend the tables of powers
 of 2 and of 3 and change the for loop limit.

 Dave

 On Dec 5, 9:36 am, Carl Barton odysseus.ulys...@gmail.com wrote:
  Ah I see, in which case could you not generalise your solution for all
  integers?
  By taking into account the size of words on the computer for example?
 
  On 5 December 2011 15:09, Dave dave_and_da...@juno.com wrote:
 
 
 
   @Carl: Yes, as coded, my algorithm is for 32-bit integers. But the
   original poster asked for a solution using bit manipulation, and
   modulus and division are arithmetic operations, not bit operations.
 
   Dave
 
   On Dec 5, 8:56 am, Carl Barton odysseus.ulys...@gmail.com wrote:
@Dave Yours only works for a certain subset of all possible powers
 or 3
doesn't it? So WgpShashank's would be more general?
 
On 5 December 2011 14:30, Dave dave_and_da...@juno.com wrote:
 
 @WgpShashank: Yours is an O(log n) solution. Mine is O(1).
 
 Dave
 
 On Dec 5, 6:21 am, WgpShashank shashank7andr...@gmail.com wrote:
  @SAMMM  have a look
 
  * *solution is to keep dividing the number by 3, i.e, do n = n/3
  iteratively. In any iteration, if n%3 becomes non-zero and n is
 not 1
 then
  n is not a power of 3, otherwise n is a power of 3
 
  check it out ?http://codepad.org/863ptoBE
 
  Thanks
  Shashank
  Computer Science
  BIT Mesrahttp://
www.facebook.com/wgpshashankhttp://shashank7s.blogspot.com/
 
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Re: [algogeeks] Re: Number theory

2011-08-17 Thread Rohit Srivastava
+1 to nitin

On Wed, Aug 17, 2011 at 2:48 PM, Vijay Kansal vijaykans...@gmail.comwrote:

 my bad 2^(n-1)...

 On Aug 17, 2:17 pm, Vijay Kansal vijaykans...@gmail.com wrote:
  @nitin it must be 2^n i think
 
  On Aug 17, 3:48 am, Bharat Kul Ratan bharat.kra...@gmail.com wrote:
 
 
 
 
 
 
 
   It might be useful:
 http://www.artofproblemsolving.com/Wiki/index.php/Partition_%28combin...

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Re: [algogeeks] Re: Number theory

2011-08-17 Thread Puneet Goyal
I think it should be 2^n -1

Explanation
We can visualize it as n balls are placed and we have to place some dividers
(max=n) in betweek to divide them into groups.

If we choose no divider its nC0 , but we dont have to include it
With 1 divider its nC1
and so on..
So the total no. of ways will be
(nC0+nC1+nC2..nCn)-nC0= 2^n-1

Regards,
Puneet

On Wed, Aug 17, 2011 at 4:05 PM, Rohit Srivastava access2ro...@gmail.comwrote:

 +1 to nitin


 On Wed, Aug 17, 2011 at 2:48 PM, Vijay Kansal vijaykans...@gmail.comwrote:

 my bad 2^(n-1)...

 On Aug 17, 2:17 pm, Vijay Kansal vijaykans...@gmail.com wrote:
  @nitin it must be 2^n i think
 
  On Aug 17, 3:48 am, Bharat Kul Ratan bharat.kra...@gmail.com wrote:
 
 
 
 
 
 
 
   It might be useful:
 http://www.artofproblemsolving.com/Wiki/index.php/Partition_%28combin...

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---
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Student of B. Tech. III Year (Software Engineering)
Delhi Technological University, Delhi
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Re: [algogeeks] Re: Number theory

2011-08-17 Thread Nitin Nizhawan
@Puneet, you are right but we can have only n-1 dividers.

On Wed, Aug 17, 2011 at 4:15 PM, Puneet Goyal puneetgoya...@gmail.comwrote:

 I think it should be 2^n -1

 Explanation
 We can visualize it as n balls are placed and we have to place some
 dividers (max=n) in betweek to divide them into groups.

 If we choose no divider its nC0 , but we dont have to include it
 With 1 divider its nC1
 and so on..
 So the total no. of ways will be
 (nC0+nC1+nC2..nCn)-nC0= 2^n-1

 Regards,
 Puneet

 On Wed, Aug 17, 2011 at 4:05 PM, Rohit Srivastava 
 access2ro...@gmail.comwrote:

 +1 to nitin


 On Wed, Aug 17, 2011 at 2:48 PM, Vijay Kansal vijaykans...@gmail.comwrote:

 my bad 2^(n-1)...

 On Aug 17, 2:17 pm, Vijay Kansal vijaykans...@gmail.com wrote:
  @nitin it must be 2^n i think
 
  On Aug 17, 3:48 am, Bharat Kul Ratan bharat.kra...@gmail.com wrote:
 
 
 
 
 
 
 
   It might be useful:
 http://www.artofproblemsolving.com/Wiki/index.php/Partition_%28combin...

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Re: [algogeeks] Re: Number theory

2011-08-17 Thread Puneet Goyal
+1 nitin
there must be n-1 dividers

On Wed, Aug 17, 2011 at 4:15 PM, Puneet Goyal puneetgoya...@gmail.comwrote:

 I think it should be 2^n -1

 Explanation
 We can visualize it as n balls are placed and we have to place some
 dividers (max=n) in betweek to divide them into groups.

 If we choose no divider its nC0 , but we dont have to include it
 With 1 divider its nC1
 and so on..
 So the total no. of ways will be
 (nC0+nC1+nC2..nCn)-nC0= 2^n-1

 Regards,
 Puneet

 On Wed, Aug 17, 2011 at 4:05 PM, Rohit Srivastava 
 access2ro...@gmail.comwrote:

 +1 to nitin


 On Wed, Aug 17, 2011 at 2:48 PM, Vijay Kansal vijaykans...@gmail.comwrote:

 my bad 2^(n-1)...

 On Aug 17, 2:17 pm, Vijay Kansal vijaykans...@gmail.com wrote:
  @nitin it must be 2^n i think
 
  On Aug 17, 3:48 am, Bharat Kul Ratan bharat.kra...@gmail.com wrote:
 
 
 
 
 
 
 
   It might be useful:
 http://www.artofproblemsolving.com/Wiki/index.php/Partition_%28combin...

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 Delhi Technological University, Delhi
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