On 12 April 2010 23:57, souri datta <souri.isthe...@gmail.com> wrote:
> Why only median of median? > > @Souri: It's because using order statistics (randomized select) , you have > an expected time complexity of theta(n) . > But the upper bound is n^2 even to find the smallest element. So to ensure selection of no.s in linear time in the worst case, we use medians of medians. @ Rohit: Your BST algo is good but not the best. > On Mon, Apr 12, 2010 at 7:51 PM, Rohit Saraf > <rohit.kumar.sa...@gmail.com>wrote: > >> Find the kth element using order statistics - O(n) <> As far as i know >> , u will have to use median of medians selection algorithm for this... >> Rest is fine.. >> >> -------------------------------------------------- >> Rohit Saraf >> Second Year Undergraduate, >> Dept. of Computer Science and Engineering >> IIT Bombay >> http://www.cse.iitb.ac.in/~rohitfeb14<http://www.cse.iitb.ac.in/%7Erohitfeb14> >> >> >> On Mon, Apr 12, 2010 at 3:20 PM, souri datta <souri.isthe...@gmail.com>wrote: >> >>> Steps: >>> 1. Find the kth element using order statistics - O(n) >>> 2. In one pass over the array, get all the elems less than the kth >>> element. >>> >>> Let me know if this is not correct. >>> >>> >>> >>> On Mon, Apr 12, 2010 at 1:57 PM, Rohit Saraf < >>> rohit.kumar.sa...@gmail.com> wrote: >>> >>>> I have already given an O(n) solution. See above ! >>>> >>>> The BST solution is O(nlogn) but is practically more nice. :) >>>> >>>> -------------------------------------------------- >>>> Rohit Saraf >>>> Second Year Undergraduate, >>>> Dept. of Computer Science and Engineering >>>> IIT Bombay >>>> http://www.cse.iitb.ac.in/~rohitfeb14<http://www.cse.iitb.ac.in/%7Erohitfeb14> >>>> >>>> >>>> On Mon, Apr 12, 2010 at 1:16 PM, Nikhil Agarwal < >>>> nikhil.bhoja...@gmail.com> wrote: >>>> >>>>> >>>>> >>>>> On Mon, Apr 12, 2010 at 12:58 PM, Rohit Saraf < >>>>> rohit.kumar.sa...@gmail.com> wrote: >>>>> >>>>>> are yaar... i meant BST... i thought that was obvious ! >>>>>> sry if i confused you.... >>>>>> >>>>> >>>>> @rohit It's ok.Actually in this group people come up with very >>>>> different and non-common solutions so its risky to take things >>>>> 'obviously'. >>>>> Rotation algo has a complexity of O(nlogn)[for constructing a BST] >>>>> +O(n) [for rotating n times]=O(nlogn) . >>>>> >>>>> Till now best algo we have is using heaps which give rise to complexity >>>>> = O(n+klogn) >>>>> >>>>> Please pass on algos having better runtime complexity. >>>>> >>>>>> >>>>>> >>>>>> -------------------------------------------------- >>>>>> Rohit Saraf >>>>>> Second Year Undergraduate, >>>>>> Dept. of Computer Science and Engineering >>>>>> IIT Bombay >>>>>> http://www.cse.iitb.ac.in/~rohitfeb14<http://www.cse.iitb.ac.in/%7Erohitfeb14> >>>>>> >>>>>> >>>>>> On Mon, Apr 12, 2010 at 12:38 PM, Nikhil Agarwal < >>>>>> nikhil.bhoja...@gmail.com> wrote: >>>>>> >>>>>>> Hey rohit.You were referring to Binary tree.Search keyword was >>>>>>> missing.Because rotation makes no sense in binary tree.Please note >>>>>>> binary >>>>>>> tree and BST are different. >>>>>>> >>>>>>> On Mon, Apr 12, 2010 at 12:33 PM, Rohit Saraf < >>>>>>> rohit.kumar.sa...@gmail.com> wrote: >>>>>>> >>>>>>>> Read the slides i uploaded. They explain what rotation does in a >>>>>>>> BST. >>>>>>>> >>>>>>>> Also you might like to refer to Red Black Trees in CLRS.... that >>>>>>>> chapter explains rotations. >>>>>>>> >>>>>>>> -------------------------------------------------- >>>>>>>> Rohit Saraf >>>>>>>> Second Year Undergraduate, >>>>>>>> Dept. of Computer Science and Engineering >>>>>>>> IIT Bombay >>>>>>>> http://www.cse.iitb.ac.in/~rohitfeb14<http://www.cse.iitb.ac.in/%7Erohitfeb14> >>>>>>>> >>>>>>>> >>>>>>>> On Mon, Apr 12, 2010 at 8:18 AM, Rohit Saraf < >>>>>>>> rohit.kumar.sa...