October 19th, 2011, 02:36 PM  #1 
Newbie Joined: Oct 2011 Posts: 15 Thanks: 0  reverse n
Hi. I was looking for a way to test if some, nonnegative, integer n is a palindrome. One way requires a nonrecursive function (r(n)) that is going to yield the reversed order of digits of some n. I derived this function, but was wondering, if anyone here ever came across this and what were their results. I'm guessing there is a better way to do this, from what I did. If someone has any ideas, you can post them and I will post what I found also. 
October 19th, 2011, 02:38 PM  #2 
Newbie Joined: Oct 2011 Posts: 15 Thanks: 0  Re: reverse n
also, to add, we are talking about base 10.

October 20th, 2011, 04:44 AM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: reverse n
How large are the numbers you're looking at?

October 20th, 2011, 06:04 AM  #4 
Newbie Joined: Oct 2011 Posts: 15 Thanks: 0  Re: reverse n
from 0 to infinity.

October 20th, 2011, 07:21 AM  #5 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: reverse n
That's not very helpful. Almost all natural numbers are too large to be stored on an xgigabyte hard drive, where x is the number of electrons in the universe. I suppose you're not trying to work with those. But what range is of interest to you? If you want to work with large numbers then you should be willing to use an algorithm that is slow for small numbers, but if small numbers are of special importance you wouldn't want that trade. I would suggest one method if you cared only about numbers up to 3 digits, another if you cared mostly about numbers up to wordsize (10 or 20 digits for 32/64 bits), another if you cared mostly about numbers below a few kilobytes in size (say, 25,000 digits and below), and yet another for larger numbers. The last would be implemented differently depending on the target size and the capabilities of the machine used. For the first group table lookup would be best; for the second, convert the whole number to decimal (ideally via BCD instructions) and then test; for the next, pulling out the most and leastsignificant words and pretesting is important, followed by a binary splitting radix conversion algorithm using Newton/Karatsuba division; the following is similar but using cachefriendly strategies and FFTbased division rather than Karatsuba; the last probably requires ondisk methods with accessfriendly strategies that involve storing large portions of the number because hard drives work best by sector. 
October 20th, 2011, 08:20 AM  #6 
Newbie Joined: Oct 2011 Posts: 15 Thanks: 0  Re: reverse n
I didn't mean a program function CRGreathouse , I am looking for a generalized way to do this for any n with the stated conditions in the first post (so that r(n)n=0, that is, n is a palindromic number). Maybe I don't understand what you mean, could you please clarify?

October 20th, 2011, 08:40 AM  #7  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: reverse n Quote:
 
October 20th, 2011, 09:02 AM  #8 
Newbie Joined: Oct 2011 Posts: 15 Thanks: 0  Re: reverse n
example: for n=321, f(n)=123. find f(n)? 
October 20th, 2011, 10:23 AM  #9 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: reverse n
f(n) is the reverse of the decimal digits of n. What more do you want?

October 20th, 2011, 10:25 AM  #10 
Newbie Joined: Oct 2011 Posts: 15 Thanks: 0  Re: reverse n
generalized expression of what comes after f(n)= 

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