The larger binary trees in this chapter were generated automatically by a program.

This was done by assigning an $(x,y)$ coordinate to each tree node, drawing a circle

around each coordinate $($this is hard to see in some pictures$),$ and connecting each

node to its parent. Assume you have a binary search tree stored in memory $($perhaps

generated by one of the routines above$)$ and that each node has two extra fields to

store the coordinates.

a$.$ The $x$ coordinate can be computed by assigning the inorder traversal number.

Write a routine to do this for each node in the tree.

b$.$ The $y$ coordinate can be computed by using the negative of the depth of the

node. Write a routine to do this for each node in the tree

c$.$ In terms of some imaginary unit, what will the dimensions of the picture be$?$

How can you adjust the units so that the tree is always roughly two$-$thirds as

high as it is wide?

d$.$ Prove that using this system no lines cross, and that for any node, $x,$ all elements

in $x\text{'}$s left subtree appear to the left of $x$ and all elements in $x\text{'}$s right subtree

appear to the right of $x.$