O(1) base conversion can here be done as follows:-(works only when numbers are in range 0 to n^2-1) *From base 10 to base n *let given base 10 no is m and we need to convert it in base n. then base n converted no is (m/n)(m%n) ie 34 base 10 in base 6 is (34/6)(34%6) ie 54
Now i think you can yourself write base n to base 10 conversion. On Sun, May 6, 2012 at 11:13 AM, saurabh singh <saurab...@gmail.com> wrote: > ^ And this completes the solution.... > > Saurabh Singh > B.Tech (Computer Science) > MNNIT > blog:geekinessthecoolway.blogspot.com > > > > On Sun, May 6, 2012 at 11:12 AM, Gene <gene.ress...@gmail.com> wrote: > >> 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. >> >> > -- > 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. > -- Arpit Gupta B.Tech Third Year Computer Science And Engineering M.N.N.I.T Allahabad arpitgupta.211...@gmail.com -- 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.
