Ah, but you can pick the radix to be n. Then at most 3 passes will always sort the array. O(3n) = O(n), so you are done.
This topic has come up before. There is code at http://groups.google.com/group/algogeeks/msg/90ce2df194aba2d2 . It is true this code assumes math including mod takes constant time, but that's normal for RAM computation models used for most algorithms. Gene On May 5, 4:32 am, saurabh singh <saurab...@gmail.com> wrote: > After giving some thought,I think even radix sort may not be sufficient. > Complexity of radix sort is O(k*n) where k is the number of buckets > required to sort the given range. > The number of buckets is proportional to the number of bits required to > represent the *maximum number in the given range.*For our case the maximum > number is O(n^2).Hence *the number of buckets required would be > proportional to log(n^2) in the worst case.* > Hence the worst case complexity for the given constraints using radix sort > would be *O(n*(log n^2)) = O(n*logn).* > This is no better than comparision sort.A slight optimization that we can > make is to use a higher base which would reduce the number of buckets > required but would add the cost of converting each number into the higher > base. > Somehow I am getting convinced worst case O(n) algorithm may not be > possible.Working on the mathematical proof. > Saurabh Singh > B.Tech (Computer Science) > MNNIT > blog:geekinessthecoolway.blogspot.com > > On Sat, May 5, 2012 at 8:37 AM, saurabh singh <saurab...@gmail.com> wrote: > > @cegprakash They are n numbers lying in the range 1 to n^2.Not necessarily > > sorted. > > eg 3 4 1 2 5 8 (6 numbers satisfying the conditions given in the problem) > > Saurabh Singh > > B.Tech (Computer Science) > > MNNIT > > blog:geekinessthecoolway.blogspot.com > > > On Sat, May 5, 2012 at 5:17 AM, Prakash D <cegprak...@gmail.com> wrote: > > >> The range 1 to n^2 is already sorted > > >> On Sat, May 5, 2012 at 12:17 AM, Algobiz <deepak.arulkan...@gmail.com> > >> wrote: > >> > How to sort n numbers in the range of 1 to n^2 in O(n).. Any ideas? > > >> > -- > >> > You received this message because you are subscribed to the Google > >> Groups > >> > "Algorithm Geeks" group. > >> > To view this discussion on the web visit > >> >https://groups.google.com/d/msg/algogeeks/-/PGgMdaIbGIsJ. > >> > 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. -- 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.
