1. Assignment 10
2015/6/2

3. R-11. 6 Our implementation of the TreeMap
R-11.6 Our implementation of the TreeMap. subtree search utility, from Code Fragment 11.4, relies on recursion. For a large unbalanced tree, Python’s default limit on recursive depth may be prohibitive. Give an alternative implementation of that method that does not rely on the use of recursion.

5. R-11.8 Draw the AVL tree resulting from the insertion of an entry with key 52 into the AVL tree of Figure 11.14b.
Page 484
In particular, let z be the first position we encounter in
going up from p toward the root of T such that z is unbalanced (see Figure 11.12a.)
Also, let y denote the child of z with higher height (and note that y must be an
ancestor of p). Finally, let x be the child of y with higher height (there cannot be a
tie and position x must also be an ancestor of p, possibly p itself ).

6. Page 486
As with insertion, we use trinode restructuring to restore balance in the tree T.
In particular, let z be the first unbalanced position encountered going up from p
toward the root of T. Also, let y be the child of z with larger height (note that
position y is the child of z that is not an ancestor of p), and let x be the child of y
defined as follows: If one of the children of y is taller than the other, let x be the
taller child of y; else (both children of y have the same height), let x be the child of
y on the same side as y (that is, if y is the left child of z, let x be the left child of
y, else let x be the right child of y). In any case, we then perform a restructure(x)
operation.