Simple!
Just traverse the doubly linked list and keep track of next and previous of
each node, and do XOR and save the result in a new pointer, what according
to you is "np".
Be careful about boundary cases, i.e head and tail, though.

On Wed, Jun 20, 2012 at 5:16 PM, Krishna Kishore
<kknarenkris...@gmail.com>wrote:

> Explain how to implement doubly linked lists using only one pointer value*np[x
> *] per item instead of the usual two (next and prev). Assume that all
> pointer values can be interpreted as
> k-bit integers, and define* np[x] to be np[x] = next[x] XOR prev[x],* the
> k-bit “exclusive-or” of next[x] and prev[x]. (The value NIL is represented
> by 0.) Be sure to describe what information is needed to access the head of
> the list. Show how to implement the SEARCH, INSERT, and DELETE operations
> on such a list. Also show how to reverse such a list in O(1) time.
>
> This is the Question in the Book "*Introduction To Algorithms" *By CORMEN
> ( MIT Press ) Page Number : 209 , Problem No: 10.2-8.
>
> Thanks in Advance.
>
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