@gmail.com> wrote: >>>>>>>> >>>>>>>>> but still the binary tree solution is of more practical use.i will >>>>>>>>> explain the solution once i reach my comp >>>>>>>>> >>>>>>>>> >>>>>>>>> On 4/11/10, Nikhil Agarwal <nikhil.bhoja...@gmail.com> wrote: >>>>>>>>> > >>>>>>>>> > >>>>>>>>> > On Sun, Apr 11, 2010 at 9:56 PM, Rohit Saraf < >>>>>>>>> rohit.kumar.sa...@gmail.com> >>>>>>>>> > wrote: >>>>>>>>> >> >>>>>>>>> >> Time complexity is O(n log n). But the last solution I gave has >>>>>>>>> O(n). >>>>>>>>> >> >>>>>>>>> >> What did u not understand abt thesolution >>>>>>>>> > >>>>>>>>> > >>>>>>>>> > @Rohit Please explain how that Binary tree solution works. >>>>>>>>> >> >>>>>>>>> >> >>>>>>>>> >> -------------------------------------------------- >>>>>>>>> >> Rohit Saraf >>>>>>>>> >> Second Year Undergraduate, >>>>>>>>> >> Dept. of Computer Science and Engineering >>>>>>>>> >> IIT Bombay >>>>>>>>> >> http://www.cse.iitb.ac.in/~rohitfeb14<http://www.cse.iitb.ac.in/%7Erohitfeb14> >>>>>>>>> >> >>>>>>>>> >> >>>>>>>>> >> On Sun, Apr 11, 2010 at 11:00 AM, Priyanka Chatterjee >>>>>>>>> >> <dona.1...@gmail.com> wrote: >>>>>>>>> >>> >>>>>>>>> >>> >>>>>>>>> >>> >>>>>>>>> >>> On 11 April 2010 10:46, Rohit Saraf < >>>>>>>>> rohit.kumar.sa...@gmail.com> wrote: >>>>>>>>> >>>> >>>>>>>>> >>>> Construct a binary tree from the data (maintain the size of >>>>>>>>> subtree >>>>>>>>> >>>> under each node). >>>>>>>>> >>>> Do rotations till the left subtree does not have size k. >>>>>>>>> Rotation is a >>>>>>>>> >>>> constant time operation. >>>>>>>>> >>>> Please prove the correctness of your algorithm with the time >>>>>>>>> complexity >>>>>>>>> >>>> >>>>>>>>> >>>> -------------------------------------------------- >>>>>>>>> >>>> Rohit Saraf >>>>>>>>> >>>> Second Year Undergraduate, >>>>>>>>> >>>> Dept. of Computer Science and Engineering >>>>>>>>> >>>> IIT Bombay >>>>>>>>> >>>> http://www.cse.iitb.ac.in/~rohitfeb14<http://www.cse.iitb.ac.in/%7Erohitfeb14> >>>>>>>>> >>>> >>>>>>>>> >>>> >>>>>>>>> >>>> >>>>>>>>> >>>> On Mon, Mar 29, 2010 at 11:15 AM, blackDiamond < >>>>>>>>> patidarc...@gmail.com> >>>>>>>>> >>>> wrote: >>>>>>>>> >>>>> >>>>>>>>> >>>>> nice solution appreciate it. but your algorithm is wasting >>>>>>>>> time in >>>>>>>>> >>>>> finding all the element... >>>>>>>>> >>>>> instead of that just find boundary line kth element which can >>>>>>>>> help as >>>>>>>>> >>>>> in finding element greater that kth and element small than >>>>>>>>> kth and that >>>>>>>>> >>>>> soluton can be done in O(N) >>>>>>>>> >>>>> >>>>>>>>> >>>>> >>>>>>>>> >>>>> On Sun, Mar 28, 2010 at 10:02 PM, CHERUVU JAANU REDDY >>>>>>>>> >>>>> <jaanu.cher...@gmail.com> wrote: >>>>>>>>> >>>>>> >>>>>>>>> >>>>>> >>>>>>>>> >>>>>> 1) Construct max heap by taking first k elements in an array >>>>>>>>> >>>>>> 2) if k+1 element less than root of max heap >>>>>>>>> >>>>>> a) Delete root of max heap >>>>>>>>> >>>>>> b) Insert k+1 element in max heap and apply heapify >>>>>>>>> method >>>>>>>>> >>>>>> 3) else skip the element >>>>>>>>> >>>>>> 4) apply above procedure for all n elements in an array >>>>>>>>> >>>>>> >>>>>>>>> >>>>>> At last you will get k smallest elements and root is kth >>>>>>>>> smallest >>>>>>>>> >>>>>> element in the array >>>>>>>>> >>>>>> >>>>>>>>> >>>>>> this is O(nlogk) >>>>>>>>> >>>>>> >>>>>>>>> >>>>>> >>>>>>>>> >>>>>> >>>>>>>>> >>>>>> ---------------------------------------- >>>>>>>>> >>>>>> CHERUVU JAANU REDDY >>>>>>>>> >>>>>> M.Tech in CSIS >>>>>>>>> >>>>>> >>>>>>>>> >>>>>> >>>>>>>>> >>>>>> On Sun, Mar 28, 2010 at 8:41 PM, abhijith reddy >>>>>>>>> >>>>>> <abhijith200...