Consider a set of elements being organized as a binary search tree $($BST$).$

The elements in the set may be of different popularity. That is$,$ a few elements are

searched for much more frequently than others. In order to improve the average

search time, one can consider moving an element in the set that is being searched

for to the top of the BST $($so that if the same element is searched for again soon,

the element is likely close to the top of the BST and is thus located with fewer

node checkings$).$ Write an algorithm Search$-$and$-$Move$($T$,$ k$)$ which searches for and

returns an element with key k in a BST whose root is pointed to by the pointer

T$.$ The algorithm should also restructure the BST so that the element with key k

becomes the root of the tree when the algorithm terminates.