Extracting the smallest from the young tableau takes O(1) and and restoring its properties takes O(m+n) (where m & n and the number of rows and columns). This is much like extracting the max from a max-heap. So extracting the kth element would be k*O(n+m) ~ k*O(2n) (when m=n as in this problem) ~ O(k * n). On Mon, Sep 14, 2009 at 11:19 PM, Anil C R <cr.a...@gmail.com> wrote:
> @dufus > if extracting the kth smallest element would tske O(kn) then extracing the > nth element would take O(n^2) right? > > > On 9/14/09, Ramaswamy R <ramaswam...@gmail.com> wrote: > >> I am not sure if constant space requirement is possible. But we can do it >> with O(k) space complexity. >> >> Maintain a max heap of k elements. For each of the n*m sums add it to the >> heap (if it ain't full with k elements) or replace the root and heapify if >> the sum is lesser than the root. >> >> >> Finally the root will have the k'th smallest sum. >> >> >> But this would require O(n*m*log k) time complexity. >> >> On Sat, Sep 5, 2009 at 5:10 AM, ankur aggarwal >> <ankur.mast....@gmail.com>wrote: >> >>> @dufus.. >>> if there is constant space requirement then ?? >>> wat will be your soln ?? >>> >>> >>> On Sat, Sep 5, 2009 at 12:35 PM, Dufus <rahul.dev.si...@gmail.com>wrote: >>> >>>> >>>> It seems EXTRACT_MIN for Z[n^2] can be done in O(n) time. >>>> http://lyle.smu.edu/~saad/courses/cse3358/ps5/problemset5sol.pdf<http://lyle.smu.edu/%7Esaad/courses/cse3358/ps5/problemset5sol.pdf> >>>> >>>> Then using it we can find the kth smallest element in O(nk) time. >>>> >>>> _dufus >>>> >>>> >>>> On Sep 4, 10:03 pm, ankur aggarwal <ankur.mast....@gmail.com> wrote: >>>> > Find nth smallest inO(n) Given two arrays of length n in sorted order >>>> > X[n] & Y[n]. >>>> > Now make another array Z[n^2]={such that z belongs to X+Y}. >>>> > AS all possible sum of x+y is there in Z. You have to give the nth >>>> smallest >>>> > no of Z in O(n) time. >>>> > Space complexity : No bound on it. But try to optimize it if possible. >>>> >>>> >>>> >>>> >>>> >>> >>> >>> >>> >>> >> >> >> >> -- >> Yesterday is History. >> Tomorrow is a Mystery. >> Today is a Gift! That is why it is called the Present :). >> >> http://sites.google.com/site/ramaswamyr >> >> >> >> > > > > -- Yesterday is History. Tomorrow is a Mystery. Today is a Gift! That is why it is called the Present :). http://sites.google.com/site/ramaswamyr --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