@gmail.com> wrote: >>>>>>>>> >>>>>>> >>>>>>>>> >>>>>>> Can any one tell how to do this when there are 'm' queries >>>>>>>>> like >>>>>>>>> >>>>>>> "query i j k" find the kth largest element in between >>>>>>>>> indices i->j in >>>>>>>>> >>>>>>> an array. >>>>>>>>> >>>>>>> When m is large even an O(n) algorithm would be slow. >>>>>>>>> >>>>>>> I thinking that each query could be answered in O(sqrt(n)) >>>>>>>>> time >>>>>>>>> >>>>>>> So any suggestions ? >>>>>>>>> >>>>>>> >>>>>>>>> >>>>>>> Thanks >>>>>>>>> >>>>>>> >>>>>>>>> >>>>>>> >>>>>>>>> >>>>>>> On Sun, Mar 28, 2010 at 7:57 PM, blackDiamond < >>>>>>>>> patidarc...@gmail.com> >>>>>>>>> >>>>>>> wrote: >>>>>>>>> >>>>>>>> >>>>>>>>> >>>>>>>> there are better solution of O(n) are posted in the >>>>>>>>> thread.......[?]. >>>>>>>>> >>>>>>>> using order statices .... >>>>>>>>> >>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>>>> >>>>>>>> On Sun, Mar 28, 2010 at 6:49 PM, Mukesh Kumar thakur >>>>>>>>> >>>>>>>> <mukeshraj8...@gmail.com> wrote: >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> Create a temp array temp[0..k-1] of size k. >>>>>>>>> >>>>>>>>> 2) Traverse the array arr[k..n-1]. While traversing, keep >>>>>>>>> updating >>>>>>>>> >>>>>>>>> the smallest element of temp[] >>>>>>>>> >>>>>>>>> 3) Return the smallest of temp[] >>>>>>>>> >>>>>>>>> Time Complexity: O((n-k)*k). >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> try it ..............for this problem[?] >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>> -- >>>>>>>>> >>>>>>>>> You received this message because you are subscribed to >>>>>>>>> the Google >>>>>>>>> >>>>>>>>> Groups "Algorithm Geeks" group. >>>>>>>>> >>>>>>>>> To post to this group, send email to >>>>>>>>> algoge...@googlegroups.com. >>>>>>>>> >>>>>>>>> To unsubscribe from this group, send email to >>>>>>>>> >>>>>>>>> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> >>>>>>>>> . >>>>>>>>> >>>>>>>>> For more options, visit this group at >>>>>>>>> >>>>>>>>> http://groups.google.com/group/algogeeks?hl=en. >>>>>>>>> >>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>>>> >>>>>>>> >>>>>>>>> >>>>>>>> -- >>>>>>>>> >>>>>>>> ~~~~BL/\CK_D!AMOND~~~~~~~~ >>>>>>>>> >>>>>>>> >>>>>>>>> >>>>>>>> -- >>>>>>>>> >>>>>>>> You received this message because you are subscribed to >>>>>>>>> the Google >>>>>>>>> >>>>>>>> Groups "Algorithm Geeks" group. >>>>>>>>> >>>>>>>> To post to this group, send email to >>>>>>>>> algoge...@googlegroups.com. >>>>>>>>> >>>>>>>> To unsubscribe from this group, send email to >>>>>>>>> >>>>>>>> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@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 >>>>>>>>> algoge...@googlegroups.com. >>>>>>>>> >>>>>>> To unsubscribe from this group, send email to >>>>>>>>> >>>>>>> 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because you are subscribed to the >>>>>>>>> Google >>>>>>>>> >>>>> Groups "Algorithm Geeks" group. >>>>>>>>> >>>>> To post to this group, send email to >>>>>>>>> algoge...@googlegroups.com. >>>>>>>>> >>>>> To unsubscribe from this group, send email to >>>>>>>>> >>>>> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@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 >>>>>>>>> algoge...@googlegroups.com. >>>>>>>>> >>>> To unsubscribe from this group, send email to >>>>>>>>> >>>> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> >>>>>>>>> . >>>>>>>>> >>>> For more options, visit this group at >>>>>>>>> >>>> http://groups.google.com/group/algogeeks?hl=en. >>>>>>>>> >>> >>>>>>>>> >>> >>>>>>>>> >>> >>>>>>>>> >>> >>>>>>>>> >>> -- >>>>>>>>> >>> Thanks & Regards, >>>>>>>>> >>> Priyanka Chatterjee >>>>>>>>> >>> Third Year Undergraduate Student, >>>>>>>>> >>> Computer Science & Engineering, >>>>>>>>> >>> National Institute Of Technology,Durgapur >>>>>>>>> >>> India >>>>>>>>> >>> http://priyanka-nit.blogspot.com/ >>>>>>>>> >>> >>>>>>>>> >>> -- >>>>>>>>> >>> You received this message because you are subscribed to the >>>>>>>>> Google Groups >>>>>>>>> >>> "Algorithm Geeks" group. >>>>>>>>> >>> To post to this group, send email to >>>>>>>>> algoge...