@above..

It seems the above formatting has messed up.. but the point being if
we calculate col by col u will get the values and it shall be easy to
understand...

@sumit
Hey, u don't u share ur NlogN approach and probably we can come up
with something better..


On Dec 28, 3:37 pm, Lucifer <[email protected]> wrote:
> For simplicity of understanding u can take a 2 dimensional array and
> jolt down the values ...
>
> For ex -
> Orig Str = abcddcabar
>               10    9     8     7     6     5     4     3     2    1
>          0     r     a     b     a     c     d     d     c    b    a
>
>     0   0     0     0     0     0     0     0     0    0    0     0
>
> 1  a   0            1
> 1                                      1
>
> 2  b   0                   2
> 1
>
> 3  c   0                                 1
> 1
>
> 4  d   0                                       2
> 1
>
> 5  d   0                                       1
> 3
>
> 6  c   0                                 1
> 4
>
> 7  a   0            1           1
> 1
>
> 8  b   0                   2
> 1
>
> 9  a   0            1           3
> 2
>
> 10 r    0      1
>
> All the above unfilled places are actually 0s..
> Value at (6,3) gives the longest even palindrome with value 4..
> Also, (6 -4 +1 = 3) as per the start index condition..
>
> On Dec 28, 2:35 pm, Lucifer <[email protected]> wrote:
>
>
>
>
>
>
>
> > Algo:
> > -----------
> > Take the reverse of the given string and find the continuous matching
> > substring of even length in the orig and rev str.
>
> > We need to take care of certain corner cases such as:
> > Say orig str = abadba
> > rev str = abdaba
>
> > On finding the continuous substring we will get "ab" which is not a
> > palindrome..
> > Hence to handle such cases we need need to also keep track of the
> > following:
> > 1) No. of chars matched.
> > 2) The start of the substring in orig str.
> > 3) The start of the substring in rev str when read from right to
> > left..
>
> > The above algo can be used to find all the following:
> > 1) Whether there is an even length palindrome
> > 2) Whether there is an odd length palindrome
> > 3) Longest even length palindrome
> > 4) Longest odd length palindrome
> > 5) Longest palindrome.
>
> > The below code is for longest even length palindrome.
> > I have added a comment in the code to show where to break if we just
> > want to find whether it has an even palindrome.
>
> > Time complexity is O(N^2)..
> > Space complexity O(N) ...
> > // It can as well be done in O(n^2) space but i don't see a benefit of
> > doing so..Hence, reduced it to O(N)..
>
> > Lets take an array X[N+1] and initialize it to 0.
>
> > The array will be used to record whether there is a palindrome of even/
> > odd length ending at index OrigStr[i] and RevStr[j]..
>
> > Lets say R(i, j) = length of continuous matching substring which ends
> > at OrigStr[i] and RevStr[j]..
>
> > Hence, the recurrence would be,
> > R(i,j) = 1 + R(i-1,j-1) , if OrigStr[i] == RevStr[j]
> >         = 0, otherwise
>
> > If R(i,j) is even and greater than the current recorded longest even
> > palindrome,
> > then check the following before making the current max..(basically to
> > ensure the validity for corner cases)
>
> > // 1 - based index for ease of understanding..
> > // Basically checking for the start indices as explained above
> > say the substring length is K..
> > If ( i - k + 1 == N - j + 1) then assign it to current max
> >                                    otherwise its not a palindrome..
>
> > Code: ( written based on 1-based indexing)
> > ----------
> > char OrigStr[N];
>
> > for (int i =0; i < N+1 ; ++i)
> >    X[i] = 0;
>
> > int pStrt = 1; // to mimic the orig str
> > int pRev = N;  // to mimic the rev str
>
> > int currMax = 0;
>
> > while ( pRev > 0)
> > {
> >   for ( pStrt = N; pStrt >=1 ; --i)
> >   {
> >      if ( OrigStr[pStrt] == OrigStr[pRev] )
> >      {
> >         X[pStrt] = 1 + X[pStrt - 1];
> >         if ( (X[pStrt] % 2 == 0) &&
> >              (currMax < X[pStrt]) &&
> >               (pStrt - X[pStrt] + 1 == pRev)
> >         {
> >             currMax = X[pStrt];
> >            // In case u r looking for any even length palindrome
> >            // then break out from the entire loop..
> >            // Also, if u want to find the exact characters u can do so
> > by storing
> >            // pStrt in a variable.. Using the currMax and pStrt you
> > can get the
> >            // exact palindrome..
> >         }
> >      }
> >      else
> >         X[pStrt] = 0;
> >   }
> >   pRev -- ;
>
> > }
>
> > On Dec 28, 10:57 am, sumit mahamuni <[email protected]>
> > wrote:
>
> > > Here I can think of O( n * log n ). can anyone think of better solution??
>
> > > On Tue, Dec 27, 2011 at 11:06 PM, atul007 <[email protected]> wrote:
> > > > Given a string of length N, find whether there exits an even length
> > > > palindrome substring.
> > > > what would be efficient way of solving this problem.?
>
> > > > --
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>
> > > --
> > > Thanks and Regards,
> > > Sumit Mahamuni.
>
> > > -- Slow code that scales better can be faster than fast code that doesn't
> > > scale!
> > > -- Tough times never lasts, but tough people do.
> > > -- I love deadlines. I like the whooshing sound they make as they fly by. 
> > > -
> > > D. Adams

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