A friend of mine has come up with an idea of proving that there is no linear time / constant memory solution by reducing the problem to a known problem for which there is no such solution (e.g. sorting). But there's no further ideas so far...
On Aug 17, 4:11 pm, "Vaibhav Jain" <[EMAIL PROTECTED]> wrote: > hello Dondi, > > in ur solution, space complexity will be O(n) in worst case. > but in my solution it will constant space with linear complexity. > > now think abt how to prove it if range is not known for numbers > then can we achieve it or not? > if not then prove it....??? > > On 8/17/07, Dondi Imperial <[EMAIL PROTECTED]> wrote: > > > > > > > if you know the range of the numbers don't you just have to create and > > array (of length k in your example) then iterate over the array and > > increment the corresponding element in the other array. > > > Ie, > > > int[] arrayValues = some array of a known range > > int[] arrayLookup = int[min_in_range - max_in_range + 1] > > > foreach(i in arrayValues) > > if(arrayLookup[i] > 0) then > > found > > else > > arrayLookup[i]++ > > > Of course range could be prohibitively large (still constant though if > > you know the range before hand). > > > On 8/17/07, Vaibhav Jain <[EMAIL PROTECTED]> wrote: > > > if u know the range of values stored in array then > > > let me assume values 1 to k then u can calculate sum of numbers stored > > in > > > array in O(n) complexity. > > > after that apply formula > > > > duplicate value= [k*(k+1)]/2 - sum of numbers stored in array > > > > it will take O(1) constant time so total complexity becomes only O(n). > > > > it can be one solution to your problem but if the range is unknown for > > > values then > > > is there any solution to come in O(n)??? > > > > On 8/16/07, dsha <[EMAIL PROTECTED]> wrote: > > > > > Hi there, > > > > > I'm interested in the following problem: there is an array of integers > > > > that contains each element only once except for one element that > > > > occurs exactly twice. Is there a way to find this element faster than > > > > O(n*log n) and with constant extra memory? If no, how can I prove it? > > > > > Thanks in advance for ideas. > > > > -- > > > Vaibhav Jain > > -- > Vaibhav Jain --~--~---------~--~----~------------~-------~--~----~ 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 [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/algogeeks -~----------~----~----~----~------~----~------~--~---
