Name: _______________________________________________

Honor Code Acknowledgment: __________________________


                 Random Quiz # 10
                 CPS 100, Fall 1994
                  November 9, 1994

problem 1 : Joyce Kilmer

In a tree of n nodes, how many edges are there?



problem 2 : Kilmer Redux

If every non-leaf node in a binary tree has exactly two children and
there are n leaves, how many non-leaf nodes are there?




problem 3 : Golden Needles

A binary search tree is said to be ``right-threaded'' if every NULL
right pointer (of a node N) in the tree is replaced by a pointer to
the inorder successor of N.  For example, in the tree below (root 22)

                   tree
                    |
                    22
                   /  \
                  /    \
                 12     49
                /  \    / \      
                5   15 30  80
               /       /       
              1      30

the right-pointer from the node labeled 1 would be replaced by a
pointer to node 5 (its inorder successor), the right-pointer of 5
would point to 12, the right pointer of 15 would point to 22, and so
on with the deepest 30 right-pointer pointing to the other 30, the


shallow 30 pointing to 49 and the 80 right pointer still NULL.  Note
that the only NULL right-pointer that remains NULL after
``right-threading'' is the right-pointer of the right-most (greatest)
leaf since it has no inorder successor.

Right a void function RightThread that takes a tree as a parameter and
right-threads it.

     void RightThread(TreeNode * t)

You may find it useful to write and call an auxiliary function
(hint:  the second parameter of the aux function could be the node that
 a NULL right pointer should point to, initially this would be NULL, but
 would change in SOME recursive calls).