Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

C-10.1
Design a variation of algorithm TreeSearch for performing the operation
findAl(k) in an ordered dictionary implemented with a binary search tree T,
and show that it runs in time O(h + s), where h is the height of T and s is the size
of the collection returned.
C-10.2
Describe how to perform an operation removeAll(k), which removes all the
entries whose keys equal k in an ordered dictionary implemented with a binary
search tree T, and show that this method runs in time O(h + s), where h is the
height of T and s is the size of the iterator returned.
C-10.3
Draw a schematic of an AVL tree such that a single remove operation could
require Ω(logn) trinode restructurings (or rotations) from a leaf to the root in
order to restore the height-balance property.
C-10.4
Show how to perform an operation, removeAll(k), which removes all entries
with keys equal to K, in a dictionary implemented with an AVL tree in time
O(slogn), where n is the number of entries in the dictionary and s is the size of
the iterator returned.
C-10.5
If we maintain a reference to the position of the left-most internal node of an
AVL tree, then operation first (Section 9.5.2) can be performed in O(1) time.
Describe how the implementation of the other dictionary methods needs to be
modified to maintain a reference to the left-most position.
C-10.6
Show that any n-node binary tree can be converted to any other n-node binary
tree using O(n) rotations.
C-10.7
Let D be an ordered dictionary with n entries implemented by means of an AVL
tree. Show how to implement the following operation on D in time O(logn + s),
where s is the size of the iterator returned:
findAllInRange(k 1 ,k 2 ): Return an iterator of all the entries in D with key k
such that k 1 ≤ k ≤ k 2 .
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