@Kamakshii: In O(n), you can determine whether the low order bit of
the missing number is 0 or 1. You can eliminate the approximately n/2
numbers that do not have this low order bit. Then, in O(n/2), you can
determine the next-to-low order bit. Etc. O(n) + O(n/2) + O(n/4) + ...
= O(n).
Dave
On Jun 26, 2:41 am, Kamakshii Aggarwal <kamakshi...@gmail.com> wrote:
> @dave:can u please give the divide and conquer solution
>
> On 6/26/11, Kamakshii Aggarwal <kamakshi...@gmail.com> wrote:
>
>
>
>
>
> > @aditya:it is given in the question that u cannot access the entire
> > element in single operaion..therefore both your above solution do not
> > hold for this question.
>
> > On 6/25/11, sunny agrawal <sunny816.i...@gmail.com> wrote:
> >> @Dave
> >> yes u r right that integers means it can be big integers too.
> >> generally when we talk about integers, they are 32 bit integers in
> >> Programing/Algorithm Questions
> >> so i was assuming that here
>
> >> and about my solution - yes it will be O(nlgn) or O(nw) not acceptable
> >> for
> >> given Q :(
>
> >> and yes a Divide and Conquer solution can do it in O(n). I just came to
> >> know
> >> ..thanks
> >> i little bit similer to my approach............Nice One
>
> >> On Sat, Jun 25, 2011 at 9:15 PM, Dave <dave_and_da...@juno.com> wrote:
>
> >>> @Sunny. You are reading too much into that. There is no mention that
> >>> the data are 32-bit integers. Perhaps they are big integers. What we
> >>> know is that the data are not characters, real numbers, rational
> >>> numbers, floating point, etc.
>
> >>> Your algorithm is O(n*w), where w is the word size. As I said, a
> >>> divide-and-conquer algorithm can find the missing number in O(n).
> >>> Furthermore, this is independent of the word size.
>
> >>> Dave
>
> >>> On Jun 24, 11:44 pm, sunny agrawal <sunny816.i...@gmail.com> wrote:
> >>> > @Dave it is given in Question that elements of array are integer
>
> >>> > On Sat, Jun 25, 2011 at 7:17 AM, Dave <dave_and_da...@juno.com> wrote:
> >>> > > @Sunny: What makes you think that the integers are 32 bits in
> >>> > > length.
> >>> > > Remember that O(.) notation applies as n --> infinity. Thus, O(n log
> >>> > > n) is correct for a naive algorithm. But a little thought can give a
> >>> > > divide-and-conquer algorithm which is O(n).
>
> >>> > > Dave
>
> >>> > > On Jun 24, 8:44 am, sunny agrawal <sunny816.i...@gmail.com> wrote:
> >>> > > > hmm i also doubt that
> >>> > > > but it is Strictly O(32n) not O(nlgn) where lgn <= 32 depending
> >>> > > > upon
> >>> > > value
> >>> > > > of n
>
> >>> > > > On Fri, Jun 24, 2011 at 1:10 PM, rizwan hudda
> >>> > > > <rizwanhu...@gmail.com
>
> >>> > > wrote:
> >>> > > > > @sunny: Think again, your solution will take O(n*log(n)), where
> >>> log(n)
> >>> > > is
> >>> > > > > the number of bits to represent
> >>> > > > > the number.
>
> >>> > > > > On Thu, Jun 23, 2011 at 6:51 PM, Sriganesh Krishnan <
> >>> 2448...@gmail.com
> >>> > > >wrote:
>
> >>> > > > >> can you explain me....what the logic is...behind the xor
> >>> > > operation?...is
> >>> > > > >> it like inversion or encryption?
>
> >>> > > > >> On Thu, Jun 23, 2011 at 11:59 AM, sunny agrawal <
> >>> > > sunny816.i...@gmail.com>wrote:
>
> >>> > > > >>> initially compute xor of all the values from 0 to n in a
> >>> > > > >>> variable
> >>> > > Temp
> >>> > > > >>> so temp = 0^1^2........^n
> >>> > > > >>> let result is used to store the missing number
> >>> > > > >>> for each ith bit of missing number where i = 0-31 we can find
> >>> > > > >>> it
> >>> as
> >>> > > > >>> following
> >>> > > > >>> ith bit of result = (xor of all ith bits of values of array)
> >>> xored
> >>> > > with
> >>> > > > >>> (ith
> >>> > > > >>> bit of temp)
>
> >>> > > > >>> On Thu, Jun 23, 2011 at 12:25 AM, oppilas . <
> >>> > > jatka.oppimi...@gmail.com>wrote:
>
> >>> > > > >>>> Is the array sorted?
> >>> > > > >>>> In A[1..n], one number is missing from 0 to N. So,
> >>> > > > >>>> A[5]={--INF, 2,1,3,0} is a valid case?
>
> >>> > > > >>>> On Wed, Jun 22, 2011 at 11:51 PM, RollBack <
> >>> rajeevr...@gmail.com
> >>> > > >wrote:
>
> >>> > > > >>>>> An array A[1...n] contains all the integers from 0 to n
> >>> > > > >>>>> except
> >>> for
> >>> > > one
> >>> > > > >>>>> number which is
> >>> > > > >>>>> missing. In this problem, we cannot access an entire integer
> >>> > > > >>>>> in
> >>> A
> >>> > > with
> >>> > > > >>>>> a single opera-
> >>> > > > >>>>> tion. The elements of A are represented in binary, and the
> >>> > > > >>>>> only
> >>> > > > >>>>> operation we can use
> >>> > > > >>>>> to access them is “fetch the jth bit of A[i]”, which takes
> >>> constant
> >>> > > > >>>>> time. Write code to
> >>> > > > >>>>> find the missing integer. Can you do it in O(n) time?
> >>> > > > >>>>> _
> >>> > > > >>>>> _ _____________________________________________
>
> >>> > > > >>>>> Rajeev N Bharshetty
> >>> > > > >>>>> I Blog @www.opensourcemania.co.cc
>
> >>> > > > >>>>> --
> >>> > > > >>>>> You received this message because you are subscribed to the
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> >>> > > > >>> --
> >>> > > > >>> Sunny Aggrawal
> >>> > > > >>> B-Tech IV year,CSI
> >>> > > > >>> Indian Institute Of Technology,Roorkee
>
> >>> > > > >>> --
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> >>> > > > >> --
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> >>> > > > > --
> >>> > > > > Thanks and regards
> >>> > > > > Rizwan A Hudda
> >>> > > > >http://sites.google.com/site/rizwanhudda
>
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> >>> > > > --
> >>> > > > Sunny Aggrawal
> >>> > > > B-Tech IV year,CSI
> >>> > > > Indian Institute Of Technology,Roorkee- Hide quoted text -
>
> >>> > > > - Show quoted text -
>
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> >>> > --
> >>> > Sunny Aggrawal
> >>> > B-Tech IV year,CSI
> >>> > Indian Institute Of Technology,Roorkee- Hide quoted text -
>
> >>> > - Show quoted text -
>
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> >> --
> >> Sunny Aggrawal
> >> B-Tech IV year,CSI
> >> Indian Institute Of Technology,Roorkee
>
> >> --
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> > --
> > Regards,
> > Kamakshi
> > kamakshi...@gmail.com
>
> --
> Regards,
> Kamakshi
> kamakshi...@gmail.com- Hide quoted text -
>
> - Show quoted text -
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