Hi all, I am new to this group.
My last post was deleted i do not know the reason behind it. I will explain my logic here:- as the range is 1 to n^2 we have a input array like input[n^2]. We can take a auxillary array of size n^2 like aux[n^2]. Scan the input array. For each input input[i] increment by one corresponding aux[input[i]]. After this just iterate through the aux array printing the index aux[i] times. This way we can sort it in O(n) time. On Sat, May 5, 2012 at 2:02 PM, 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. > -- *Thanks, Jeevitesh Shekhar Singh.* -- 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.
