@Amir: Presumably, since these are digits in a number, they are bounded on the bottom by 0 and on the top by radix-1. So in decimal, if a digit is 7 and the absolute difference between it and the next digit is 3, there is only one possibility for the next digit, 7-3 = 4, since 7+3 is too large. So only some subset of the 2^(n-1) combinations of addition and subtraction may be possible.
Dave On Dec 13, 4:15 am, Amir hossein Shahriari <amir.hossein.shahri...@gmail.com> wrote: > actually there are infinite number of sequences that match it > for example if the absolute differences are 3 2 5 1 > one possible sequence is 6 3 5 0 1 one other is 7 4 6 1 2 or 8 5 7 2 3 > and you can add any integer value to all elements and the result will still > be valid > actually you can start with any number and and then the second number will > be equal to the first number that you chose plus/minus the first absolute > difference and so on > > so if we are given the first element of the sequence there are 2^(n-1) ways > to find a valid sequence because for each absolute difference we can either > add the absolute difference to the last sequence element or subtract the > absolute difference from it > > > > On Mon, Dec 12, 2011 at 9:01 PM, KAY <amulya.manches...@gmail.com> wrote: > > If for a number n digits long, the absolute difference between > > adjacent digits is given, how to find out the number of different > > numbers with these absolute differences ? > > > for eg, > > if n=5 > > and the absolute differences are > > 3 2 5 1 > > then 1 possible number is > > 6 3 5 0 1 (because |6-3|=3,|3-5|=2 and so on...) > > > How many such numbers will be there? > > > -- > > You received this message because you are subscribed to the Google Groups > > "Algorithm Geeks" group. > > To post to this group, send email to algogeeks@googlegroups.com. > > To unsubscribe from this group, send email to > > algogeeks+unsubscr...@googlegroups.com. > > For more options, visit this group at > >http://groups.google.com/group/algogeeks?hl=en. -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to algogeeks@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
