$3.$ In certain programming languages like C$/$C$++,$ links are represented by pointers, and we are allowed to do $$pointer arithmetic$,$ such as bitwise XORing two pointers together. Under the assumption that this is legal, show how a doubly$-$linked list can be implemented with only one $$link$$ variable.

$($a$)(15$ points$)$ Implement in pseudocode the Access$($i$)$ operation that returns the node at index i in linear time.

$($b$)(15$ points$)$ Implement in pseudocode the Remove$($i$)$ operation that removes the node at index i in linear time.

$($c$)(10$ points$)$ Given a link to a node old, is it possible to implement a constant time operation Remove$($old$)$ similar to the one discussed in class for the usual implementation of doubly$-$linked lists that contain two links per node? Why or why not?

With regards to link arithmetic, assume that the NULL link is represented by an all zero bitstring. $[$Hint: Remember that for any two bitstrings a and b$,$ we have $($a XOR b$)$ XOR b $=$ a$.]$