One more approach using XOR to find the element repeated thrice. Complexity: O(n). Space :0
http://codepad.org/p82TGhjR main() { int arr[]= {5,3,3,1,5,5,7,7,8,8}; int len, set_bit_no, x,y,i; int xor, prev; len = sizeof(arr)/sizeof(arr[0]); xor = arr[0]; x = y=0; for(i=1;i<len;i++) { xor ^= arr[i]; } printf("xor:%d\n",xor); for(i=0;i<len;i++) { xor ^= arr[i]; if(xor == 0 && prev == arr[i]) { printf("Found:%d\n", arr[i]); break; } prev = arr[i]; } } On Thu, Jul 8, 2010 at 6:46 AM, jalaj jaiswal <jalaj.jaiswa...@gmail.com>wrote: > @ any solution less then nlogn would do + O(1) space > > > On Thu, Jul 8, 2010 at 12:38 AM, souravsain <souravs...@gmail.com> wrote: > >> @jalaj >> >> Are we looking for a better than )(nlogn) time and O(1) space >> solution? What if our target? >> >> If a solution is required simple, then as mentioned by Satya, sort the >> numbers in O(nlogn) time and scan once in O(n) time. So we get the >> number repeated 3 times in O(nlogn) time and O(1) space. >> >> Sourav >> >> On Jul 7, 7:36 pm, Priyanka Chatterjee <dona.1...@gmail.com> wrote: >> > > I am sceptical whether any XOR solution exits for your question. But >> if >> > > the question is modified as : >> > >> > > *Only one number repeats once,* some no.s repeat twice and only one >> number >> > > repeat thrice, here is the XOR solution for that. >> > >> > > suppose the sample array is A[]={1, 3,3,5,5,5, 7,7,8,8} >> > > in the example 1 repeats once and 5 repeats thrice. >> > >> > > 1>let T= XOR( all elements)= 1^5. (all elements occurring even no of >> times >> > > nullify) -O(N) >> > >> > > ( let x=1, y=5 >> > > As we know the no. repeating once and the no. repeating thrice are >> unequal, >> > > there must exist some bit 'k' such that x[k]!=y[k]. There may be more >> than >> > > such bits in x and y. But one such bit certainly yields T[k]=1 after >> x^y) >> > >> > > 2> Now traverse along each bit of T( in binary) from left or right >> and >> > > consider T[i] =1 which is encountered first. store it . let b=i; >> > > (O(M) time and O(M) space to store binary if M is the bit length of >> T.) >> > >> > > 3> T1= XOR(all elements in given array having bit b as 1)..... (O(N) >> time >> > > and O(M) space) ( time is O(MN) but as M<=32 , complexity remain O(N)) >> > >> > > 4> T0= XOR( all elements in given array having bit b as 0) (O(N) time >> and >> > > O(M) space) >> > >> > > One of (T1,T0) gives the no. that repeats once and the other gives >> the no >> > > that repeats thrice. >> > >> > > 6> Now traverse the along array A and compute count for T1 and T0. The >> > > count that equals 3 gives the corresponding no. repeating thrice. >> -O(N) >> > >> > > Time complexity is O(N+M) . Linear >> > > space complexity is O(M) to store binary form. >> > >> > > But this algo certainly fails if more than one no. repeats once. >> > >> > -- >> > Thanks & Regards, >> > Priyanka Chatterjee >> > Final Year Undergraduate Student, >> > Computer Science & Engineering, >> > National Institute Of Technology,Durgapur >> > Indiahttp://priyanka-nit.blogspot.com/- Hide quoted text - >> > >> > - Show quoted text - >> >> -- >> 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. >> >> > > > -- > With Regards, > Jalaj Jaiswal > +919026283397 > B.TECH IT > IIIT ALLAHABAD > > -- > 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. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
