v22.0310-003: Homework 6
Due date: Thursday December 16 (before
11pm). If you stuff under my door, be sure to
place it in an envelop with your name.
This last homework is OPTIONAL.
Only do it if you think you need extra
credit to boost your grades.
It has only a written part.
Look here for additional information
after the original posting of
assignment:
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Exercise 10.14 (Page 331). Double hashing.
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Exercise 11.9 (Page 360). Insertion into a 2-3 tree.
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What is the advantage of B+-trees over B-trees?
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Suppose each key takes 10 bytes and each pointer
takes 4 bytes. Let T be a B-tree
of order m where each node of a B-tree
has 512 bytes.
Determine the maximum value of m.
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Exercise 13.5 (pagte 417). Splay tree searching.
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Is it true that splaying a tree always reduce its
height? If so, argue why. If not, give a counter
example.
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Reduce the problem of Hamiltonian Cycle to
the Traveling Salesman problem. See p.459, exercise
15.5 for a definition of Hamiltonian cycle.
CLARIFICATION: I mean, do exercise 15.5. This
amounts to reducing Hamiltonian Cycle to Traveling
Salesman.
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Exercise 15.3 (page 459), multiplying matrices.
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RECOMMENDED EXTRA PROBLEMS:
Do not hand in, as they will not be graded.
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Write a Java program to rotate a node. Assume that
each node has three references, point to
its parent, its left and right child.
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Exercise 11.15 (page 361). Min and Max number
of records in B+ tree.
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Show that the problem of Vertex Cover is in NP.
See p.459, exercise 15.6
for a definition of Vertex Cover.