2011–03–19
14.00 – 18.00
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No help materials are allowed, except for an English dictionary.
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You may answer in Swedish or English.
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Total number of credits is 24. Limits:
3: 12p, 4: 16p, 5: 20p.
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Jour (person on duty): Jonas Wallgren, tel. 178594
(endast telefonjour (only by phone))
1

Explain what is ment in OOA and OOD by the following concepts/”slogans”: a)(1.5p) Divide and conquer b)(1.5p) Iterate and increment c)(1.5p) Reuse and recycle d)(1.5p) Strong cohesion and low coupling
Describe the following situation using a class diagram (3p):
A City has a number of Districts.
A District consists a number of Blocks.
A Block consists of number of Buildings.
A Dwelling-house is a Building.
An Office building is a Building.
A Block of flats is a Dwelling-house.
A Villa is a Dwelling-house.
A Block of flats is occupied by a number of Families.
A Villa is occupied by one Family.
A Family consists of several Persons.
An Employee is a Person.
An Office building contains several Employees.
2

a)(1.5p) Construct the AVL tree from the keys (in the given order) 7, 6, 5, 4, 3, 2, 1.
You only need to show the result after completing the insertion of 2 and the final tree.
b)(1.5p) Remove 20 from the following AVL tree. Draw the tree transformations step by step.
20
/\
/
/
/ \
\
\
1
/
10
/\
/ \
30
/\
/ \
7 14 25 35
/ \ / /
3 9 12 22
Both of these subproblems use the splay tree given in a) as its starting-point.
Solving one subproblem doesn’t influence the other one.
a)(1.5p) Add the value 54 to the following splay tree. Show the transformations step by step.
20
/ \
10 30
/\ \
7 14 35
\
39
\
46
/\
41 55 b)(1.5p) Remove the value 55 from the splay tree above. Show the transformations step by step.
3

a)(1.5p) Show what happens step by step when you remove the values 40, 39, 3 from the following (2,4)-tree:
+----+
| 20 |
/
/
+----+
\
\
+----+
| 10 |
+----+
| |
+----+----+----+
| 30 | 40 | 50 |
+----+----+----+
/ | \ \
+---+ +----+ +----+ +----+ +----+ +----+
| 3 | | 18 | | 23 | | 39 | | 44 | | 59 |
+---+ +----+ +----+ +----+ +----+ +----+ b)(1.5p) What is the maximum height of a (2,4)-tree with n nodes? (Explain your answer.)
a)(1.5p) In a hashtable using linear hashing of size 11 insert: 56 22 78 67 15 41 37 87 25 33, in that given order.
Describe where each element is placed and comment/explain why.
b)(1.5p) What is the complexity of introducing one piece of data into the hashtable?
In what situations are hashtables preferred to trees?
(3p) Build a skip list for the elements 1, 3, 5, 7, 2, 4, 6, 8 in that order.
The results of the coin tossing are (H=head, T=tail) H, H, T, T, over and over again.
4