@googlegroups.com. >>>>>>>>> >>> To unsubscribe from this group, send email to >>>>>>>>> >>> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@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<algogeeks%2bunsubscr...@googlegroups.com> >>>>>>>>> . >>>>>>>>> >> For more options, visit this group at >>>>>>>>> >> http://groups.google.com/group/algogeeks?hl=en. >>>>>>>>> > >>>>>>>>> > >>>>>>>>> > >>>>>>>>> > >>>>>>>>> > -- >>>>>>>>> > Thanks & Regards >>>>>>>>> > Nikhil Agarwal >>>>>>>>> > Junior Undergraduate >>>>>>>>> > Computer Science & Engineering, >>>>>>>>> > National Institute Of Technology, Durgapur,India >>>>>>>>> > http://tech-nikk.blogspot.com >>>>>>>>> > >>>>>>>>> > >>>>>>>>> > -- >>>>>>>>> > You received this message because you are subscribed to the >>>>>>>>> Google Groups >>>>>>>>> > "Algorithm Geeks" group. >>>>>>>>> > To post to this group, send email to algoge...@googlegroups.com. >>>>>>>>> > To unsubscribe from this group, send email to >>>>>>>>> > algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> >>>>>>>>> . >>>>>>>>> > For more options, visit this group at >>>>>>>>> > http://groups.google.com/group/algogeeks?hl=en. >>>>>>>>> > >>>>>>>>> >>>>>>>>> >>>>>>>>> -- >>>>>>>>> >>>>>>>>> -------------------------------------------------- >>>>>>>>> Rohit Saraf >>>>>>>>> Second Year Undergraduate, >>>>>>>>> Dept. of Computer Science and Engineering >>>>>>>>> IIT Bombay >>>>>>>>> http://www.cse.iitb.ac.in/~rohitfeb14<http://www.cse.iitb.ac.in/%7Erohitfeb14> >>>>>>>>> >>>>>>>> >>>>>>>> -- >>>>>>>> You received this message because you are subscribed to the Google >>>>>>>> Groups "Algorithm Geeks" group. >>>>>>>> To post to this group, send email to algoge...@googlegroups.com. >>>>>>>> To unsubscribe from this group, send email to >>>>>>>> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> >>>>>>>> . >>>>>>>> For more options, visit this group at >>>>>>>> http://groups.google.com/group/algogeeks?hl=en. >>>>>>>> >>>>>>> >>>>>>> >>>>>>> >>>>>>> -- >>>>>>> Thanks & Regards >>>>>>> Nikhil Agarwal >>>>>>> Junior Undergraduate >>>>>>> Computer Science & Engineering, >>>>>>> National Institute Of Technology, Durgapur,India >>>>>>> http://tech-nikk.blogspot.com >>>>>>> >>>>>>> >>>>>>> -- >>>>>>> You received this message because you are subscribed to the Google >>>>>>> Groups "Algorithm Geeks" group. >>>>>>> To post to this group, send email to algoge...@googlegroups.com. >>>>>>> To unsubscribe from this group, send email to >>>>>>> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> >>>>>>> . >>>>>>> For more options, visit this group at >>>>>>> http://groups.google.com/group/algogeeks?hl=en. >>>>>>> >>>>>> >>>>>> -- >>>>>> You received this message because you are 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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 algoge...@googlegroups.com. >>>> To unsubscribe from this group, send email to >>>> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@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 algoge...@googlegroups.com. >>> To unsubscribe from this group, send email to >>> algogeeks+unsubscr...@googlegroups.com<algogeeks%2bunsubscr...@googlegroups.com> >>> . >>> For more options, visit this group at >>> http://groups.google.com/group/algogeeks?hl=en. >>> >> >> -- >> You received this message because you are 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